X-Planes: X-52, the Designation Refused

In 2006 somebody asked for the number 52 and was told no. The designation X-52A was requested for a programme to test active aeroelastic wing technology, and it was disapproved because of possible confusion with the B-52 series, and the designation X-53A was allocated to the programme instead [Missing USAF and DOD Aircraft Designations].

This is the fifty-third article in the X-Planes series, following the X-1, the X-2, the X-3, the X-4, the X-5, the X-6, the X-7, the X-8, the X-9, the X-10, the X-11, the X-12, the X-13, the X-14, the X-15, the X-16, the X-17, the X-18, the X-19, the X-20, the X-21, the X-22, the X-23, the X-24, the X-25, the X-26, the X-27, the X-28, the X-29, the X-30, the X-31, the X-32, the X-33, the X-34, the X-35, the X-36, the X-37, the X-38, the X-39, the X-40, the X-41, the X-42, the X-43, the X-44, the X-45, the X-46, the X-47, the X-48, the X-49, the X-50, and the X-51.

Every other article in this series on a designation is about an aeroplane, or about a number that never became one. This one is about a number that was refused, which differs from both. The X-39 was reserved and then lost because nobody wrote the letter that would have assigned it [Missing USAF and DOD Aircraft Designations]. The X-52 was asked for in writing, considered, and declined. The paperwork was done correctly and the answer was no.

The article turns on the reason given. Not that the aircraft was unworthy, not that the programme was cancelled, and not that the number had been used. The number was refused because it resembled a number already in use [Missing USAF and DOD Aircraft Designations].

The record does not say through which sense. It gives possible confusion as the reason, in one clause. Whether the worry was a radio, a maintenance card or a line in a budget is not stated anywhere this article could find, and the sections below argue for the radio from the neighbouring cases rather than from this one.

The Research Question

The designation X-52 had no research question of its own, because it never named a vehicle. The number was requested for a programme to test active aeroelastic wing technology, and that programme’s question belonged to the aircraft that received X-53A instead [Missing USAF and DOD Aircraft Designations]. That question is the subject of the next article in this series and is not pursued here.

The question this article asks is administrative rather than aeronautical. It asks under what rule a design number that the sequence named could be refused for resembling another number already in use, and what that refusal shows about the designation system. The record supplies the reason, and the article sets out to find the rule behind it.

Programme Origin, What the Record Says Happened

The request was for X-52A and the answer was X-53A. The specialist registry that maintains the record of United States military aerospace vehicle designations states the case in two sentences [Missing USAF and DOD Aircraft Designations]. No other public source read for this article adds to them, and the encyclopedia entry for the X-53 repeats the reason in a single sentence [Boeing X-53 Active Aeroelastic Wing]. The designation X-52A was requested in 2006 for a programme to test active aeroelastic wing technology. It was disapproved because of possible confusion with the B-52 series, and X-53A was allocated instead.

The programme was the Active Aeroelastic Wing. A modified F/A-18A, flown at the space agency’s flight research centre at Edwards in cooperation with the Air Force Research Laboratory and Boeing Phantom Works, to find out whether a wing can be twisted deliberately to roll an aeroplane rather than being stiffened until it stops twisting [Active Aeroelastic Wing Flight Research, NASA Facts FS-2005-03-061 DFRC] [Air Force Research Laboratory]. It had already flown before it had a number. The programme began in 1996, the aircraft first flew in modified form in November 2002, and the flight research concluded in March 2005 [Clarke et al. 2005] [Boeing X-53 Active Aeroelastic Wing].

The number arrived over a year after the flying stopped. The encyclopedia entry for the aircraft dates its designation as X-53 to 16 August 2006, by memorandum of the Air Force Deputy Chief of Staff for Strategic Plans and Programs [Boeing X-53 Active Aeroelastic Wing], and the Air Force Research Laboratory announced on 11 December 2006 that the demonstrator had been assigned the Mission Design Series number X-53 [Active Aeroelastic Wing flight research vehicle receives X-53 designation, Air Force Research Laboratory, 11 December 2006]. The announcement gives no date for the memorandum, so the August date rests on the encyclopedia entry alone. The space agency’s account of the programme calls the aircraft X-53 and gives no date [F/A-18 Active Aeroelastic Wing, NASA]. What the aeroplane did with the number is left for later.

The Office That Said No

The decision was made by one office and the instruction names it. A request for a designation goes from the programme office to the Department of Defence Control Point, which the 2005 instruction names as the Asset Identification Branch of Air Force Materiel Command at Wright-Patterson [Air Force Joint Instruction 16-401, 14 April 2005], and that office checks the proposal against the regulations and forms a recommendation. The recommendation and the original request then both go to the Directorate of Programs, Program Integration Division at the Pentagon, where the decision is made [Allocation of Official Aerospace Vehicle MDS Designations].

That office changed its own designator in the year it refused this one. Its symbol was HQ USAF/XPPE and became AF/A8PE with effect from 1 February 2006 [Allocation of Official Aerospace Vehicle MDS Designations]. The office that refused a number for resembling another number spent that same year renaming itself, and nothing in the record suggests anybody noticed.

Refusal is the exception and not the rule. The registry’s account of the process records that in most cases the originally requested designation is approved even when the coordinating office recommends a different one, and gives the F-35 and the KC-767A as the examples [Allocation of Official Aerospace Vehicle MDS Designations]. A request that is refused outright is therefore unusual, and this one was refused on a ground the instruction does not mention.

The Rule That Refused It Is Not in the Instruction

The governing document is a joint instruction of the Air Force, the Army and the Navy, and the issue in force in 2006 was dated 14 April 2005 [Air Force Joint Instruction 16-401, 14 April 2005]. It is not long. It says what a designation is made of, who may ask for one, and who decides. It was read for this article, in full, and the reading is the article’s central evidence.

It requires the next number and provides no way of skipping one. Section C, paragraph 5 directs that the coordinating office will assign and reserve the next available consecutive design number within each basic mission for new vehicles [Air Force Joint Instruction 16-401, 14 April 2005]. There is no qualification, no exception and no discretion attached to it. Formally, if $A_m$ is the set of design numbers already used up within basic mission $m$, whether allocated or passed over, the instruction defines what is to be assigned as

\[n^{\star}(m) \;=\; \min\bigl\{\,k \in \mathbb{N} \;:\; k \notin A_m \,\bigr\} \tag{1}\]

and in 2006 every X number from 1 to 51 had been used up, although two of them, X-23 and X-39, were never allocated to anything [Missing USAF and DOD Aircraft Designations], so $n^{\star}(X) = 52$. The number that was refused is the number the instruction names.

The rule describes a set that only ever shrinks. Writing $V_m(t)$ for the numbers still available within basic mission $m$ at time $t$, and taking the range the instruction gives,

\[V_m(t) \;=\; \{1, 2, \ldots, 999\} \setminus A_m(t), \qquad n^{\star}(m) \;=\; \min V_m(t). \tag{2}\]

Nothing returns a number to that set. The instruction directs that a retired designation is not used again for another vehicle [Air Force Joint Instruction 16-401, 14 April 2005], so the allocated set is non-decreasing in time and the available set is non-increasing,

\[t_1 \leq t_2 \;\implies\; A_m(t_1) \subseteq A_m(t_2) \;\implies\; V_m(t_2) \subseteq V_m(t_1). \tag{3}\]

A design number is therefore consumed and not borrowed.

But a refusal consumes one by a route this model has no term for. The instruction knows two states, allocated and available, and the master list of designations records a third. The C-16 correspondence directs that the number be marked not used [Missing USAF and DOD Aircraft Designations], which is neither, so the used-up numbers divide in two and the full partition is

\[\{1, 2, \ldots, 999\} \;=\; \underbrace{A_m(t)}_{\text{allocated}} \;\sqcup\; \underbrace{U_m(t)}_{\text{marked not used}} \;\sqcup\; \underbrace{V_m(t)}_{\text{available}}, \tag{4}\]

with $n^{\star}(m) = \min V_m(t)$ as before. The instruction defines the first and the third and never mentions the second, and yet the X-52 went into the second, along with C-16, C-42, C-43, C-44, P-6, F-19 and the design numbers 13 that custom skips [Missing USAF and DOD Aircraft Designations].

What was assigned is not what the sequence rule names. With $n^{\star}(X) = 52$ and 53 allocated,

\[\text{assigned} \;-\; n^{\star}(X) \;=\; 53 - 52 \;=\; 1, \tag{5}\]

which states the anomaly as arithmetic.

The word skip does not appear in the 2005 issue at all. Neither does discretion, nor any criterion by which a proposed number might be judged unsuitable. The issue provides that requesters are notified of approval or disapproval, but it states no ground for disapproval and no authority to pass over the next available number [Air Force Joint Instruction 16-401, 14 April 2005]. The document that governed the decision contains no provision under which the next number could be passed over.

Nor did the issues before it. The 1997 issue of the same joint instruction and the 1994 issue it superseded were read as well, and they say the same things in the same order. The coordinating office will assign the next available consecutive design number within each basic mission for new vehicles. Design numbers run consecutively from 1 to 999. Requested popular names are checked for duplication against the master list, the Judge Advocate General conducts a trademark search of them, and final coordination comes from the Assistant Secretary of Defence for Public Affairs. The only mention of confusion attached to a designator is the prohibition of I and O as series symbols [Air Force Joint Instruction 16-401, 1 September 1997] [Air Force Joint Instruction 16-401, 1994] [United States Department of Defense Aerospace Vehicle Designation].

So the instruction carried no authority to skip a design number for nearly twenty years, across at least three issues, while the practice of skipping them ran from before the earliest issue read here to after it, from P-6 in 1962 and C-16 in 1981 to X-52A in 2006 [Missing USAF and DOD Aircraft Designations].

The Instruction Screens the Other Half of the Name for Confusion

The document did not forget about confusion. It has an apparatus for it, pointed somewhere else. Section E governs the popular name, meaning the word Stratofortress rather than the string B-52. A requested popular name is checked for duplication against the master list of popular names. It is reviewed by public affairs at command level and then at service level. The Air Force Judge Advocate General conducts a trademark search of the proposed name. It is coordinated among the services, the Secretary and the Chief of Staff both coordinate on it, and the Assistant Secretary of Defence for Public Affairs concurs or does not [Air Force Joint Instruction 16-401, 14 April 2005].

A design number goes through none of that. It is issued in sequence by a logistics office [Air Force Joint Instruction 16-401, 14 April 2005] [Allocation of Official Aerospace Vehicle MDS Designations].

The instruction also states which half is the official one. Section F states that the designation is the official identification, that it represents a specific category of vehicles for operations, support and documentation, and that the popular name characterises the mission and aids communications and media references [Air Force Joint Instruction 16-401, 14 April 2005]. So the confusability controls, the duplication check, the legal search and the four levels of review sit on the informal half of the identifier, and the half the instruction calls official is issued by a counter.

The Only Written Anti-Confusion Rule for the Designator Concerns Two Letters

There is exactly one. The series symbol, the letter that follows the design number and identifies the production model, runs consecutively from A, and the instruction prohibits the letters I and O for that symbol in order to avoid confusion [Air Force Joint Instruction 16-401, 14 April 2005]. The confusion in question is with the digits 1 and 0, a claim about how a character looks on a page or a panel.

The consequence is a smaller alphabet,

\[|S| \;=\; 26 - 2 \;=\; 24, \tag{6}\]

so a design number supports twenty-four production models before the instruction requires the design number to advance to the next unused value [Air Force Joint Instruction 16-401, 14 April 2005].

The two limits together give the size of a mission’s designation space. With design numbers running from 1 to $999$ and twenty-four permitted series symbols,

\[N_m \;=\; 999 \times 24 \;=\; 23{,}976, \tag{7}\]

and the 2020 issue, which expands the design number to four digits once 999 is reached [Department of the Air Force Instruction 16-401, 3 November 2020], raises that to

\[N_m' \;=\; 9{,}999 \times 24 \;=\; 239{,}976. \tag{8}\]

Fifty-one of the nine hundred and ninety-nine design numbers had been consumed when the request was made, and the X series had used no more than a few of the twenty-four series symbols under any of them [List of X-planes]. Scarcity is not why 52 was refused, and no reading of the instruction suggests that it was.

That rule exhausts the system’s written thinking about a confusable designator, and its subject is typography. It does not consider what happens when the number is spoken. It does not consider another mission series.

The Authority Was Written Down Eight Years Later

The instruction was reissued on 16 May 2014 and again on 3 November 2020, the later issue jointly as a Department of the Air Force Instruction, an Army Regulation and a Naval Air Systems Command Instruction [Air Force Instruction 16-401, 16 May 2014] [Department of the Air Force Instruction 16-401, 3 November 2020]. Both carry a clause that the 2005 issue does not.

In both, Attachment 2, paragraph A2.1.6.1.2 reads that the office, HAF/A8PE in 2014 and AF/A8PE in 2020, reserves the authority to skip design number at discretion. The 2014 issue adds that skipped design numbers cannot be requested or used [Air Force Instruction 16-401, 16 May 2014].

That is one sentence, it names the office that refused the X-52A, and it supplies no criterion whatsoever. It does not say to avoid confusion. It does not say when, or on what evidence, or subject to what review. It converts a thing that office had been doing into a thing that office is entitled to do, and it does so without describing the thing.

The two intervals that matter are both long and they are the article’s timeline in one line,

\[\underbrace{2014 - 2006}_{8 \ \text{years after the refusal}} \qquad\text{and}\qquad \underbrace{2014 - 1994}_{20 \ \text{years after the earliest issue read here}}. \tag{9}\]

The practice ran throughout the second interval and the authority arrived at the end of it.

Every other provision quoted above survives into the 2020 issue unchanged in substance. Design numbers still run consecutively. The series symbol still forbids I and O to avoid confusion with the design number. The popular name still goes to a trademark search and still gets its four levels of review [Department of the Air Force Instruction 16-401, 3 November 2020]. The two later issues add one more provision that bears on this article, and it points the same way. The 2014 issue, at paragraph 4.2.1.3.1, states that for vehicles with an extensive history of designations requests are not accepted for designators in reverse or skipped sequences, and the 2020 issue, at paragraph 4.2.1.3, states the same without the qualification [Air Force Instruction 16-401, 16 May 2014] [Department of the Air Force Instruction 16-401, 3 November 2020]. A requester may not ask to leave the sequence and the office may leave it at discretion, so the departure the X-52A decision made is now reserved to the office that made it.

The Same Office Had Manufactured the Same Collision Four Years Earlier

In 2001 the Joint Strike Fighter needed a designation and the sequence said F-24. The nomenclature office recommended that number, on the stated ground that design numbers are to be assigned consecutively, the same provision the X-52A refusal set aside [Non-Standard DOD Aircraft Designations].

It was overruled. The number that was approved on 5 June 2002, by HQ USAF/XPPE, was 35 [Non-Standard DOD Aircraft Designations] [Lockheed Martin F-35 Lightning II]. It came from a press conference, at which the Under Secretary and the programme manager announced the production aircraft by taking the demonstrator’s designation and replacing the X with an F. No designation had been reserved or approved for the production aircraft at that point.

So the F-35 exists because somebody deliberately made a production fighter share a number with an experimental aeroplane across a series boundary [Lockheed Martin X-35].

Four years later the same office, under a symbol it had changed in the interim, refused a number because it would have shared a number with a bomber across a series boundary.

The structure of the two cases is identical. In each, two designations differ only in the mission symbol and agree in the design number. In 2002 that identity was treated as desirable continuity worth breaking the sequence rule to obtain. In 2006 it was treated as a hazard worth breaking the sequence rule to avoid. The instruction in force said the same thing in both years and it authorised neither [Air Force Joint Instruction 16-401, 1 September 1997] [Air Force Joint Instruction 16-401, 14 April 2005].

Sizing From First Principles

There was no vehicle to size. The X-52 was a number that was requested and refused, and no airframe, engine or mass was ever attached to it. The aircraft the number was requested for was a modified F/A-18A that had already flown and finished its flight research before the request was made [Clarke et al. 2005], and its engineering is treated with the X-53.

This article sizes only the designation space. It is derived above from the instruction’s limits, being 999 design numbers and twenty-four permitted series symbols, and fifty-one of the design numbers had been consumed in the X series when the request was made. Scarcity of numbers did not drive the refusal.

Dependent Systems

A designation depends on paperwork rather than hardware, and the record names the offices this one passed through. The request went from the programme office to the Department of Defence Control Point, the Air Force Asset Identification Branch at Wright-Patterson, and from there to the Directorate of Programs, Program Integration Division at the Pentagon, where the decision was made [Allocation of Official Aerospace Vehicle MDS Designations]. The governing document was the joint instruction in its 14 April 2005 issue [Air Force Joint Instruction 16-401, 14 April 2005], and the outcome is recorded by the specialist registry [Missing USAF and DOD Aircraft Designations].

The aircraft the number was meant for depended on three partners, being the space agency’s flight research centre at Edwards, the Air Force Research Laboratory and Boeing Phantom Works [Active Aeroelastic Wing Flight Research, NASA Facts FS-2005-03-061 DFRC] [Air Force Research Laboratory]. Its systems are not described here.

The Flight Test Record

Nothing flew as the X-52. The number was refused, so no flight was ever made under it [Missing USAF and DOD Aircraft Designations].

The aircraft for which it was requested had already completed its flying. The programme began in 1996, the modified aircraft first flew in November 2002, and the flight research concluded in March 2005, more than a year before the designation X-53 was issued, on 16 August 2006 by the encyclopedia entry’s account and in any case before the laboratory announced it on 11 December 2006 [Clarke et al. 2005] [Boeing X-53 Active Aeroelastic Wing]. This article states only that the aircraft’s flight record existed and that it preceded the number.

Comparison With Ground Prediction

There is no flight result to set beside a ground prediction, because nothing flew under this designation. The record reports no wind tunnel work, analysis or simulation attached to the X-52, and the aeronautical predictions made for the Active Aeroelastic Wing are left to the X-53 article.

The only prediction in this record is the refusal’s. The deciding office anticipated possible confusion with the B-52 series [Missing USAF and DOD Aircraft Designations], and because the number was refused, that forecast was never exposed to an outcome. No confusion between an X-52 and a B-52 could occur, so none was observed, and the record can neither confirm nor refute the forecast.

The nearest the record comes to a forecast set against an outcome runs the other way. The 1953 requests to redesignate two drones were made because confusion with unmodified aircraft was already occurring, and they were refused, a case set beside the X-52 decision below under The System Declined to Fix the Confusion It Actually Had. A later section, Measuring the Judgement That Was Not Recorded, supplies the kind of measure a stated forecast would have needed, and records that no measure or threshold accompanied the decision.

What the Data Changed, What the Anomaly Reveals About the Designation System

The Refusal Belongs to a Documented Family

The X-52 is not an isolated decision, and the registry that records it records the others [Missing USAF and DOD Aircraft Designations].

C-16 was skipped, and the reported reason names the mechanism precisely. The number was on reservation for the aircraft that became the C-17, and the nomenclature office recommended C-16A on the ground that 16 was the next available number and that skipping it conflicted with the regulation then in force. One day later that letter was withdrawn and replaced by one concurring in C-17, and C-16 was to be marked in the master list as not used. No reason was recorded. It is reported that the number was skipped because of concerns over confusing the plane with the F-16 during the stress of high combat radio traffic [Missing USAF and DOD Aircraft Designations] [Boeing C-17 Globemaster III] [General Dynamics F-16 Fighting Falcon].

That sentence is the clearest statement in the record of what these refusals concern. It points away from the register, the paperwork and the eye, and toward a voice, a radio, and a crew under load.

Civil aviation studied that hazard and counted it. The United Kingdom’s aviation authority published a dedicated call sign confusion study in April 2000, drawing on the 482 call sign confusion reports filed by controllers and flight crews in 1997 [CAP 704, Aircraft Call Sign Confusion Evaluation Safety Study, United Kingdom Civil Aviation Authority]. Of those 482, 405 involved call signs whose suffixes are numbers only, and 198 involved call signs ending in the same two digits [CAP 704, Aircraft Call Sign Confusion Evaluation Safety Study, United Kingdom Civil Aviation Authority], the same shape as every collision this article examines. The European guidance that followed recommends avoiding phonetically similar call signs on the same frequency at the same time and names the formats most likely to be confused [Air-Ground Communications Briefing Note 2, Call Sign Confusion]. The hazard the C-16 note gestures at in passing has a literature, a reporting scheme and a count, and none of it is referenced anywhere in the designation instruction.

C-43 and C-44 were skipped to avoid confusion with the existing T-43 and T-44, and the registry reports unofficial information from the department that an informal policy is in effect to avoid duplication of well-known numbers [Missing USAF and DOD Aircraft Designations]. An informal policy is a rule that is not written down, and the X-52 case reaches the same finding from the other side.

P-6 was skipped for the Navy in 1962, on the nomenclature forms themselves, most probably to avoid future confusion with the P6M. T-50A is reserved and unassigned because a foreign trainer is marketed under that number and assigning it to a different model was regarded as too confusing. C-42 was skipped over concern about legal exposure to a widely sold light aircraft marketed as the C42 [Missing USAF and DOD Aircraft Designations].

XV-14 was allocated and then withdrawn, and the withdrawal letter is quoted. In May 1973 the Army and the space agency asked for a designation for a tilt-rotor demonstrator and XV-14 was allocated on 30 May. On 7 August a change was requested to avoid confusion with the Bell X-14B, and the request argued the point at length. Both aircraft were built by companies known shortly as Bell. Both would be flying at the same research centre. It warned of serious errors if the service and maintenance records of the two were mixed up, and of unnecessary resultant confusion to the aeronautical research and development community in general. The redesignation was approved on 22 August and the aircraft became the XV-15 [Missing USAF and DOD Aircraft Designations] [Bell XV-15].

And F-19 was skipped under a stated reason that the registry says was not the real one. The official explanation was to avoid confusion with the MiG-19. The manufacturer had in fact asked to skip it because it wanted an even number to distinguish its export fighter from Soviet competitors that all used odd ones, and the approving letter repeated the confusion story anyway [Missing USAF and DOD Aircraft Designations] [Northrop F-20 Tigershark]. Confusion is available as a reason whether or not it is the reason, and a reader of the two-sentence entry about the X-52 should hold that in mind.

A number is also skipped for reasons that have nothing to do with confusion. F-13 was rejected by the manufacturer or the Navy for superstitious reasons, and since the late 1960s it has been an unwritten rule that a design number 13 is always skipped, which has cost A-13, C-13, G-13, Q-13 and V-13 as well [Missing USAF and DOD Aircraft Designations]. A system that skips the number 13 by unwritten custom will not find skipping 52 difficult.

That custom is measurable, and it accounts for the largest single deletion in the record. Counting the mission symbols whose thirteenth number is absent by it,

\[\bigl| \{\, m \in M \;:\; 13 \notin A_m \text{ by custom} \,\} \bigr| \;=\; 6, \tag{10}\]

being the fighter, attack, cargo, glider, drone and vertical-take-off series. One unwritten rule has removed six numbers, and no line of the instruction mentions it.

Every One of These Collisions Crosses a Series Boundary

Look at what collides in each case. X-52 with B-52. C-16 with F-16. C-43 and C-44 with T-43 and T-44. V-14 with X-14. P-6 with P6M. In every instance the two designations differ in the mission symbol and agree in the design number.

A designation is formally a pair. Writing $M$ for the set of basic mission symbols and $A_m$ for the numbers issued within mission $m$, an assigned designation is an element of

\[\mathrm{MDS} \;=\; \bigl\{ (m, n) \;:\; m \in M,\; n \in A_m \bigr\}, \tag{11}\]

and within that space the pairs are unique by construction, because each mission counts its own sequence. X-52A and B-52H are distinct elements and no rule of the instruction is broken by having both.

The refusals are evidence that somebody did not believe the first coordinate survives the journey. If the channel a designation travels down preserves only the number, the effective identifier is the projection

\[\sigma(m, n) \;=\; n, \tag{12}\]

and under $\sigma$ the two designations are the same object. The C-16 reason names that channel explicitly as a radio.

The designations a listener cannot separate are the fibre of that projection, and its size is the quantity the rest of this section turns on,

\[\sigma^{-1}(k) \;=\; \bigl\{\, (m, k) \;:\; m \in M,\ k \in A_m \,\bigr\}, \qquad \bigl| \sigma^{-1}(k) \bigr| \;=\; o_k. \tag{13}\]

The problem lies in the sizes of the two spaces, which differ greatly. The register holds

\[\sum_{m \in M} \bigl| A_m \bigr| \tag{14}\]

distinct designations, while a listener who hears only the number can distinguish at most

\[\Bigl| \bigcup_{m \in M} A_m \Bigr| \;=\; \max_{m \in M}\, \max A_m \tag{15}\]

of them. The first grows with the number of mission series and the second does not. Adding a mission symbol adds capacity to the register and adds none to the radio.

Collisions are therefore not accidents in this system. They are its arithmetic. Writing $o_k$ for the number of mission series that have issued the design number $k$,

\[o_k \;=\; \bigl| \{\, m \in M \;:\; k \in A_m \,\} \bigr|, \tag{16}\]

the count of colliding pairs across the register is

\[C \;=\; \sum_{k \geq 1} \binom{o_k}{2}, \tag{17}\]

which is zero only if no number is ever issued twice across all series. Every low design number in this system has been issued in several series, because every series starts at one and counts up. There is an X-4 and an F-4. There is an X-5 and an F-5. There is an X-15 and an F-15, an X-16 and an F-16, an X-22 and an F-22, an X-35 and an F-35 [List of X-planes] [1962 United States Tri-Service Aircraft Designation System].

The average of $o_k$ over the numbers in use is the factor by which the register outruns the radio,

\[R \;=\; \frac{\sum_{m \in M} \bigl| A_m \bigr|} {\Bigl| \bigcup_{m \in M} A_m \Bigr|} \;=\; \operatorname*{mean}_{k \,\in\, \bigcup_m A_m} o_k, \tag{18}\]

and $R > 1$ whenever any two series have both reached the same number. The public record does not permit computing $R$ for this system, because no complete allocated set is published for every mission symbol, and the article claims no value for it.

If the mission letter is lost, the chance of attributing a spoken number to the right series is at best

\[P(\text{correct} \mid k) \;=\; \frac{1}{o_k} \tag{19}\]

under a uniform prior over the series holding that number. This is an idealisation and the article says so, since a listener has context, expectation and an aerodrome full of clues. It is stated because it shows the shape of the thing. The quantity the system controls is $o_k$, and the system increases it every time a new series is opened.

The same quantity in bits is the part of the identifier the channel throws away. A listener who has heard the number and not the letter carries a residual uncertainty of

\[H(k) \;=\; \log_2 o_k \tag{20}\]

bits, which is zero when a number belongs to one series and one bit when it belongs to two.

The two decisions this article compares act on that quantity in opposite senses, at two different numbers, and by the same one bit. One of them spent the bit and the other withheld it. The X-35 had been allocated and the F-35 was approved on top of it, so

\[\Delta H(35) \;=\; \log_2 2 - \log_2 1 \;=\; +1 \ \text{bit}. \tag{21}\]

The B-52 had been allocated and X-52A was refused, so the multiplicity stayed where it was and

\[\Delta H(52) \;=\; \log_2 1 - \log_2 1 \;=\; 0 \ \text{bits}, \tag{22}\]

against the $+1$ bit the approval would have added.

One office added a bit of ambiguity in 2002 and declined to add the same bit in 2006, and wrote down its reason for neither.

The System Declined to Fix the Confusion It Actually Had

Two designations were requested in 1953 for the express purpose of ending a confusion that was already happening, and both requests were refused.

The Wright Air Development Center asked to redesignate a drone converted from the B-17 as Q-7, and a drone converted from the F-80 as Q-8. The stated reason was problems and delays in the production and support of the drones, because they were too easily confused with unmodified aircraft of the type they were built from. That is not a hypothetical about a radio. It is a report of a supply system misdelivering. The Air Research and Development Command did not concur with the reasoning and turned both requests down in March 1954 [Missing USAF and DOD Aircraft Designations].

Set the two decisions beside each other. In 1954 an office declined to change a designation although confusion was occurring and was costing time and parts. In 2006 an office declined to issue a designation because confusion might occur. The same system, on the same question, refused to act on evidence and acted on possibility.

That asymmetry is the sharpest thing the X-52 case reveals, and it shows only because the registry preserved the failures as carefully as the successes.

A Number Is Occupied for as Long as the Aeroplane Lives

A design number becomes unavailable when it is allocated and stays unavailable until the last aircraft carrying it retires, since the instruction directs that a retired designation is not used again for another vehicle [Air Force Joint Instruction 16-401, 14 April 2005]. The duration is

\[T_{\text{occupied}} \;=\; t_{\text{retire}} \;-\; t_{\text{allocate}}, \tag{23}\]

and for most aeroplanes this is a few decades.

The B-52 is the extreme value of that quantity, by a wide margin. The Air Force has operated it since 1955 and its operational aircraft are expected to serve into the 2050s, a working life approaching a century [Boeing B-52 Stratofortress]. Taking 1955 and 2050 gives

\[T_{\text{occupied}} \;\geq\; 2050 - 1955 \;=\; 95 \ \text{years}, \tag{24}\]

and at the moment of the refusal in 2006 the aeroplane had already held the numeral for fifty-one of them.

Split at the year of the decision, the two halves are of comparable size and both are large.

\[\underbrace{2006 - 1955}_{51 \ \text{years already served}} \;+\; \underbrace{2050 - 2006}_{44 \ \text{years still expected}} \;=\; 95 \ \text{years}. \tag{25}\]

Whoever refused the number in 2006 was standing near the middle of its occupancy and not near the end of it.

So the request in 2006 was not unlucky in some general way. It asked for a number held by an aeroplane that had already served for fifty-one years and was expected to serve for more than forty more. A request for 52 made at any time in that span would have met the same aeroplane.

The aeroplane whose number blocked the X-52 is named in the prose of ten of the fifty-two articles that precede it in this series, which is 19.2 percent of them, across 26 mentions. The count includes its lettered variants and leaves aside the titles of surveyed records and of cited sources. It carried the X-15, the X-24, the X-38, the X-43 [Boeing B-52 Stratofortress] and the X-51 aloft. The article immediately before this one is about an aeroplane a B-52 dropped, and the number immediately after that aeroplane’s was refused because of the aeroplane that dropped it.

Nothing Was Lost

Compare the two anomalies without a vehicle that this series has now examined.

The X-39 produced a permanent hole. The number was reserved and the allocation request was never submitted, and the reservation was never cancelled either, so the number could not be reused before the next one was allocated. Two documents were never written, the request and the cancellation, and once the next number was allocated the gap was permanent [Allocation of Official Aerospace Vehicle MDS Designations].

The X-52 produced nothing of the kind. The request was made, considered and refused. The programme got a designation. The register records why 52 is absent [Missing USAF and DOD Aircraft Designations]. The cost of this refusal, measured in anything the designation system exists to provide, is zero.

That makes it the cleanest case in the series for asking what the rule is for. There is no damage to argue about and no cancellation to explain. There is only a decision, a reason, and an instruction that does not contain the reason.

Measuring the Judgement That Was Not Recorded

The refusal was a similarity judgement, and no measure, threshold or method was recorded with it. This section states what such a judgement looks like when it is written down. It offers analysis and gives no account of anything the Air Force did.

The standard measure of how far apart two strings are is the edit distance, being the least number of single-character insertions, deletions and substitutions that turns one into the other [Levenshtein Distance]. For strings $a$ and $b$ it is computed by the recurrence

\[d_{i,j} \;=\; \begin{cases} \max(i, j), & \min(i, j) = 0, \\[4pt] \min\bigl\{\, d_{i-1,j} + 1, \; d_{i,j-1} + 1, \; d_{i-1,j-1} + \mathbb{1}[\,a_i \neq b_j\,] \,\bigr\}, & \text{otherwise}, \end{cases} \tag{26}\]

with the edit distance being the value at the far corner, where $\ell_a$ and $\ell_b$ are the lengths of the two strings. The letters $m$ and $n$ are not reused here, since they name the basic mission symbol and the design number above. For the pair in question the value is 1, since substituting B for X is the only operation required. Normalised against the longer string,

\[s(a, b) \;=\; 1 - \frac{d_{\ell_a,\, \ell_b}}{\max(\ell_a,\, \ell_b)} \;=\; 1 - \frac{1}{4} \;=\; 0.75. \tag{27}\]

Three of the four characters are shared, and the three that are shared are the ones the instruction issues in sequence. Those three form the longest common subsequence, which gives a second measure that agrees with the first,

\[s_{\mathrm{LCS}}(a, b) \;=\; \frac{\bigl| \mathrm{LCS}(a, b) \bigr|}{\max(\ell_a,\, \ell_b)} \;=\; \frac{3}{4} \;=\; 0.75. \tag{28}\]

The measure a drug regulator uses is its own, and the program that computes it is public. The Food and Drug Administration screens every proposed prescription drug name against the names already approved, using a program it wrote called Phonetic and Orthographic Computer Analysis, and it makes the program publicly available [Phonetic and Orthographic Computer Analysis Program] [Phonetic and Orthographic Computer Analysis, public access]. A third measure works on character bigrams, comparing the sets of adjacent letter pairs rather than the positions, so that it does not depend on aligning the two strings. The two names give

\[\mathcal{B}(\text{X-52}) = \{\,\texttt{X-},\ \texttt{-5},\ \texttt{52}\,\}, \qquad \mathcal{B}(\text{B-52}) = \{\,\texttt{B-},\ \texttt{-5},\ \texttt{52}\,\}, \tag{29}\]

sharing two of three, and the Dice coefficient on those sets is

\[s_{\mathrm{Dice}}(a, b) \;=\; \frac{2 \bigl| \mathcal{B}(a) \cap \mathcal{B}(b) \bigr|} {\bigl| \mathcal{B}(a) \bigr| + \bigl| \mathcal{B}(b) \bigr|} \;=\; \frac{4}{6} \;\approx\; 0.667. \tag{30}\]

Three measures, three values between 0.667 and 0.75, and not one of them is a decision.

Saying It Aloud Moves the Two Names Closer Together

If the refusal was about a spoken designation, the spoken forms are the ones that matter, and measuring them reverses the intuitive answer. Rendered as they would be said, ex fifty two against bee fifty two, the character edit distance is 2 over strings of 12 and 13 characters, so

\[s\bigl(\text{ex fifty two},\ \text{bee fifty two}\bigr) \;=\; 1 - \frac{2}{13} \;\approx\; 0.846. \tag{31}\]

That is higher than the 0.75 the written pair scores, and higher means closer. Spelling the designation out does not separate the two names. It pushes them together, because the shared part expands into two long words while the part that distinguishes them stays one short syllable at the front.

At the level of whole words the picture is the reverse again, since one token in three differs,

\[s_{\text{word}} \;=\; 1 - \frac{1}{3} \;\approx\; 0.667. \tag{32}\]

So the answer depends on what you think a listener is matching, and a decision that records no measure has not said which of these it meant, or whether it meant any of them.

The Missing Threshold

Every one of the measures above is a number in the unit interval. Turning one into a refusal takes one more object, a threshold, and the rule is then

\[\text{refuse } b \quad \text{if and only if} \quad \max_{a \,\in\, \mathcal{A}} s(a, b) \;\geq\; \tau, \tag{33}\]

where $\mathcal{A}$ is the set of designations already in use, $s$ is whichever measure has been adopted, and $\tau$ is where the line is drawn.

The 2006 decision supplies $b$ and it supplies the outcome. It supplies no $s$, no $\tau$ and no $\mathcal{A}$. The 2014 instruction, which finally granted the authority, supplies none of them either, and nor does its 2020 successor.

The Other Naming Authority Publishes All Three

A comparison is available, and it does not flatter the designation system. The Food and Drug Administration’s guidance on proprietary drug names states the measure, the comparison set and the thresholds, in a numbered document with a date on it [Best Practices in Developing Proprietary Names for Human Prescription Drug Products, Guidance for Industry, December 2020].

The comparison set is named. A proposed name is queried against drug reference databases, so $\mathcal{A}$ is a specific list rather than an unstated one.

The measure is named, being the combined orthographic and phonetic score the program returns.

And the thresholds are published as three bands,

\[\text{band}(s) \;=\; \begin{cases} \text{highly similar}, & s \geq 70\%, \\[2pt] \text{moderately similar}, & 55\% \leq s \leq 69\%, \\[2pt] \text{low similarity}, & s \leq 54\%, \end{cases} \tag{34}\]

with a highly similar pair at greater risk of confusion and a moderately similar pair sent for further evaluation. The screening threshold itself is stated to rest on evidence, the guidance recording that the combined score of 55 percent is set on the validation work done on the algorithms rather than chosen for looking reasonable [Best Practices in Developing Proprietary Names for Human Prescription Drug Products, Guidance for Industry, December 2020].

Run the article’s own measures against those bands and the two answers differ. The bigram coefficient computed above is about 66.7 percent, which falls in the moderately similar band. The normalised edit similarity is 75 percent, which falls in the highly similar band. This is an illustration and not a result, since neither figure is the combined score that program returns, and the comparison is offered only to show that the choice of measure decides the band.

That contrast is the finding this section exists to report. One authority publishes the measure, the comparison set, the thresholds and the evidence the thresholds rest on. The other refused a designation in 2006 and recorded a phrase.

None of this proves the refusal was wrong, and none of it proves the refusal was right. What the measurement establishes is that the judgement was of a kind that can be made explicit, and was not. The literature surveyed below holds, among much else, the record of other people making this kind of judgement explicit, under published criteria, in fields where getting it wrong kills somebody.

The Contemporary Literature

Cluster	Records
Measuring how alike two strings are	359
Names refused because another name was near them	247
Medication safety, which is where this question is studied hardest	171
Identifiers as administered objects	147
Reading a code, and the shapes of its characters	114
Confusing similarity as a legal test	112
Call signs, readback and the spoken identifier	96
Confusable sounds and words in perception and memory	55
Aviation, and the designations it actually uses	21
Human error, and the taxonomies built to describe it	13
Total	1,335

Measuring how alike two strings are

The largest cluster, and it is the one the refusal actually needed. Edit distance, phonetic encoding, approximate matching, name matching, record linkage and the similarity measures built on them. AF/A8PE made a similarity judgement in 2006 and recorded no measure, no threshold and no method, and this shelf is what such a judgement looks like when somebody is required to show their working.

359 records. [Abdel Ghafour et al. 2011] [Aborot 2017] [Abraham and Raj 2014] [Afanasev and Lyashevskaya 2024] [Ahmed et al. 2022] [Aksoy et al. 2019] [Akutsu 1994] [Akutsu 1995] [Akutsu 2006] [Akutsu et al. 2006] [Akutsu et al. 2008] [Al-Bakry and Al-Rikaby 2016] [Aldwairi and Flaifel 2012] [Amir et al] [Amir et al. 2010] [Annisa Sihotang 2024] [Approximate String Matching 1994] [Peng and Mackay 2014] [Aratsu et al. 2009] [Aratsu et al. 2010] [Arslan 2006] [Arslan and Egecioglu] [Ashish et al. 2016] [Atallah et al. 2001] [Audhkhasi and Verma 2007] [Austin 1957] [Author 2026] [Ayad et al. 2016] [Aygun 2017] [Baeza-Yates and G. Navarro 1999] [Baeza-Yates and Navarro] [Baeza-Yates and Navarro 1996] [Baeza-Yates and Navarro 1997] [Baeza-Yates and Perleberg 1992] [Baeza-Yates and Perleberg 1996] [Bakar et al. 2000] [Baloi et al. 2023] [Baroni et al. 2002] [Bartolini et al. 2002] [Barton et al. 2014] [Batu et al. 2006] [Beck and Kerschbaum 2013] [Belazzougui and Venturini 2012] [Belazzougui and Venturini 2015] [Berghel et al] [Bernard and Ajah 2025] [Bille 2011] [Bille et al] [Bille et al. 2009] [Blair et al. 2021] [Boitsov 2002] [Branting 2003] [Bunke and Csirik 1995] [Bánki et al. 2023] [Calvo-Zaragoza et al. 2016] [Cantone et al. 2025] [Carbonnel and Anquetil] [Chang and Lampe 1992] [Chang and Lawler] [Chang and Lawler 1994] [Chang and Marr 1994] [Chaware and Rao 2010] [Chernyak 2017] [Chi-Chien Pan et al. 2002] [Christen 2006] [Christen and Gayler 2015] [Christopher Jaisunder et al. 2017] [Chung et al. 2011] [Ciobanu and Dinu 2014] [Cole and Hariharan 2002] [Colomer 2012] [Cormode and Muthukrishnan 2007] [Crochemore and Lecroq] [Dai and Zhao 2009] [DanishAli and Farooqui 2013a] [DanishAli and Farooqui 2013b] [Das et al. 2025] [Davuth and Kim 2013] [de la Higuera and Micó 2008] [Debbarma et al. 2014] [Degroot 2004] [Degroot 2014] [Dimov 1994] [Ding et al. 2009] [Dinh 2023] [Dong Deng et al. 2013] [Droppo and Acero 2010] [Duan et al. 2020] [El-Mabrouk and Crochemore 1996] [Essex 2019] [Fenna 1984] [Fered et al. 2026] [Ferri et al. 2018] [Fiori et al. 2021] [Fischer 1982] [Fredriksson 2003] [Fredriksson 2004] [Fredriksson 2006] [Fredriksson and Navarro 2003] [Fredriksson and Navarro 2004b] [Fredriksson and Navarro 2004a] [Gadd 1988] [Gali et al. 2019] [Galil and Giancarlo 1988] [Galil and Park 1990] [Gawrychowski 2012] [Generalized String Matching 2015] [Gewurz and Vietri 2007] [Giegerich et al. 1997] [Gong et al. 2009] [Grigor’eva 1983] [Guo et al. 2019] [Gvasalia et al. 2025] [Hall and Dowling 1980] [Hancox and Polatidis 2013] [Hanmei et al. 2019] [Heggarty et al. 2005] [Hema 2024] [Herzog et al] [Herzog et al] [Ho et al. 2017] [Holub and Melichar 2000] [Hon et al] [Howard 2020] [Hrbek and Holub 2016] [Htun Htet Htet and Sornlertlamvanich Virach 2018] [Huerta 2010] [Huynh et al. 2004] [Hyyrö 2003] [Hyyrö 2004] [Hyyrö 2005b] [Hyyrö 2005a] [Hyyrö 2008] [Hyyrö and Navarro 2002] [Hyyrö and Navarro 2004] [Ifada et al. 2023] [Jeong et al. 2014] [Jiang et al. 2013] [Jiang et al. 2014] [Jin Hwan Park] [Jokisch and Hain 2017] [Judson 2005] [Jumde and Keskar 2020] [Jupin et al. 2012] [Jupin et al. 2016] [Kaleem et al. 2014] [Kamali 2026] [Kant et al. 2020] [Karpov et al. 2023] [Kashyap and Oommen 1981] [Katsumata and Miura 2009] [Katsumata et al. 2010] [Kavros and Tzitzikas 2022] [Kessler 2005] [Khalid et al. 2022] [Khan et al. 2022] [Kianfar et al. 2018] [Kiawkaew et al. 2023] [Kim 2021] [Kim and Shawe-Taylor 1992] [Kirubakaran and Aramudhan 2018] [Kiwi et al] [Kiwi et al. 2011] [Klensin et al. 1998] [Knox 2019] [Komatsu et al. 2014] [Kondrak 2003] [Kondrak 2005] [Kondrak and Sherif 2006] [Koneru et al. 2016] [Kontorovich and Trachtenberg 2012] [Korotkov 2010] [Krauthgamer 2013] [Kuboi et al. 2014] [Kucherov et al. 2014] [Kucherov et al. 2016] [Kunchukuttan and Bhattacharyya 2021] [Kunchukuttan et al. 2018] [Kysela 2018] [Kärkkäinen and Na 2007] [Kärkkäinen et al. 2000] [Ladefoged 1969] [LaMonica 2014] [Landau and Vishkin 1989] [Li et al. 2013] [Li et al. 2023] [Libovický and Fraser 2022] [Lin and Chen 2002] [Lin and Wang 2011] [Lin et al. 2014a] [Lisbach 2011a] [Lisbach 2011c] [Lisbach 2011b] [Lisbach 2011d] [Lisbach and Meyer 2013a] [Lisbach and Meyer 2013c] [Lisbach and Meyer 2013d] [Lisbach and Meyer 2013b] [Liu et al. 2007] [Liu et al. 2014] [Liu et al. 2025b] [Loo 2014] [Lopresti and Tomkins 1997] [Lopresti and Wilfong] [Lu et al. 2013] [Lu et al. 2014] [Luján-Mora and Palomar 2001] [Man et al. 2013] [Martinek et al. 2007] [Marzal et al. 2003] [Matsumoto et al] [Matveev] [McCallum et al. 2005] [McCarley 2009] [McClanahan and Li 2024] [Mednis and Aurich 2012] [Melichar 1995] [Mergen 2022] [Michailidis and Margaritis] [Mishra et al. 2013] [Mittal et al. 2014] [Mohammed and Aliwy 2024] [Mohd Anuar et al. 2014] [Mollineda et al] [Montalvo et al. 2012] [Moreau et al. 2008] [Morris et al. 2026] [Mutalib and Noah 2011] [Muthukrishnan] [Myers 1998] [Nakagawa et al. 2018] [Nakano 2012] [Nakano 2013] [Narita et al. 2012] [Navarro 2001] [Navarro 2008] [Navarro 2016] [Navarro and Baeza-Yates 1999a] [Navarro and Baeza-Yates 1999b] [Navarro and Chávez 2006] [Navarro and Fredriksson 2004] [Navarro et al] [Navarro¹² 1997a] [Navarro¹² 1997b] [Nguyen and Conrad 2014] [Nguyen and Conrad 2015] [Novitra 2023] [Ohtake et al. 2004] [Owolabi and Ferguson 1988] [Owolabi and McGregor 1988] [Vinod-prasad 2016] [Howard 2018] [Papamichail and Papamichail 2009] [Paramonov et al. 2016] [Perbandingan Algoritma Edit Distance 2014] [Petty et al. 2022] [Pevzner and Waterman] [Phoophuangpairoj et al. 2024] [Phuduhudu et al. 2025] [Piskorski et al. 2009] [Pissis and Retha 2015] [Policriti and Prezza 2015] [Post and Toussaint 2011] [Pouliquen 2008] [Rama and Borin 2015] [Rani and Singh 2018] [Revesz 2021] [Ribeiro et al. 2025] [Rice et al. 1997] [Rico-Juan et al. 2020] [Ristad and Yianilos 1998] [Rochmawati and Kusumaningrum 2016] [Russo et al] [Russo et al. 2008] [Russo et al. 2009] [Sadeh] [Saikrishna and Ray 2013] [Salmela and Tarhio 2010] [Salmela et al. 2009] [Chaware and Rao 2011] [Sangurai et al. 2024] [Sariyar 2027] [Sastry and Ranganathan] [Sauleau et al. 2005] [Schraagen 2011] [Schumacher et al. 2023] [ShabnamHasan et al. 2015] [Shah and Singh 2014b] [Shah and Singh 2014a] [Shaikh et al. 2011] [Shang and Merrettal 1996] [Shapira and Storer 2003] [Shelake and Shekokar 2022] [Siew 2018] [Sihotang 2023] [Simpson et al. 2010] [Sitbon et al. 2007] [Smith and Pierzchala] [Snae and Brueckner 2009] [Stanchev et al. 2019] [Sukharev et al. 2014] [Sun and Wang 2018] [Sung 2008] [Sung 2016] [Sung-Hwan Kim and Hwan-Gue Cho 2017] [Susik 2017] [Sutinen and Tarhio 1996] [Tagliacozzo et al. 1970] [Tai 2018] [Takabatake et al. 2014] [Takabatake et al. 2016] [Takasu] [Takeda 2001] [Tarhio and Ukkonen 1990] [Tarhio and Ukkonen 1993] [Telsang et al. 2025] [Ternikov 2024] [The Role of Orthographic 2019] [Thumsuwan et al. 2024] [Tissot and Dobson 2019] [Top et al. 2007] [Treeratpituk and Giles 2021] [Tseng and Chen 2016] [Tsur 2010] [Tsuruoka et al. 2007] [Ukkonen] [Ukkonen 1983] [Ukkonen 1985] [Ukkonen 1992] [Ukkonen 1993] [Ukkonen and Wood 1993] [Uryupina 2004] [Vaiwsri et al. 2024] [Valarakos et al. 2004] [Van Court and Herbordt] [Van Court and Herbordt 2007] [Varol and Talburt 2011] [Vilares et al. 2004] [Wang et al. 2011] [Wang et al. 2014] [Watcharapinchai and Rujikietgumjorn 2017] [Wieling et al. 2012] [Winkler 2014] [Winter et al. 2020] [Kang 2015] [Wright 1994] [Yan et al. 2026] [Yang et al. 2022] [Yarkoni et al. 2008] [Yencken Lars and Baldwin Timothy 2008] [Yu et al. 2016] [Yuan et al. 2014] [Žgank and Kacic 2012] [Zhang and Zhang 2020] [Zhang et al. 2014] [Zhang et al. 2017] [Zhou et al. 2006] [Zobel and Dart 1996] [Ögeyik 2022]

Most of it is algorithmics rather than judgement. 166 of its 359 titles name string matching and 80 name edit distance or Levenshtein, against 54 that name a name. The measures are mature, and what the cluster rarely asks is where a measure should be cut to turn a score into a decision, which is the subject of Thin Subjects below.

Names refused because another name was near them

The same administrative act, performed somewhere it is studied. Look-alike and sound-alike names, proprietary against nonproprietary naming, and the refusal of a proposed name because an approved one is near it. A drug regulator does what the Air Force did to X-52A, and does it against criteria it publishes [Best Practices in Developing Proprietary Names for Human Prescription Drug Products, Guidance for Industry, December 2020].

147 of its 247 titles name look-alike or sound-alike medicines, which is the pharmacist’s term for exactly the hazard the registry recorded in one clause about the B-52.

Medication safety, which is where this question is studied hardest

A discipline built around counting the consequences of a confusable name. Medication error, its prevention, and above all the reporting systems built to count it. The pharmacology is not the subject and none of it is cited for any claim here. What is relevant is that an entire safety literature exists on the judgement the Air Force made without recording one.

171 records. [Abdulrouf et al. 2019] [Abuelsoud 2018] [Agoglia et al. 2024] [Tumuhaise and Namukwaya 2026] [Aljedaani et al. 2025] [Alsaif 2018] [Alshaikh et al. 2013] [Anderson et al. 2009] [andNa 1985] [andNa 1993] [andNa 1995] [andNa 1999] [andNa 2004] [andNa 2005] [andNa 2005] [andNa 2011] [Antonow et al. 2000] [Arora 2020] [Aydemi̇r and Esenkaya 2023] [Baghcheghi and Koohestani 2025] [Bailey] [Balan and Irawati 2026] [Barriers to Reporting Medication 2009] [Bassi et al. 2025] [Bc et al. 2015] [Birdwell et al. 2003] [Blum et al. 1988] [Boyer et al. 2009] [Brabcová et al. 2014] [Byrne and Bury 2018] [Cavell et al. 2001] [Chalasani and Madhan 2017] [Chalasani et al. 2018] [Chanyagorn et al. 2016] [Chauhan and Gaur 2025] [Cohen 1996] [Costello et al. 2007] [Crossman 2009] [Cunningham 2012] [Cusano et al. 2008] [Davis 2000a] [Davis 2000b] [Dejos 2021] [Dickens et al. 2007] [Dodek et al. 2010] [Dyab et al. 2018] [Edgar et al. 1994] [ElLithy et al. 2023] [Elnour et al. 2007] [Elvretta et al. 2021] [Fayaz-Bakhsh and Khezri 2014] [Folli et al. 1987] [Friedman 2005] [Furukawa et al. 2003] [George et al. 2018] [Goedecke et al. 2016] [Grant 2017] [Grindrod et al. 2002] [Grissinger et al. 2019] [Guo et al. 2025] [Hajibabaee et al. 2014] [Handler et al. 2004] [Hartnell et al. 2012] [Hauk 2018] [Hayati and Piramoon 2023] [Hicks and Becker 2006] [Holmström et al. 2012] [Holmström et al. 2015] [Horsham 2015] [Hritz et al. 2002] [Hung et al. 2015] [Hung et al. 2016] [Hutchinson et al. 2015] [Jae Jeong 2017] [Jember et al. 2018] [Joiner 1994] [Keefer et al. 2017] [Kennedy and Littenberg 2004] [Keshtkar et al. 2023] [Kim 2012] [Kim 2013b] [Kim 2016] [Kim and McPherson 2012] [Kim et al. 2022] [Koo 2012] [Kuitunen et al. 2023] [Lee 2016] [Tidman 2022] [Mansour and AL-Gethami 2013] [Maidment and Thorn 2005] [Manik 2020] [Marappa and Reha Mallika 2020] [Masmali et al. 2020] [Massah et al. 2021] [Mathew et al. 2021] [McArdle et al. 2003] [McKaig et al. 2014] [McNally and Sunderland 1998] [Khan 2021] [Medication Error Prevention 2004] [Medication Error Prevention 2017] [Devine 2012] [Medication Error Reporting System 2008] [Medication Safety and Error 2020] [Mehanna et al. 2024] [Miller 2006] [Miller 2007] [Mohanty 2016] [Moureaud et al. 2020] [Mukriani 2026] [Natalia et al. 2026] [Ni et al. 2023] [Novi Yulianti et al. 2019] [Nydert et al. 2020] [Ogamba et al. 2023] [Ohunyon et al. 2026] [Pal et al. 2025] [Panca et al. 2018] [Paparella 2008] [Patrician and Brosch 2009] [Perez 2026] [Peshek and Cubera 2004] [Naif H. Helman et al. 2020] [Phillips 2001] [Phillips 2014] [Poornima et al. 2015] [Rached] [Rask et al. 2006] [Rawat 2008] [Richmond 2011] [Ringseis and Caird 1995] [Rinke et al. 2010] [Rutledge et al. 2018] [Saad et al. 2025] [Saada 2023] [Saada et al. 2023] [Samaei et al. 2017] [Samsiah et al. 2016b] [Samsiah et al. 2016a] [Samundeeswari 2018] [Sandlin 2008] [Santos 2020] [Sarvadikar et al. 2010] [Savage et al. 2005] [Scheirman 2001] [Schlosser et al. 2025] [Sears and Generali 2005] [Senft 2007] [김민정 and SeongSook Jun 2016] [Shanty] [Shiima et al. 2022] [Shivanand H Honakeri et al. 2026] [Smetzer 2001] [Smetzer and Cohen 2007] [Smith et al. 2006] [Statutory Protection for Medication-Error 2019] [Stump 2000] [Sulastri et al. 2023] [Thabet et al. 2022] [The Pharmacy Technician’s Role 2014] [Tisdale 1986] [Tumuhaise and Namukwaya 2024] [Utilisation of Neonatal Medication 2018] [Vallabhaneni et al. 2023] [Weant et al. 2007] [Weant et al. 2010] [Wertheimer 2014] [Witt et al. 2024] [Wysocki et al. 2022] [Yoo and Keshavarzi 2020] [Zellmer 1993]

114 of its 171 titles concern the reporting of errors, which is the same instrument the civil aviation authority used to count call sign confusion.

Identifiers as administered objects

Identifiers considered as things somebody has to issue, keep and retire. Namespaces, numbering schemes, part numbering, registries and unique identifier standards. The designation system is one of these, and many of the titles are other issuers’ published rules for assignment and registration.

Reading a code, and the shapes of its characters

The identifier as a thing seen rather than heard. Legibility, typography, character and digit confusion, alphanumeric codes and labelling. The instruction’s only written anti-confusion rule for a designator lives in this cluster, being the prohibition on the series letters I and O because they resemble the digits 1 and 0.

114 records. [Adhe et al. 2023] [Alexeeva 2023] [AlJassmi and Perea 2024] [Alwitt 1973] [Aten et al. 2002] [Barbre and Price 1983] [Barnard et al. 1978] [Bell 1967] [Bernard et al. 2001] [Bhise and Hammoudeh 2004] [Brown and Goodman 1983] [Butterbaugh 1981] [Butterbaugh and Rockwell 1982] [Cai 2011] [Cai 2017] [Cardosi 1986] [Chapanis et al] [Chaparro et al. 2006] [Charness and Dijkstra 1999] [Chastain 1982] [Chrysler et al. 2001] [Cohen 2000a] [Colby 1992] [Dorris and Davis 2003] [Duncan and Konz 1974] [Dunn-Rankin et al. 1968] [Effects of Perceptual Similarity 2005] [Eggemeier et al. 1990] [Erdmann and Neal 1968] [Fell and Laughery 1969] [Fox et al. 2008] [Garvey et al. 2001] [Godwin et al. 2013] [Gonzales et al. 2018] [Greco et al. 2008] [Greene et al. 1994] [Greene et al. 1995] [Gunderson et al. 1991] [Harris et al. 2013] [Hemingway and Erickson 1969] [Ho et al. 2016] [Hsiao and Cheung 2015] [Kelso 1965] [Kim et al. 2000] [Kimura et al. 2020] [Kinney et al. 1966] [Kinoshita et al. 2021] [Koehler et al. 1994] [Kovesdi 2022] [Laarni 1999] [Legibility of Colored Print 2006] [Li and Liu 2013] [Liang et al. 2023] [Lippert 1963] [Lippert and Lee 1965] [Little 1973] [Loucks 1944] [McGlannan and Thorson 1976] [McLean 1965] [McTyre 1982] [McTyre and Frommer 1985] [Menneer et al. 2014] [Micrographics. Alphanumeric computer output] [Moody] [Morrison and Rayner 1985] [Mustonen et al. 2004] [Nilsson and Kaiserman 2004] [Olson and Bernstein 1979] [Pastoor 1990] [Petrun et al. 1985] [Phonetic features, vocalisation and 2019] [Plaisant and Sears 1992] [Podgorny and Garner 1979] [Preczewski and Fisher 1990] [Rasmussen et al. 1980] [Riley and Glenn 1996] [Roca et al. 2018] [Rose and Cornog 1964] [Rose and Cornog 1967] [Sawyer et al. 2017] [Schieber 1994] [Schieber 1998] [Schieber 2005] [Schieber and Kline 1994] [Schnell and Zwahlen 1999] [Serrano et al. 2016] [Sheedy et al. 2005] [Showman 1967] [Shurtleff 1966] [Shurtleff and Wuersch 1979] [Sivak et al. 1981] [Smith 1979] [Snyder 1979] [Sohn et al. 2024] [Some Factors Affecting Legibility 1981] [Spiker and Rogers 1984] [Spoto and Babu 1989] [Starrfelt et al. 2015] [Tullis 1981] [Tullis 1983] [van Nes 1988] [Van Nes and Bouma 1980] [Vartabedian 1970] [Vaughan et al. 1982] [Wang et al. 2024] [Ward et al. 1995] [West 1954] [Wetzel and Hernandez 2010] [Williams 1967] [Wolf 1982] [Wolff 1971] [Young et al. 1992] [Zineddin et al. 2003] [Zwaga 1979]

Confusing similarity as a legal test

The same judgement made where it has to be defended. Trademark, likelihood of confusion, passing off and consumer confusion. A court deciding whether two marks are confusingly similar is doing what AF/A8PE did, and the instruction itself sends popular names to a trademark search while sending design numbers to nobody.

112 records. [Assessment of the Risk 2022] [Assessment of the Similarity 2023] [Austin 2008] [Bartholomew 2025] [Bartow 2005] [Basire and Darnand 2017] [Batty 2025] [Batykov 2020] [Bayrak 2026] [Beebe 2006] [Beebe and Fromer 2020] [Beebe et al. 2026b] [Beebe et al. 2026a] [Blum et al. 2009] [Boling 2015] [Brengman et al. 2001] [Buerke 2016] [Bunker* 2015] [Carraway 1994] [Celik and Koc 2026] [Chiampi Ohly 2024] [Choi 2026] [Dornis 2017] [Eko 1998] [Empirical Studies of Trademark 2019] [Fhima 2026] [Fhima 2024] [Fhima and Denvir 2015] [Fhima and Gangjee 2019a] [Fhima and Gangjee 2019b] [Fhima and Gangjee 2019c] [Foxman et al. 1990] [Foxman et al. 1992] [Fritch 2006] [Bone 2021] [Gao and Wang 2018] [Giannino 2022] [Giordani 2025] [Greene 2003] [Greene 2006] [Guvenkaya 2026] [Jacoby 2000] [Jiang 2024] [Jintcharadze 2024] [Kaeding 1992] [Kaur 2026] [Kearny and Mitchell 2001] [Kim 2024] [Kuncheria 2008] [Laustsen 2019b] [Laustsen 2019a] [Laustsen 2019c] [Laustsen 2020] [Lee 2008] [Leek and Kun 2006] [Lemley and McKenna 2026] [Levy 2018] [Li 2018] [Likelihood of Confusion between 2022] [Likelihood of Confusion 2020] [Lutzker 2013] [Liu and Cheng 2019] [Loken et al. 1986] [Lomax et al. 1999] [Lou 2024] [Lunsford 1949] [Lutzker 2002] [Maksurov 2021] [McCutcheon 2023] [Miaoulis and D’Amato 1978] [Mishra et al. 2026] [Mitchell and Kearney 2002] [Mitchell and Papavassiliou 1999] [Mixed Messages 2024] [Moon 2018] [Morrin and Jacoby 2000] [Mupangavanhu and Vuke 2023] [Nadeau 1937] [No Cumulative Protection against 2023] [No Likelihood of Confusion 2025] [Nowak-Gruca 2018] [Ortolani 2009] [Peterson et al. 2024] [Radack 2002] [Reichert 2025] [Reichert 2026a] [Reichert 2026d] [Reichert 2026c] [Reichert 2026e] [Reichert 2026b] [Ritchie 2026] [Salim 2026] [Schweizer 2005b] [Schweizer 2005d] [Schweizer 2005c] [Schweizer 2005e] [Schweizer 2005a] [Scott 2013] [Sheff 2024] [Shiu 2021] [Strauch 2006] [Chen and ITing Cheng 2012] [Thouvenin et al. 2025] [Trade-Mark Registration. Similarity 1938] [Walsh 2023] [Wang 2024] [Wang 2025] [Yash 2020] [Zeisel and Kaye 1997] [Zhang and Cui 2022] [Zhou 2024b] [Zhou 2024a]

37 of its 112 titles name the likelihood of confusion, the test by which a court records, in a reasoned judgement, the comparison the designation office did not record.

Call signs, readback and the spoken identifier

The channel the X-52 would have travelled down. Call sign confusion, readback and hearback, radiotelephony phraseology, the phonetic alphabet and pilot-controller communication. This is the cluster nearest the reason actually given for the C-16 skip, which was recorded as concern about confusing an aircraft with the F-16 during the stress of high combat radio traffic.

96 records. [A Fused Situational Awareness 2025] [Monan 1983] [Allott 2016] [An error-resistant linguistic protocol for air traffic control] [Morrow et al. 1990] [Andrade 2023] [Aragão and Scaramucci 2020] [Blatt et al. 2022] [Bogush and Kovtun 2019] [Borowska 2025] [Boschen and Jones] [Brammer 2003] [Brown 2004] [Busch and King 1964] [Chen 2016] [Cheng et al. 2018a] [Chung 2026] [Clark and Williams 2020] [Corps Of Engineers Washington Dc 1986] [Dai 2022] [Pranoto and Susanto 2024] [DaPolito et al. 1989] [Air Force Instruction 33-217 1997] [Design of the Teaching 2024] [Digital Voice Communication Systems 2008] [Drayton] [Drayton and Coxhead 2023] [Eier and Kampichler 2026] [Falzon 2009] [Giolas et al. 1971] [Giolas et al. 1973] [Glushanytsia 2020] [Guclu 2017] [Hamzah et al. 2022] [Huang and Wang 2015] [Improved Air-Traffic Control Voice-Communications 2005] [Lees and Williamson 2013a] [Ishihara and Lee 2021] [Jia and Li 2022] [Jia et al. 2017] [Jia et al. 2018] [Johnson 1994] [Kerpatenko et al. 2024] [Kim 2013a] [Kim 2023] [Kocour et al. 2021] [Lees and Williamson 2020] [Lees and Williamson 2022] [Lombardi et al. 2024] [Lu et al. 2016] [Lynn] [Manning et al. 2002] [Mattox 1990] [Moe 1970] [Montalyo and Lebacqz 1994] [Monteiro 2022] [Morrow et al. 1993] [Morrow et al. 1994] [Morrow and Lebacqz 1994] [Murry 1970] [Neely 1956] [Nitayaphorn] [Osipova 2016] [Pan et al. 2025] [Pellegrini et al. 2019] [Pidlubna 2019] [Pilot-Controller Communication 2020] [Pilot-Controller Communication Problems 2016] [Prokhozhay 2011] [Lees and Williamson 2013b] [Radul 2025] [Rakas and Yin 2005] [Rakas et al. 2022] [Rakas et al. 2023] [Rakas et al. 2024] [Rosenshine 1968] [Rosmayanti et al. 2024] [Sadler et al. 2023] [Shen and Jia 2025] [Shetty et al. 2022] [Siti Fitriani 2021] [Skaltsas et al. 2011] [Skaltsas et al. 2013] [Smith 2008] [Stahel 2008] [Stuntz 1963] [Tavares Monteiro] [The Communicative Aspect 2023] [Tuncal 2026] [Vallioor et al. 2025] [Xiang et al. 2012] [yanqing et al 2025] [Jae-Yun and Choi 2023] [Yuniar et al. 2024] [Zhu and Ma 2015] [Zuluaga-Gomez et al. 2020]

It is mostly a literature of language rather than of names. 41 of its 96 titles name radiotelephony, much of it aviation English and phraseology, against ten that name a call sign.

Confusable sounds and words in perception and memory

How listeners and readers confuse what they hear and read. Confusion matrices of speech sounds, acoustic confusion in short-term memory, and the effect of similar letters, sounds and lexical neighbours on the recognition and recall of words. The section headed Saying It Aloud asks what a listener is matching, and these are the experiments that measure it.

55 records. [Aguasvivas et al. 2021] [Allington 1977] [Andrews 1997] [Baddeley 1971] [Bisson 2024] [Brochhagen et al. 2025] [Bruder and Silverman 1972] [Burt and Porter 2022] [Cebrian et al. 2025] [Clopper et al. 2010] [Corter 1987] [Cutler 2005] [Duñabeitia et al. 2007] [Frances et al. 2020] [Frances et al. 2021] [Frances et al. 2022] [Hacquard and Walter 2003] [Hall and Hume 2013] [Han and Oh 2018] [Hartmann and Fosler-Lussier 2009] [Hashem 2025] [Hershenson and Ryder 1982] [Hout et al. 2023] [Jani et al. 2015] [Kang and Cohen 2016] [Khan 2013] [Kim et al. 2021] [Klassen 2022] [Lee and Taft 2010] [Lin et al. 2014b] [Lupker 1982] [Manning and Shofner 1991] [Morgan et al. 1973] [Morris and Still 2012] [Moser et al. 1961] [Murray 1968] [Nelson and Borden 1973] [Nozawa and Wayland 2025] [Pelamatti et al. 1983] [Peressotti et al. 2003] [Post and Carrecker 2002] [Room 2013] [Scarborough 2003b] [Scarborough 2003a] [Scott and Baddeley 1969] [Sergent 1983] [Kinoshita and Lupker 2004] [Weisenberger 1996] [Westbury and Yang 2024] [Yang and Chen 2026] [Yencken and Baldwin 2008] [Yoneyama 2001] [Yuan and Shih 2004] [Zhang and Osth 2024] [Zhou et al. 2023]

Aviation, and the designations it actually uses

Aviation safety reporting, cockpit speech intelligibility, controller-pilot data link communication, aircraft identification training and two flight reports on the aircraft that received X-53A. Not one record takes aircraft designation as a subject in its own right. The literature of why the X-52 was refused lies almost entirely outside aircraft designation, and an article in a series about aeroplanes should say so rather than pad this row.

21 records. [Bergeron 1983] [Bogunenko et al. 2010] [Chan and Simpson 1990] [Connell and Reynard 1993] [Corrie and Corrie 1997] [Cui and Liu 2019] [Clarke et al. 2005] [Gurtov et al. 2018] [Subalakshmi 2025] [Khan et al. 2021] [Kristanto and Indriyanto 2024] [Lehto et al. 2021] [Mackintosh et al. 1999] [NASA Aviation Safety Reporting 1978] [NASA Aviation Safety Reporting 1980] [O’Leary and Srivastava 2012] [Orye et al. 2023] [Rankin and Mattson] [Stanford and Homan 1990] [Lizotte and Allen 2007] [Vicory 1968]

Human error, and the taxonomies built to describe it

Small, and small for a reason worth stating. Error taxonomies, slips and lapses, human error identification and human reliability. The cluster is small because the partition counts each record once, so a paper about call sign error is counted with call signs and a paper about medication error with medication.

13 records. [Butterbaugh 1982] [5Chapter Human Error Identification 2009] [Dekker 2017] [Hartwig et al. 1991] [Hull 1976] [Human Error Identification 2009] [Human Error Identification 2017] [Human Error in Medication 2003] [Human-Error Identification in Human-Computer 2007] [Human-Error Identification in Human 2009] [Sankaran and Rajkumar 2016] [Task Analysis for Error 1992] [Williamson 2009]

Where the Framing Breaks Down

The series framing assumes an aeroplane, and this article has none. Every canonical section that asks about sizing, systems, flight or flight data returns the same answer here, that the number never named a vehicle. The framing is kept so that the X-52 sits in its place in the sequence, and the sections it imposes are short because the record is.

The framing of a decision with a recorded reason also breaks down. The registry gives the reason as possible confusion with the B-52 series, but no document giving the reasoning has been seen, and whether that phrase quotes the decision or paraphrases it cannot be determined [Missing USAF and DOD Aircraft Designations]. The F-19 case shows that confusion can be stated as a reason when it is not the reason, so the stated ground is evidence of what was written and not necessarily of what was weighed.

The argument for a spoken channel is borrowed rather than found. The opening states that the radio is argued from the neighbouring cases and not from this one, and the C-16 note is the only entry in the family that names a radio. The Epistemic State section below separates what the record establishes from what this article infers, and the inference that the refusal lacked written authority stands on an absence in a document, weaker evidence than a presence would be.

The Source Base

The thirty curated sources that carry the argument and the 1,335 research records that map the field are different things, and this article keeps them apart on purpose.

The evidentiary base is small because the subject is. Thirty curated references and four books carry every claim made here, and the ones that matter most are the five issues of the governing instruction that precede and follow the decision. Those are not commentary on the evidence. They are the evidence, because the central question is what a document does and does not contain, and the only way to settle that is to read it.

The survey base maps the field. Its 1,335 research records are drawn from the scholarly registry of digital object identifiers, Crossref, and from two report servers, the Defense Technical Information Center and the space agency’s Technical Reports Server. A few of them are cited in the prose, being the flight test report of the aircraft that received X-53A, for that programme’s dates, the three report-server studies of pilot-controller communication named under The Definition of Primary, and the titles named under Thin Subjects to show what the literature does and does not contain. None is cited for a claim about the X-52 decision, and the argument about the decision would stand unchanged without the survey.

The research survey holds 1,335 research records drawn from Crossref, the Defense Technical Information Center and the NASA Technical Reports Server, of which 30 are report primaries, being 2.2 percent, by the identifier rule set out under The Definition of Primary. The median publication year is 2012. Of the 1,280 dated records, 843 were published in 2006 or later, the year of the refusal and after it, being 65.9 percent.

The Definition of Primary

Primacy is a property of the document, and this survey derives it from the identifier. A record is a report primary when its address is on the space agency’s Technical Reports Server, the Defense Technical Information Center or the energy department’s report server, or when it carries a digital object identifier under the 10.21236 prefix, which Crossref registers for Defense Technical Information Center reports.

The report-primary fraction is 2.2 percent, being 30 records of 1,335, which is the third-lowest of the 72 articles in this series that carry research references, counting in each article the research definitions whose address meets that rule. The lowest is the X-39, an anomaly without a vehicle, at 0.52 percent, being 4 records of 768, and that is not a coincidence. The second-lowest is the later article on the seven numbers from X-69 to X-75, at 1.79 percent, being 22 records of 1,232, and its subject is likewise a run of designations that no aeroplane carries.

The measure means less here than it does anywhere else in this series and the article will not dress it up. It counts identifiers issued by the space agency’s report server and the defence technical information centre, which is the right instrument when the subject is an aeroplane and the wrong one when the subject is a refusal. The primary documents this article actually argues from are the five issues of the governing instruction, the registry that records the decision, the drug regulator’s naming guidance and the civil call sign study, and not one of them carries an identifier the measure can see.

So the count is reported alongside the fraction. Eleven curated sources are primary documents rather than descriptions of one, being five issues of the governing instruction, three of the drug regulator’s naming publications, the civil aviation call sign study, the air-ground communications briefing note and the flight research centre’s own fact sheet. A number that falls because the subject changed is reporting something true, and the X-39, the seven numbers from X-69 to X-75 and the X-52, whose subjects are administrative acts rather than aeroplanes, are the three at the bottom of the ranking.

The report literature of the armed services does not hold this subject. It holds aeronautical engineering, and the confusability of spoken identifiers is studied in medicine, in civil aviation safety and in linguistics. The report literature that does bear on it is the space agency’s own study of addressee errors in air traffic control communications, which treats the call sign problem directly, with its neighbours on pilot-controller communication [Monan 1983] [An error-resistant linguistic protocol for air traffic control] [Morrow et al. 1990].

Thin Subjects

Six subjects that this article’s derivations depend on have thin literatures. Each count below is the number of research records in this survey whose title carries at least one of the listed terms, with a hyphen read as a space. Where a row joins two groups of terms with the word together, a title must carry a term from each group.

Subject	Title terms counted	Records
a threshold for deciding that two names are too alike	threshold, cutoff, decision rule, false positive, false negative, ROC, sensitivity and specificity, or a word beginning criteri, discriminat or validat	9
the longest common subsequence	longest common subsequence, LCS	0
the bigram set and the Dice coefficient	bigram, bigrams, Dice	1
aircraft designation as a subject	designation, designations, nomenclature together with aircraft, airplane, aeroplane, military, Air Force, Navy, Army	2
the reuse or retirement of an issued identifier	reuse, recycle, retire, reassign and their inflections together with identifier, number, numbering, name, code, designation	0
a collision between issued identifiers	collision, collisions, collide, colliding together with identifier, namespace, name, DOI, number	3

A threshold is the thing this literature most rarely names, and the evidence a threshold would rest on is a pharmacy literature. Of the 9 titles that carry a threshold term, two concern the similarity of strings or sounds as such, being [Fischer 1982] and [Austin 1957], and one the criteria of the likelihood of confusion in trademark law [Moon 2018]. The term rule misses the closest work, which is a small literature whose titles relate a measure of drug name similarity to experimental data or to observed errors [Lambert et al. 1999] [Lambert et al. 2002] [Tamaki et al. 2012] [Lambert et al. 2015a] [Sagawa et al. 2024]. The drug regulator’s guidance states that its screening threshold rests on the validation work done on its algorithms, and that in its postmarketing experience the combined similarity measure has been positively correlated with errors involving name confusion [Best Practices in Developing Proprietary Names for Human Prescription Drug Products, Guidance for Industry, December 2020]. The claim that a similarity threshold can rest on evidence therefore has a literature, and nothing comparable exists for designations.

Two of the three measures the article computes have almost no titles of their own. No title names the longest common subsequence, and the one title that names a bigram concerns open-bigram coding of letters in recognition memory rather than a similarity coefficient.

Aircraft designation is not a subject of this literature. The two titles that pair designation or nomenclature with an aircraft or service term are standards naming aircraft hydraulic, pneumatic and oxygen equipment, and neither concerns a mission design series designation.

The occupancy argument has no literature, and collision between issued identifiers has three titles. No title concerns the reuse or retirement of an issued identifier, which is the rule on which the B-52’s occupancy of the number 52 rests. The three titles on collision concern namespace collisions, collisions between author names, and colliding digital object identifiers.

What the Survey Admits

A record is admitted only when a person reading its title finds it on this article’s subject, which is the refusal of an identifier because an identifier already in use is near it, together with what such a refusal draws on. That means the similarity of strings, names and spoken forms, confusable names and their screening, medication error where names, labels or reporting are concerned, the spoken and the written identifier, the administration of identifiers, the legal test of confusing similarity, human error, the perception of confusable sounds and words, and aviation’s own designations and channels. The survey therefore reaches into medicine, law, linguistics and psychology where a title concerns confusable names or identifiers, because refusing a proposed drug name because an approved name is near it is the same administrative act as refusing X-52A because a B-52 exists. The pharmacology is not the subject. The refusal is.

The survey has no residual cluster. Every admitted record belongs to one of the ten named literatures in the table above, under the same rule.

Several classes are excluded because this subject’s words also name other things. Readback names the signal read back from storage and from programmable logic, as well as the pilot’s repetition of a clearance. Radiotelephony names a branch of radio engineering as well as a phraseology, and verbal communication names a social skill as well as a spoken exchange. A generic name is a rank in the naming of fungi and trematodes as well as the pharmacist’s term for a nonproprietary drug name. Legibility names a social and political idea as well as a property of print. An identifier is also a molecular tag, a device fingerprint and a name in a program, a namespace is also a library of program classes, and a numbering system is also a numeral system, a notation for teeth and a term of textiles. Also excluded are confusion as a clinical symptom or a conceptual muddle, the brand name as a marketing or pricing variable, consumer confusion over sustainable products, machine recognition of speech, characters and images where the machine is the subject, similarity measures on graphs, trees, images, trajectories, music and molecules, the similarity of documents by meaning, exact pattern matching, orthography and phonetics studied as philology, medication error with no name, label or reporting element, glossary definitions of terms, drug handbook name lists, textbook appendices, correction notices and second deposits of one document. A review of a book, a notice such as front matter, an editorial or a news item, and a reference or definition entry of two pages or fewer are excluded on the same ground, since none of them is a research work in its own right.

Doubtful classes are kept where the title concerns a confusable, spoken or issued identifier, and a reader may reasonably discount them. They are consumer confusion studied as a marketing construct, because confusion between similar brands is one of its kinds, general medication error prevention, machine recognition of call signs and readbacks, numbering schemes for tools, alloys and engine positions, unique identifiers designed for data systems, and encyclopedia entries on string matching and record linkage.

Every research title has been read for relevance, so the off-topic share that remains is a matter of reading judgement. A reading of titles cannot show that a record is relevant in substance, so this is a statement about titles only.

The Literature of This Refusal Is Not a Literature of Aircraft Designation

Of the 1,335 research records, 21, or 1.57 percent, sit in the aviation cluster, and not one of them is about aircraft designation as a subject in its own right. Seven concern aviation safety reporting, ten controller-pilot data link communication, one cockpit speech intelligibility, one aircraft identification training, and two are flight reports on the aircraft that received X-53A. The aviation literature the survey does hold is the literature of the radio channel, being the 96 records of the call sign cluster, which concern phraseology, readback and miscommunication rather than designations. The literature of why the X-52 was refused lies almost entirely outside aircraft designation, and an article in a series about aeroplanes should report that rather than pad the row.

The Book Identifiers Match Title and Author

All four resolve to the books the labels name [Cushing, Fatal words] [Reason, Human error] [Bowker and Star, Sorting things out] [Norman, The psychology of everyday things]. The match is made in the repository’s search index on title and author, because its work endpoint returns the same internal error for records that exist and for keys that do not, so it cannot tell a wrong identifier from a dead one.

Epistemic State

Historical Fact

The designation X-52A was requested in 2006 for a programme to test active aeroelastic wing technology, was disapproved because of possible confusion with the B-52 series, and the designation X-53A was allocated to the programme instead. This is recorded by the specialist registry of United States military aerospace vehicle designations [Missing USAF and DOD Aircraft Designations].

The Active Aeroelastic Wing programme began in 1996, first flew in modified form in November 2002, and concluded its flight research in March 2005 [Active Aeroelastic Wing Flight Research, NASA Facts FS-2005-03-061 DFRC] [Clarke et al. 2005] [Boeing X-53 Active Aeroelastic Wing]. The fact sheet gives the start of flight testing as late 2002 and the flight test report as November 2002.

The aircraft was designated X-53 by memorandum of the Air Force Deputy Chief of Staff for Strategic Plans and Programs, dated 16 August 2006 by the encyclopedia entry [Boeing X-53 Active Aeroelastic Wing], and the Air Force Research Laboratory announced the designation on 11 December 2006 [Active Aeroelastic Wing flight research vehicle receives X-53 designation, Air Force Research Laboratory, 11 December 2006].

The office symbol of the deciding office changed from HQ USAF/XPPE to AF/A8PE with effect from 1 February 2006 [Allocation of Official Aerospace Vehicle MDS Designations].

The F-35 designation was approved on 5 June 2002 against a nomenclature office recommendation of F-24A made on the ground that design numbers are to be assigned consecutively [Non-Standard DOD Aircraft Designations].

The requests to redesignate two drones as Q-7 and Q-8, made because the drones were being confused with unmodified aircraft, were refused in March 1954 [Missing USAF and DOD Aircraft Designations].

The Food and Drug Administration screens proposed prescription drug names against approved names using its Phonetic and Orthographic Computer Analysis program, makes that program publicly available, and publishes three similarity bands, being a combined match percentage score of 70 percent or more for a highly similar name pair, 55 to 69 percent for a moderately similar pair, and 54 percent or less for a low similarity pair. The guidance states that the 55 percent screening threshold is set on the validation work done on the algorithms [Best Practices in Developing Proprietary Names for Human Prescription Drug Products, Guidance for Industry, December 2020] [Phonetic and Orthographic Computer Analysis Program].

The United Kingdom’s civil aviation authority published a dedicated call sign confusion study in April 2000, resting on the 482 call sign confusion reports of 1997, of which 435 were filed by controllers, 44 by flight crews and 3 by both [CAP 704, Aircraft Call Sign Confusion Evaluation Safety Study, United Kingdom Civil Aviation Authority].

Verified by Reading the Document

The following are statements about the contents of five issues of one instruction and were checked against the text of each rather than by consulting a description of any of them.

The 14 April 2005 issue of the joint instruction directs that the coordinating office will assign and reserve the next available consecutive design number within each basic mission for new vehicles [Air Force Joint Instruction 16-401, 14 April 2005].

That issue contains no authority to skip a design number, no occurrence of the word skip, and no criterion by which a proposed design number may be judged unsuitable.

Its duplication check, its trademark search and its four levels of review apply to the popular name and not to the designation.

Its only provision citing confusion in connection with a designator is the prohibition of the letters I and O as series symbols [Air Force Joint Instruction 16-401, 14 April 2005].

The 1 September 1997 issue of the same instruction and the 1994 issue it superseded carry the same sequence requirement, the same popular-name duplication check and trademark search, and the same prohibition of I and O, and likewise contain no authority to skip a design number [Air Force Joint Instruction 16-401, 1 September 1997] [Air Force Joint Instruction 16-401, 1994].

The 16 May 2014 issue adds, at Attachment 2 paragraph A2.1.6.1.2, that HAF/A8PE reserves the authority to skip design number at discretion and that skipped design numbers cannot be requested or used, and attaches no criterion to the authority [Air Force Instruction 16-401, 16 May 2014]. The 3 November 2020 issue keeps the authority at the same paragraph under AF/A8PE, and at paragraph 4.2.1.3 it states that requests are not accepted for designators in reverse or skipped sequences [Department of the Air Force Instruction 16-401, 3 November 2020].

Analysis

The edit distance between the strings X-52 and B-52 is 1, the normalised edit similarity is 0.75, the longest common subsequence is three characters giving the same 0.75, and the Dice coefficient on character bigrams is two thirds. These are computed and not quoted from any source.

Rendered as they would be spoken, the two names are more similar than they are in writing. The character edit distance between ex fifty two and bee fifty two is 2 over strings of 12 and 13 characters, giving a normalised similarity of about 0.846 against the written pair’s 0.75. At the level of whole words one token in three differs, giving about 0.667, so the ordering depends on what a listener is taken to be matching.

The X-35 was allocated before the F-35 was approved, so that approval raised the number of series holding the design number 35 from one to two and added one bit of residual uncertainty to a listener who hears the number without the mission letter. The refusal of X-52A held the corresponding quantity at 52 unchanged and added none.

The B-52 has been operated by the Air Force since 1955 and is expected to serve into the 2050s, so the numeral has been and will be occupied for something near a century, and had been occupied for fifty-one years at the moment of the refusal [Boeing B-52 Stratofortress].

Every collision named in this article is between two designations that differ in the mission symbol and agree in the design number.

The count of cross-series numeric collisions in a system where each mission series counts from one is structurally non-zero and grows as series are added.

Placing this article’s own similarity figures in the drug regulator’s published bands is an illustration and not a result. The bigram coefficient of about 66.7 percent would fall in the moderately similar band and the normalised edit similarity of 75 percent in the highly similar band, but neither figure is the combined orthographic and phonetic score that program computes, and no claim is made that the program would return either value.

Inference

That the X-52A refusal was made under an authority the instruction did not then contain is an inference from the absence of any such provision in the 2005 issue, and an absence in a document is weaker evidence than a presence. It is possible that the authority existed in another issuance not consulted here.

That the 2014 clause regularised the practice is an inference from its content and its timing, and no document has been seen that connects the two.

That the F-35 and X-52 decisions are inconsistent is an interpretation. The two were made four years apart under one office symbol and then another, and the individuals need not have been the same. The inconsistency asserted here is of the system and not of any person.

What the Record Does Not Settle

Who asked for X-52A is not stated in any source consulted. The registry says the request was made for a programme to test active aeroelastic wing technology and does not name the requesting office.

The date within 2006 is not stated, so whether the request preceded or followed the 1 February office-symbol change is unknown.

No document giving the reasoning has been seen. The phrase possible confusion with the B-52 series is the registry’s summary. Whether it quotes the decision or paraphrases it is not determinable from the public record.

Whether the B-52 was named in the decision because of its fame, its longevity, or its role as the carrier aircraft for X-planes is unknown, and the third possibility is the one this article finds most interesting and has the least evidence for.

Whether anyone considered the F-35 precedent in 2006 is unknown.

Whether the refusal was correct is not settled by anything here. No measure and no threshold were recorded, and this article supplies a measure only to show what was missing, not to supply the answer retrospectively.

Out of Scope

The Active Aeroelastic Wing itself. The aeroelastic engineering, the control laws, the roll-reversal problem and the flight-test results belong to the next article in this series, which is about the X-53. This article names the programme and stops.

The unmanned series consuming numbers from the same pool. The X-58 and X-67 slots were taken by aircraft designated XQ-58A and XQ-67A, a different mechanism from a refusal, treated in its own articles later in the series [Missing USAF and DOD Aircraft Designations].

The pre-1962 designation systems. Everything here concerns the joint system implemented in September 1962 [1962 United States Tri-Service Aircraft Designation System].

Foreign designation systems, and the question of whether they exhibit the same behaviour.

The surveyed literature itself. The survey is a map for a reader who wants to pursue the general question, and its records are listed by title. None of them is cited for a claim about the X-52 decision. The cluster commentary carries one citation and it is a curated source rather than a survey record, being the drug regulator’s naming guidance, which is cited because the commentary makes a claim about what that regulator publishes.

Conclusion

The X-52 is the only number in the X-series that was asked for properly and refused on the merits of its own string. The registry’s other missing X numbers are the X-23, requested in 1965 and refused because the vehicle was unmanned and then never requested again, the X-39, reserved and never requested, and the X-58 and X-67, whose slots were skipped after aircraft designated in another series took the numbers [Missing USAF and DOD Aircraft Designations].

The instruction in force required the next number in sequence, provided no authority to skip one, and reserved its entire confusability apparatus for the popular name, the half of the identifier it describes as aiding communications and media references rather than the half it calls official. Its only written anti-confusion rule for a designator is that the series letters I and O are prohibited because they look like digits.

On the issues read here, the refusal was therefore made under a rule that did not exist in writing, and eight years later a sentence was added to the instruction granting the office the authority to skip a design number at discretion, with no criterion attached. The issue before the one in force said the same as the one in force, so the authority was absent for nearly twenty years while the practice ran throughout them.

The decision was not eccentric. It sits in a long and documented family, and the reasons recorded across that family are operational rather than clerical. A radio under combat load. Maintenance records mixed up between two aircraft built by two companies both called Bell. In every case the collision crosses a mission boundary, so the system’s formal guarantee of uniqueness depends on a coordinate that the channel does not carry.

And the same office had spent 2002 manufacturing such a collision on purpose, taking the X-35’s number for the F-35 against its own nomenclature office’s advice that numbers are assigned consecutively.

A judgement of that kind can be written down, and elsewhere it is. The drug regulator that screens every proposed prescription name against the names already approved publishes the program it uses, the databases it compares against, and three numbered similarity bands, and records that its screening threshold rests on validation work rather than on somebody’s ear. Measured against those bands, the two designations land in different categories depending on which measure is chosen, and for that reason the choice of measure has to be stated. One naming authority publishes all of it. The other refused a designation and recorded a phrase.

What the X-52 case finally shows is a designation system doing something a numbering scheme is not supposed to do. A counter does not care what its numbers resemble. This one does, the record of it weighing resemblance runs back to at least 1954, it has never written down what it is comparing or against what threshold, and in 2006 it looked at a bomber that had already been flying for fifty-one years and was expected to be flying more than forty years longer, and said no.

Equations

This section collects the 34 display equations of the article in the order they appear, each under its number and reproduced exactly as it stands in the text. A title in bold names an established result, and a title in italics beginning with the word Bespoke names a construction made for this analysis. Of the 34, 18 are established and 16 are bespoke. Design numbers, counts and multiplicities are dimensionless integers, durations are in years, the ambiguity measure is in bits, and every similarity score is a dimensionless number between zero and one that depends on which measure and which rendering of the two names is adopted, so scores from different measures are not interchangeable.

Equation 1, Bespoke Next Available Design Number. The article formalises the instruction’s next available consecutive number as the least natural number not already used up within the basic mission, counting numbers passed over as used up. Air Force Joint Instruction 16-401, 14 April 2005

\[n^{\star}(m) \;=\; \min\bigl\{\,k \in \mathbb{N} \;:\; k \notin A_m \,\bigr\} \tag{1}\]

Equation 2, Available Design Numbers Within a Mission. The numbers still available are those of the instruction’s range from one to 999 that are not already used up, and the next assignment is the least of them. Air Force Joint Instruction 16-401, 14 April 2005

\[V_m(t) \;=\; \{1, 2, \ldots, 999\} \setminus A_m(t), \qquad n^{\star}(m) \;=\; \min V_m(t). \tag{2}\]

Equation 3, Monotonicity of the Allocated and Available Sets. Because the instruction forbids reuse of a retired designation, the used-up set can only grow over time and the available set can only shrink. Air Force Joint Instruction 16-401, 14 April 2005

\[t_1 \leq t_2 \;\implies\; A_m(t_1) \subseteq A_m(t_2) \;\implies\; V_m(t_2) \subseteq V_m(t_1). \tag{3}\]

Equation 4, Bespoke Three-State Partition of the Design Numbers. The article partitions the range into allocated, marked not used and available numbers, adding the middle state that the master list records and the instruction never mentions. Missing USAF and DOD Aircraft Designations

\[\{1, 2, \ldots, 999\} \;=\; \underbrace{A_m(t)}_{\text{allocated}} \;\sqcup\; \underbrace{U_m(t)}_{\text{marked not used}} \;\sqcup\; \underbrace{V_m(t)}_{\text{available}}, \tag{4}\]

Equation 5, Departure of the Assigned Number From the Sequence Rule. The assigned number 53 exceeds the number 52 that the sequence rule names by one. Missing USAF and DOD Aircraft Designations

\[\text{assigned} \;-\; n^{\star}(X) \;=\; 53 - 52 \;=\; 1, \tag{5}\]

Equation 6, Size of the Series Symbol Alphabet. Excluding the letters I and O, which the instruction prohibits as series symbols, leaves an alphabet of twenty-four letters. Air Force Joint Instruction 16-401, 14 April 2005

\[|S| \;=\; 26 - 2 \;=\; 24, \tag{6}\]

Equation 7, Designation Space of a Mission Under the 2005 Issue. With 999 design numbers and twenty-four series symbols, a basic mission can hold 23,976 designations. Air Force Joint Instruction 16-401, 14 April 2005

\[N_m \;=\; 999 \times 24 \;=\; 23{,}976, \tag{7}\]

Equation 8, Designation Space of a Mission Under the 2020 Issue. Extending the design number to four digits, as the 2020 issue provides, raises the space to 239,976 designations. Department of the Air Force Instruction 16-401, 3 November 2020

\[N_m' \;=\; 9{,}999 \times 24 \;=\; 239{,}976. \tag{8}\]

Equation 9, Intervals Before the Written Authority to Skip. The 2014 issue that first grants the authority to skip came eight years after the refusal and twenty years after the earliest issue read. Air Force Instruction 16-401, 16 May 2014

\[\underbrace{2014 - 2006}_{8 \ \text{years after the refusal}} \qquad\text{and}\qquad \underbrace{2014 - 1994}_{20 \ \text{years after the earliest issue read here}}. \tag{9}\]

Equation 10, Count of Missions Skipping Thirteen by Custom. Six basic mission series lack the design number 13 by the unwritten custom of skipping it. Missing USAF and DOD Aircraft Designations

\[\bigl| \{\, m \in M \;:\; 13 \notin A_m \text{ by custom} \,\} \bigr| \;=\; 6, \tag{10}\]

Equation 11, Designation as a Pair of Mission and Number. An assigned designation is a pair of a basic mission symbol and a design number issued within that mission, and such pairs are unique by construction.

\[\mathrm{MDS} \;=\; \bigl\{ (m, n) \;:\; m \in M,\; n \in A_m \bigr\}, \tag{11}\]

Equation 12, Bespoke Projection Onto the Design Number. The article models a channel that preserves only the design number as a projection that discards the mission symbol, a supposition it infers from the refusals.

\[\sigma(m, n) \;=\; n, \tag{12}\]

Equation 13, Bespoke Fibre of Indistinguishable Designations. The designations that a listener hearing only the number cannot separate form the fibre of the projection, and its size is the multiplicity of that number.

\[\sigma^{-1}(k) \;=\; \bigl\{\, (m, k) \;:\; m \in M,\ k \in A_m \,\bigr\}, \qquad \bigl| \sigma^{-1}(k) \bigr| \;=\; o_k. \tag{13}\]

Equation 14, Number of Distinct Designations in the Register. The register holds as many distinct designations as the sum of the sizes of the allocated sets over all missions.

\[\sum_{m \in M} \bigl| A_m \bigr| \tag{14}\]

Equation 15, Bespoke Number of Designations Distinguishable by Number Alone. The count of design numbers in use is equated with the largest number issued in any mission, which holds only when every number up to that maximum has been issued in at least one series.

\[\Bigl| \bigcup_{m \in M} A_m \Bigr| \;=\; \max_{m \in M}\, \max A_m \tag{15}\]

Equation 16, Multiplicity of a Design Number. The multiplicity of a design number is the number of basic mission series that have issued it.

\[o_k \;=\; \bigl| \{\, m \in M \;:\; k \in A_m \,\} \bigr|, \tag{16}\]

Equation 17, Bespoke Count of Colliding Designation Pairs. The article measures collisions as the number of unordered pairs of series that share a design number, summed over all numbers.

\[C \;=\; \sum_{k \geq 1} \binom{o_k}{2}, \tag{17}\]

Equation 18, Bespoke Ratio of Register Size to Channel Capacity. The article defines the factor by which the register outruns a number-only channel as the ratio of designations to distinct numbers, equal to the mean multiplicity.

\[R \;=\; \frac{\sum_{m \in M} \bigl| A_m \bigr|} {\Bigl| \bigcup_{m \in M} A_m \Bigr|} \;=\; \operatorname*{mean}_{k \,\in\, \bigcup_m A_m} o_k, \tag{18}\]

Equation 19, Bespoke Probability of Correct Attribution. Under a uniform prior over the series that hold a number, an idealisation the article states, a listener attributes a spoken number correctly with probability one over its multiplicity.

\[P(\text{correct} \mid k) \;=\; \frac{1}{o_k} \tag{19}\]

Equation 20, Bespoke Residual Uncertainty in Bits. The same uniform prior gives a residual uncertainty of the base-two logarithm of the multiplicity, the information a number-only channel discards.

\[H(k) \;=\; \log_2 o_k \tag{20}\]

Equation 21, Bespoke Ambiguity Added by Approving the F-35. Approving the F-35 on top of the X-35 doubled the multiplicity of 35 and so, under the uniform prior, added one bit of ambiguity.

\[\Delta H(35) \;=\; \log_2 2 - \log_2 1 \;=\; +1 \ \text{bit}. \tag{21}\]

Equation 22, Bespoke Ambiguity Withheld by Refusing the X-52. Refusing the X-52 left the multiplicity of 52 at one, so under the uniform prior the refusal added no ambiguity.

\[\Delta H(52) \;=\; \log_2 1 - \log_2 1 \;=\; 0 \ \text{bits}, \tag{22}\]

Equation 23, Occupancy Duration of a Design Number. A number is occupied from its allocation until the last aircraft carrying it retires, since the instruction forbids reuse. Air Force Joint Instruction 16-401, 14 April 2005

\[T_{\text{occupied}} \;=\; t_{\text{retire}} \;-\; t_{\text{allocate}}, \tag{23}\]

Equation 24, Bespoke Occupancy of the Number 52. The occupancy of the B-52 is bounded below by taking 2050 as the retirement year, a representative value the article takes from expected service into the 2050s. Boeing B-52 Stratofortress

\[T_{\text{occupied}} \;\geq\; 2050 - 1955 \;=\; 95 \ \text{years}, \tag{24}\]

Equation 25, Bespoke Split of the B-52 Occupancy at the Refusal. The ninety-five year occupancy is divided at 2006 into fifty-one years served and forty-four expected, the latter resting on the assumed retirement year of 2050. Boeing B-52 Stratofortress

\[\underbrace{2006 - 1955}_{51 \ \text{years already served}} \;+\; \underbrace{2050 - 2006}_{44 \ \text{years still expected}} \;=\; 95 \ \text{years}. \tag{25}\]

Equation 26, Levenshtein Edit Distance Recurrence. The edit distance between two strings is the least number of single-character insertions, deletions and substitutions, computed by the standard dynamic programming recurrence. Levenshtein Distance

Equation 27, Normalised Edit Similarity of X-52 and B-52. One minus the edit distance divided by the length of the longer string gives a similarity of 0.75 for the written pair.

\[s(a, b) \;=\; 1 - \frac{d_{\ell_a,\, \ell_b}}{\max(\ell_a,\, \ell_b)} \;=\; 1 - \frac{1}{4} \;=\; 0.75. \tag{27}\]

Equation 28, Longest Common Subsequence Similarity. The length of the longest common subsequence divided by the length of the longer string also gives 0.75 for the written pair.

\[s_{\mathrm{LCS}}(a, b) \;=\; \frac{\bigl| \mathrm{LCS}(a, b) \bigr|}{\max(\ell_a,\, \ell_b)} \;=\; \frac{3}{4} \;=\; 0.75. \tag{28}\]

Equation 29, Character Bigram Sets of the Two Designations. Each designation is reduced to its set of adjacent character pairs, and the two sets share two of their three members.

\[\mathcal{B}(\text{X-52}) = \{\,\texttt{X-},\ \texttt{-5},\ \texttt{52}\,\}, \qquad \mathcal{B}(\text{B-52}) = \{\,\texttt{B-},\ \texttt{-5},\ \texttt{52}\,\}, \tag{29}\]

Equation 30, Dice Coefficient on Character Bigrams. The Dice coefficient, twice the shared bigrams over the total, is about 0.667 for the written pair.

\[s_{\mathrm{Dice}}(a, b) \;=\; \frac{2 \bigl| \mathcal{B}(a) \cap \mathcal{B}(b) \bigr|} {\bigl| \mathcal{B}(a) \bigr| + \bigl| \mathcal{B}(b) \bigr|} \;=\; \frac{4}{6} \;\approx\; 0.667. \tag{30}\]

Equation 31, Bespoke Edit Similarity of the Spoken Forms. The edit similarity is evaluated on the spoken renderings ex fifty two and bee fifty two, a spelling of the spoken forms the article chooses, and gives about 0.846.

\[s\bigl(\text{ex fifty two},\ \text{bee fifty two}\bigr) \;=\; 1 - \frac{2}{13} \;\approx\; 0.846. \tag{31}\]

Equation 32, Bespoke Word-Level Similarity of the Spoken Forms. Treating the spoken forms as sequences of three words, a tokenisation the article chooses, one differing word in three gives about 0.667.

\[s_{\text{word}} \;=\; 1 - \frac{1}{3} \;\approx\; 0.667. \tag{32}\]

Equation 33, Bespoke Threshold Rule for Refusing a Designation. The article states the decision rule that a written refusal would need, refusing a proposed designation when its greatest similarity to any designation in use reaches a threshold.

\[\text{refuse } b \quad \text{if and only if} \quad \max_{a \,\in\, \mathcal{A}} s(a, b) \;\geq\; \tau, \tag{33}\]

Equation 34, Similarity Bands of the Drug Name Guidance. The Food and Drug Administration guidance classes a combined orthographic and phonetic score as highly similar at seventy percent or more, moderately similar from fifty-five to sixty-nine percent and of low similarity at fifty-four percent or less. Best Practices in Developing Proprietary Names for Human Prescription Drug Products, Guidance for Industry, December 2020

Notation

$n^{\star}$, the next available design number that the sequence rule names
$A_m$, the set of design numbers used up within basic mission $m$
$V_m$, the set of design numbers still available within basic mission $m$
$U_m$, the set of design numbers marked not used within basic mission $m$
$M$, the set of basic mission symbols
$ S $, the number of permitted series symbols
$N_m$, the size of the designation space of a basic mission
$\mathrm{MDS}$, the set of assigned designations, each a pair of mission symbol and design number
$\sigma$, the projection that keeps only the design number
$o_k$, the multiplicity of design number $k$, the number of series that have issued it
$C$, the count of colliding designation pairs
$R$, the ratio of register size to the number of distinct design numbers
$H(k)$, the residual uncertainty in bits after hearing design number $k$ alone
$T_{\text{occupied}}$, the time a design number stays occupied
$d_{i,j}$, the edit distance between the first $i$ characters of $a$ and the first $j$ characters of $b$
$\ell_a$, the length of string $a$, with $\ell_b$ that of string $b$
$s(a, b)$, the normalised edit similarity of two strings
$s_{\mathrm{LCS}}$, the longest common subsequence similarity
$\mathcal{B}$, the set of character bigrams of a string
$s_{\mathrm{Dice}}$, the Dice coefficient on character bigrams
$\mathcal{A}$, the set of designations already in use
$\tau$, the similarity threshold for refusal

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The Research Question

Programme Origin, What the Record Says Happened

The Office That Said No

The Rule That Refused It Is Not in the Instruction

The Instruction Screens the Other Half of the Name for Confusion

The Only Written Anti-Confusion Rule for the Designator Concerns Two Letters

The Authority Was Written Down Eight Years Later

The Same Office Had Manufactured the Same Collision Four Years Earlier

Sizing From First Principles

Dependent Systems

The Flight Test Record

Comparison With Ground Prediction

What the Data Changed, What the Anomaly Reveals About the Designation System

The Refusal Belongs to a Documented Family

Every One of These Collisions Crosses a Series Boundary

The System Declined to Fix the Confusion It Actually Had

A Number Is Occupied for as Long as the Aeroplane Lives

Nothing Was Lost

Measuring the Judgement That Was Not Recorded

Saying It Aloud Moves the Two Names Closer Together

The Missing Threshold

The Other Naming Authority Publishes All Three

The Contemporary Literature

Measuring how alike two strings are

Names refused because another name was near them

Medication safety, which is where this question is studied hardest

Identifiers as administered objects

Reading a code, and the shapes of its characters

Confusing similarity as a legal test

Call signs, readback and the spoken identifier

Confusable sounds and words in perception and memory

Aviation, and the designations it actually uses

Human error, and the taxonomies built to describe it

Where the Framing Breaks Down

The Source Base

The Definition of Primary

Thin Subjects

What the Survey Admits

The Literature of This Refusal Is Not a Literature of Aircraft Designation

The Book Identifiers Match Title and Author

Epistemic State

Historical Fact

Verified by Reading the Document

Analysis

Inference

What the Record Does Not Settle

Out of Scope

Conclusion

Equations

Notation

References

Primary Sources, Peer-Reviewed

Primary Sources, Non-Peer-Reviewed

Secondary Sources

Commercial Sources

Tertiary Sources

Related Posts

Related posts

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