Type–Token Distinction¶

Version: v4 · 2026-08-30 · History
Prime #: 1474
Origin domain: Philosophy Logic
Subdomain: ontology and semiotics → Philosophy Logic
Aliases: Type Token, Class Instance Distinction, Universal Particular Instantiation
Related primes: Abstraction

Core Idea¶

How many words are in "the cat sat on the mat"? Six, or five, and the question has no answer until it is settled which of two things is being counted: the numerically distinct inscriptions that occur in that line, or the repeatable vocabulary items they are inscriptions of, since "the" occurs twice. ^[1] The type–token distinction names that pair of levels and stops them from being counted together. A type is a repeatable form — a kind, pattern, symbol, or specification — that admits of many occurrences without being used up by any of them. A token is one such occurrence: located somewhere, dated, made of something, and numerically distinct from every other occurrence, including occurrences it cannot be told apart from.

Predication then splits in two. What holds of the type holds once and holds of every occurrence: the English definite article is spelled with three letters, whatever inscription of it you point at. What holds of a token holds of that occurrence alone: this one is faded, that one sits at the start of the line, and burning the page leaves the word-type and its other occurrences entirely untouched. ^[2] Two occurrences can be qualitatively indistinguishable and still be two, which is why a count of tokens is never recoverable from any description of the type.

Two features of the relation are routinely overlooked and do most of the real work. The first is that it is relative to a criterion of identity rather than absolute. "The" and "the" are one type under an orthographic criterion that folds case and two under one that does not; "bank" is one type by spelling and two by sense; a letterform, a phoneme, a lemma, and a citation form each carve the same stretch of text into different populations of repeatable forms. A count at the upper level is therefore always a count under a stated sameness relation, and moving the relation moves the answer without a single occurrence having changed. ^[3]

The second is that the two levels are not a fixed two-storey building. What is a token at one level is routinely a type at another. A typeface is a repeatable form whose occurrences are the glyphs it sets, and is itself an occurrence of a broader design family. A viral strain is an occurrence of its species and a repeatable form over the individual virions carrying it. A software class stands over the objects that instantiate it and under the design pattern it follows. The relation can be re-applied indefinitely; it is not a partition of the world into two kinds of thing. ^[4]

Structural Signature¶

One repeatable form + a stated criterion of sameness → many numerically distinct occurrences, with every predicate sorted to exactly one of the two levels.

Recurring features:

Cardinality asymmetry. One form stands over zero, one, or indefinitely many occurrences; the count runs in one direction only, and a form with no occurrences yet is perfectly well constituted.
Non-consumption. Producing an occurrence does not deplete the form it is an occurrence of, and destroying an occurrence leaves the form and its siblings intact — the relation obeys no conservation law.
Qualitative sameness without numerical sameness. Sibling occurrences may match on every describable property and remain two, because their distinctness is carried by position and history rather than by description.
Criterion-relativity. Membership is fixed by a sameness relation that can be tightened or loosened; tightening it splits one form into several without creating or destroying anything at the lower level.
Level re-entrancy. Any occurrence can be treated as a form over a finer population, and any form as an occurrence of a coarser one, so the pair of levels is a window that slides rather than a floor and a ceiling.
Predicate sorting. Each predicate is well formed at exactly one level; asserting a lower-level property of the upper level, or the reverse, produces a malformed claim rather than a false one.
Localisation asymmetry. Occurrences carry position, duration, material, state, and causal history; the form they occur of carries none of these and is unchanged by whatever befalls them. ^[2]

What It Is Not¶

This is not a claim that types are real things residing somewhere. Whether the distinction can be drawn without thereby admitting repeatable forms as abstract objects is itself disputed: nominalists hold that a repeatable form is nothing over and above its occurrences, or a stipulated convenience of a counting scheme, while realists argue that talk of repeatable forms resists any such paraphrase. Nothing that follows here turns on the outcome. What is required is only that some predicates attach to the repeatable form, others to the occurrence, and that the two counts can come apart. ^[5]

Neither is it the abstract–concrete divide wearing a different name. Repeatable forms are frequently concrete in every sense that matters — a part number, a strain, a model of pump — and occurrences are frequently as abstract as what they occur of, as when a particular proof is an occurrence of an argument form. Nor is it the general–specific spectrum. Something maximally specific is still repeatable: "the exact configuration shipped on 14 March" becomes a repeatable form the moment a second unit is built to it.

It is also not the contrast between an original and its copies. That contrast ranks occurrences by lineage, asking which came first and which derives from which. Here nothing is ranked. A later occurrence is no less an occurrence than the first, a form with a single occurrence to date is not thereby demoted, and the earliest occurrence enjoys no special standing.

Finally, this is not the loose everyday use of "type" as a rough grouping — "that type of argument", "people of that type". Everyday typing tolerates fuzzy edges and disputed cases because nothing is being counted and nothing is being routed. The relation described here does work only where a definite sameness criterion is in force, because it is the criterion that fixes how many forms there are^[6] and which occurrences fall under which.^[7] Where no such criterion can be stated, what one has is treated here as a loose grouping rather than the two-level structure. ^[8]

Broad Use¶

The relation becomes load-bearing wherever a population of occurrences has to be administered against a shared specification, and the fields that do this well have usually built the two levels into their identifiers.

Manufacturing and asset management assign the levels separate numbering schemes on purpose. A part number designates the repeatable form; a serial number designates one unit. Engineering changes, certification, and recall scope attach to the first; installed location, running hours, inspection status, and repair history attach to the second. ^[9]

Epidemiology counts cases against a disease, and its case definitions are precisely the sameness criterion deciding which presentations count as occurrences of which condition. Incidence and prevalence are counts at the lower level indexed to a population and an interval; aetiology, transmissibility, and the definition itself sit at the upper one.

Computing bakes the pattern into its languages: a class is instantiated by objects, string literals may be interned so that many occurrences share one stored representation, and value semantics let two occurrences with equal contents count as one for comparison while remaining two in memory.

Law and standards work the same way: a statute or a specification is a repeatable form, and each offence, filing, or conforming article is an occurrence of it. Amending the text changes the form prospectively and leaves completed occurrences where they are.

Scores stand over performances, certificate policies over issued certificates, alleles over the copies individuals carry, and denominations over notes with their own serial numbers and their own wear.

Clarity¶

The confusion the distinction dissolves is a specific equivocation: one question, asked in one form of words, silently admits two answers, and an argument can travel from a true premise to a false conclusion without any step looking wrong. "How many?" is the usual site. So is "the same". Two people agreeing that they read the same book may be agreeing about a work or about a physical volume passed between them, and the agreement dissolves the moment one of them spills coffee on it. ^[2]

Once the levels are separated, a family of apparent paradoxes stops being paradoxical. A defect can be reported four hundred times and still be one defect. A word can be short while an inscription of it is three metres tall. A song can be performed nightly for a decade without wearing out while every recording of it degrades. A specification can be exactly right while every unit built to it is out of tolerance. Each is a pair of unremarkable claims made at two levels, mistaken for a contradiction only while the levels are collapsed into one.

The clarification is diagnostic rather than merely tidy: it tells you where to look when two competent parties disagree about a number, neither has made an arithmetic error, and more data never settles it.

Manages Complexity¶

The distinction earns its keep by letting a shared description be stated once and then never re-derived, re-checked, or re-stored per occurrence. Everything true of every occurrence in virtue of the form it is an occurrence of moves upward, and each occurrence's record shrinks to what is genuinely its own: where it is, what state it is in, what has happened to it. A fleet of ten thousand identical valves does not require ten thousand descriptions of a valve; it requires one specification and ten thousand short records of position, hours, and condition. ^[10]

The saving compounds in both directions. Reasoning at the upper level can proceed without enumerating occurrences, which is what makes it possible to say something true of a population that has not been fully built or observed. Reasoning about one occurrence can proceed without consulting its siblings, because nothing that happens to them bears on it. The two levels are inferentially insulated from each other, and that insulation is what keeps the marginal cost of an added occurrence roughly constant instead of growing with the population.

The corresponding failure mode is equally specific: store a property belonging to the form against each occurrence instead, and every occurrence becomes a place the shared description can drift, without any single edit looking wrong.

Abstract Reasoning¶

The distinction licenses a short, repeatable audit of any claim about a population. Ask the counting question first: if "how many?" forks into two defensible answers, both levels are live and the claim must declare which one it is about. Then state the sameness criterion explicitly, since it is the criterion rather than the subject matter that fixes the upper-level count. Then apply the non-consumption test — does producing another occurrence deplete anything? — and the survival test — does destroying this occurrence change the others? A yes to either means the candidate is a stock, a resource, or a coupled system, not a repeatable form.

The same procedure yields a diagnostic for level-slip. Take an inference that looks valid, restate each premise at the opposite level, and watch whether the truth values move. If the argument survives only when one premise is read at the upper level and another at the lower, its validity is an artefact of the equivocation. This catches a large class of errors before any data is collected: a metric whose numerator counts occurrences and whose denominator counts forms; a guarantee stated of a specification but enforced against units; a rate that becomes meaningless because the sameness criterion was loosened partway through the series.

It also licenses a constructive move. When lower-level variation stops being noise and starts being systematic — when some subset of occurrences reliably behaves differently from the rest — the correct response is not to widen the form's tolerance until the outliers fit, but to introduce a level: split the form, or promote the recurring variation into a form of its own with the original standing above it. ^[11]

Knowledge Transfer¶

What this entry takes to move between substrates is the skeleton and the diagnostics: two levels of predication, a count that runs in one direction, non-consumption, insulation between siblings, and the fact that a level confusion surfaces as an arithmetic discrepancy rather than as an obviously false statement.^[5] Someone who has debugged a deduplication pipeline and someone who has argued about how many species a genus contains are exercising one competence, but reading across is not automatic: retrieval of a structurally analogous problem is the step solvers have difficulty executing on their own. ^[12]

What does not move is the identity criterion. Every substrate supplies its own, those criteria are frequently contested inside their own fields, and importing one wholesale is exactly how the analogy breaks. Case definitions in epidemiology, same-work criteria in cataloguing, equality semantics in a programming language, and conformity tests in standards are not versions of one another and cannot be substituted. Cost structure does not move either. Producing an occurrence is free in a formal language, expensive in manufacturing, and irreversible in biology, so intuitions about how freely one may reason downward from a form to its occurrences do not survive the crossing.

Two further limits are worth naming. Whether a form is discovered or stipulated varies by substrate and changes what a dispute about that form is even about. And where occurrences are not discrete — a continuous field, a mass, an unbounded stream — the lower level has no natural count at all, so the structure applies only after a segmentation has been imposed, and it is then the segmentation, not the distinction, that carries the analytic weight.

Examples¶

Formal/abstract¶

Take the string "the cat sat on the mat" and treat its lower level formally: an occurrence is a pair of a symbol and a position, so the six occurrences are distinct by construction, no two sharing a position. The upper level is the set of equivalence classes those occurrences fall into under a chosen sameness relation on symbols. Under exact match the classes are {the@1, the@5}, {cat}, {sat}, {on}, {mat} — five forms over six occurrences.

Now vary only the relation. Fold case, and a sentence-initial "The" joins the class of "the": the lower count is unchanged at six, the upper count falls. Lemmatise, and "sat" joins the class headed by "sit". Count by part of speech instead, and "cat" and "mat" merge into a single noun form while the two determiner occurrences stay one, giving four. Segment by character rather than by word and the same string yields seventeen letter occurrences over nine forms, or twenty-two over ten if the spaces are counted too. ^[13]

Throughout, one number moves and one does not. The lower count is fixed by the string and the segmentation alone. The upper count is a function of the sameness relation and can be driven anywhere from one to the number of occurrences by tightening or loosening it. This is why a type–token ratio measures the criterion at least as much as the text, and why comparing such ratios across corpora normalised differently compares two different questions rather than two texts.

Mapped back: The formal case isolates the load-bearing feature. The two levels are not two populations sitting in the world waiting to be counted; they are one population of occurrences plus a relation imposed on it. Fixing that relation is the whole of the modelling work, and once it is fixed the two counts, the two sets of predicates, and the insulation between them all follow without further choices.

Applied/industry¶

A pump manufacturer ships a model designated by a part number, and every unit leaving the line carries its own serial number. Design geometry, material specification, rated duty, and certification attach to the part number; installed site, hours run, seal condition, and repair history attach to the serial. Neither list is derivable from, or altered by, the other.

A field failure arrives, and the investigation's first question is which level the fault lives at, because the two answers imply entirely different actions and costs. If the impeller geometry is wrong, the fault is upper-level: every unit built to that part number is implicated whether or not it has failed, the remedy is a design change plus a recall scoped by part number, and the population at risk is readable from the production record without inspecting anything. If one seal was installed backwards, the fault is lower-level: the population at risk is a single serial, and a recall scoped to the part number would be an expensive category error. The test that separates the two is the survival test — would a correctly built unit of the same part number fail the same way? ^[14]

Level re-entrancy shows up immediately afterwards. The part number is itself an occurrence of a design lineage: revisions A and B are two part numbers, each standing over its own serialised units and both occurrences of one engineering family. A recall scoped to the family is a third population, distinct from either revision's units, and an organisation whose identifier scheme stops at two levels can only express it as a hand-maintained list of part numbers — which is what a missing level looks like in practice.

Mapped back: The identifier scheme is this distinction made operational, and the failure modes it prevents are the ones the structure predicts. Store an upper-level property against serials and the specification drifts unit by unit. Store a lower-level property against the part number and every remedy is over-scoped. Provide no identifier for the level above the part number and a real population becomes unnameable. Each is a level error before it is ever a process error.

Structural Tensions¶

T1 — The level relativity has no natural floor. Because any occurrence can be re-read as a form over a finer population, no level is the one at which analysis is forced to stop. Glyphs decompose into strokes, strains into lineages, part numbers into revisions. The stopping point is chosen by what the analysis must act on, not discovered in the subject matter. Teams that treat their current bottom level as the real particulars are ambushed when systematic variation appears beneath it, and have no vocabulary ready in which to name the new population.

T2 — Metrics that switch levels mid-count. The commonest quiet failure is a number whose numerator counts occurrences and whose denominator counts forms, or a series whose normalisation changed partway through. Unique users against sessions, distinct defects against reports, species against specimens: each pair is legitimate and each ratio is meaningless unless both halves are pinned to one level. The error survives review because both counts are individually correct and the arithmetic is sound. Only the referents have moved, and nothing in the number itself records the move.

T3 — Discovered or stipulated. Some forms look found — a chemical species, an allele — and others are plainly decided, like a product line or an accounting category. The practical difference appears when occurrences resist. With a discovered form, an anomalous occurrence is evidence that the form was described wrongly; with a stipulated one, it is evidence that the criterion should be revised. Fields inherit a stance on this without stating it, and most disputes about whether a type is "real" turn out to be disputes about which of the two moves is licensed.

T4 — The identity criterion does the work and is rarely inspected. The upper-level count, the population at risk, and every guarantee stated of a form all follow from the sameness relation, yet that relation is usually inherited from a tool, a legacy schema, or a field convention rather than chosen. Changing it silently re-partitions history: yesterday's two forms become one, trends break at the seam, and systems that fold case or normalise differently compare different objects while appearing to compare the same ones. The criterion deserves the version control its derived data receives.

T5 — Membership versus conformity. A form used as a specification supports two incompatible readings of a defective occurrence. Under membership, a unit built to a part number is an occurrence of it whatever its condition, and the form's stated properties are claims that some occurrences violate. Under conformity, an out-of-tolerance unit is simply not an occurrence of that form at all. Warranty scope, recall scope, and quality statistics each depend on which reading is in force, and organisations routinely count under one reading while arguing under the other.

T6 — Open populations and retro-typing. A form may have no occurrences yet, and its population is generally open, so every claim made at the upper level is defeasible by an occurrence not yet produced. The reverse move is just as common: a novel occurrence is recognised as the first of its kind, a form is created behind it, and earlier occurrences are then re-read as belonging to it. Both make upper-level claims quietly time-indexed in a way the tidy one-over-many picture hides, and both invalidate counts computed before the re-typing.

Structural–Framed Character¶

Type Token Distinction sits at the structural end of the structural–framed spectrum, with an aggregate of 0.0 and all five diagnostics at zero. What travels is a two-level relation: one repeatable form with zero, one, or many numerically distinct occurrences, a membership or realization criterion linking them, and two levels of predication — properties shared across occurrences attach to the type, while location, history, state and identity attach to a token.

Vocabulary travel is the diagnostic doing most of the work, and it reads 0.0. The entry's claim is that words and inscriptions, scores and performances, software classes and objects, designs and manufactured units, diseases and cases preserve the distinction without translation — the same two levels, not local analogues that must be mapped onto one another.

Evaluative weight reads zero: the two levels rank nothing; a token is no lesser thing than its type. Institutional origin reads zero as well — the entry declines the metaphysical commitments that universal–particular would add, and treats class–instance as a formal-system specialization rather than a source. Human-practice-bound is zero: diseases and their cases, or designs and manufactured units, hold the relation with no one attending to it. Import-vs-recognize is recognition — one identifies the repeatable form, its occurrences, and the criterion of membership already in place.

The grade means the distinction applies directly wherever those roles are found, and its practical value is routing: claims and operations go to the level whose identity they affect, since changing one token need not change the type or its siblings.

Substrate Independence¶

Type–Token Distinction is about as substrate-independent as a prime can be — composite 5 / 5 on the substrate-independence scale. What travels is a two-level membership relation fixed by counting and predication alone: a repeatable form stands over numerically distinct occurrences under a stated criterion of sameness, each predicate is well formed at exactly one level, and no occurrence depletes the form it belongs to. Vocabulary items and their inscriptions, a score and its performances, a class and its objects, a design and the units built to it, a disease and its cases, a message and its transmissions: each pair is the same relation, unrenamed. The levels also re-enter, any form serving as an occurrence of a coarser one, so abstraction, reach and demonstrated use converge.

Composite substrate independence — 5 / 5
Domain breadth — 5 / 5
Structural abstraction — 5 / 5
Transfer evidence — 4 / 5

Relationships to Other Abstractions¶

Current abstraction Type–Token Distinction Prime

Parents (1) — more general patterns this builds on

Type–Token Distinction presupposes Abstraction Prime

Recognizing a repeatable type presupposes abstracting away token-specific location, time, state, and history while retaining the structure shared by its occurrences.

Children (2) — more specific cases that build on this

Abstract Work Prime is a kind of Type–Token Distinction

Abstract Work is the enriched work-and-carrier species of the bare type-and-token split, adding a content identity criterion, attribution, and lineage.
Item (Copy) Domain-specific is a decomposition of Type–Token Distinction

Removing the child’s frame leaves the reusable structure named by Type Token Distinction.

Hierarchy path (1) — routes to 1 parentless root

Type–Token Distinction → Abstraction

Neighborhood in Abstraction Space¶

Type–Token Distinction sits in a moderately populated region (56^th percentile for distinctiveness): it has near-neighbors but no dense thicket of synonyms.

Family — Equivalence, Inversion & Formal Structure (14 primes)

Nearest neighbors

Computed from structural-signature embeddings · 2026-09-10

Not to Be Confused With¶

The type–token distinction must be separated from Abstraction, which it presupposes without reducing to. Abstraction is an operation: selecting some structure and discarding the rest. It is what produces and maintains the upper level here, since a repeatable form is what remains once position, time, material, and history are set aside. But abstraction can terminate in a model, an interface, or a summary with no occurrence layer, and nothing in it requires that its product be instantiable. This distinction is not an operation but a standing two-level structure with a membership criterion, and its distinctive content is the split in predication that abstraction alone does not supply. One abstracts in order to have a repeatable form; one does not thereby have occurrences of it.

It is not Template Instantiation, though the two are easy to conflate because both set one repeatable thing over many derived ones. A template is a generative pattern with open slots: it is defined by what must be supplied to it, and instantiating it is an operation that binds payloads into those slots and yields something the template alone did not determine. A type is a category its tokens belong to, not a frame with holes to fill; there is nothing to bind, and a token is not the output of applying anything. The tests come apart cleanly. Two tokens of a type may be indistinguishable, whereas two instantiations of a template differ precisely by their bindings. A template can fail slot-fit and can drift as a frame; a type can only be satisfied or not by a candidate occurrence. And an occurrence can exist without ever having been produced from its form at all — a naturally arising case of a disease is a case of it, though nothing was filled in to make it.

Nor is it an Equivalence Relation, though it consumes one. An equivalence relation partitions a set by a reflexive, symmetric, transitive relation, and the classes it yields are sets of the very elements partitioned. That is the machinery behind the sameness criterion, and an upper level can be recovered as a quotient. What the relation does not supply is the asymmetry that makes the distinction useful. An equivalence class is an aggregate of its members and changes as they change; a repeatable form is not a collection of its occurrences, survives having none, and gains no properties when another occurrence appears. Forms are also routinely identified before their classes can be exhibited — a specification names one before any unit exists — which no quotient construction can do.

The distinction is not Classification. Classification assigns entities to categories under rules, and it is entirely possible to classify with no two-level structure present: sorting unique objects into bins yields categories whose members are not occurrences of them in any sense. What classification lacks is the split in predication. A bin does not have the properties its contents have, and no one says of a category that it is spelled with three letters or rated for a given duty. Here the upper level is itself a bearer of the shared properties, which is why it supports routing operations by level — something sorting alone never licenses.

It is not Abstract Work, which is a strengthening of this structure for one particular case. Abstract Work takes a content identity and adds an explicit same-work criterion, attribution, and a lineage among carriers, so that questions about translations, editions, adaptations, and forks get determinate answers. The relation here carries none of that: it needs a sameness criterion but takes no position on authorship, on which occurrence came first, or on how far an occurrence may deviate before it belongs elsewhere. Every abstract work sits inside a two-level structure of this kind; most such structures — a part number, a phoneme, a currency denomination — contain no work identity to preserve.

Finally, it should not be run together with Criteria of Individuation, which supplies what this distinction consumes. Individuation criteria fix what counts as one entity: when parts compose a whole, when two presentations are the same thing, and which kind supplies persistence over time. Those criteria make the lower level countable at all, and the sameness relation fixing the upper level is drawn from the same family. But individuation is settled for a domain independently of whether anything in it repeats: a domain of wholly unrepeatable particulars is fully individuated with no upper level at all. Individuation settles how many things there are; this distinction settles which of two questions "how many" was asking.

Solution Archetypes¶

No catalogued solution archetypes reference this prime yet.

References¶

[1] Peirce, Charles S. "Prolegomena to an Apology for Pragmaticism". The Monist 16(4), 1906, 492-546. Introduces the Type/Token terminology out of the counting question about a page carrying some twenty occurrences of the one English word 'the'. registry ↩

[2] Wetzel, Linda. Types and Tokens: On Abstract Objects. MIT Press, 2009. Shows that predicates attaching to a type need not attach to any token of it, and works through the ambiguity of counting questions such as how many words a sentence contains. registry ↩a ↩b ↩c

[3] Wetzel, Linda. "Types and Tokens". Stanford Encyclopedia of Philosophy, Winter 2016 edition. Distinguishes orthographic, phonological, morphological, lexical, grammatical, onomastic, lexicographical and statistical criteria for word types, on which the same expression counts as one type or several. registry ↩

[4] Object Management Group. Meta Object Facility (MOF) Core Specification, Version 2.5.1. OMG document formal/19-10-01, 2019. Section 7.3 states that the classifier-to-instance relation can be used to handle any number of layers and that MOF permits any number of meta-layers greater than or equal to two, with worked examples at two, three and four levels. registry ↩

[5] Liebesman, David. "Types and Tokens". Stanford Encyclopedia of Philosophy, 2026. Sets out the realist treatment of types as abstract objects alongside the nominalist rejection of them, treating the existence of types as a substantive rather than a settled question. registry ↩a ↩b

[6] Brysbaert, Marc, Michaël Stevens, Paweł Mandera, and Emmanuel Keuleers. "How Many Words Do We Know? Practical Estimates of Vocabulary Size Dependent on Word Definition, the Degree of Language Input and the Participant's Age." Frontiers in Psychology, vol. 7 (2016): 1116. Supports the dependence of a count on the individuation criterion in one measured case, vocabulary size: "the number depends on how a word is defined." It does not establish this as a general law about forms and their occurrences. registry ↩

[7] Miller, J. T. M. "Words, Species, and Kinds." Metaphysics, vol. 4, no. 1 (2021): 18–31. Supports only that a criterion of identity is what settles which occurrences fall under which form. Its project is "specifying the necessary and sufficient conditions on kind membership to provide the criterion of identity for words", so for this entry's paradigm case the criterion is something still to be supplied rather than something in hand; the paper says nothing about groupings that lack one. registry ↩

[8] Frege, Gottlob. The Foundations of Arithmetic. 1884, §§54 and 62. Supports only that an identity claim requires a criterion which decides "in all cases whether b is the same as a", and that counting requires a concept that delimits its objects definitely. The contrast drawn here with everyday loose typing, and the converse rule that a grouping without a statable criterion is merely loose, are this entry's own stipulations and are stated by none of the sources cited in this paragraph. registry ↩

[9] U.S. Department of Defense. "DFARS 252.211-7003, Item Unique Identification and Valuation". Defense Federal Acquisition Regulation Supplement, 2023. Requires serialization within the part, lot or batch number, so that the part number designates the design and the serial number distinguishes one item from all other like and unlike items. registry ↩

[10] Gamma, Erich, Richard Helm, Ralph Johnson, and John Vlissides. Design Patterns: Elements of Reusable Object-Oriented Software. Addison-Wesley, 1995. The Flyweight pattern stores context-independent intrinsic state once in the shared object and leaves context-dependent extrinsic state with each client, which is exactly the per-occurrence saving the passage describes. registry ↩

[11] Fowler, Martin. "Replace Type Code with Subclasses". Catalogue entry for Refactoring: Improving the Design of Existing Code, 2^nd edition, Addison-Wesley, 2019. Prescribes introducing a subclass level when a code marks a subset of instances that behaves differently, rather than absorbing the variation inside the original class; listed with the earlier name Extract Subclass as an alias. registry ↩

[12] Novick, Laura R., and Keith J. Holyoak. "Mathematical Problem Solving by Analogy." Journal of Experimental Psychology: Learning, Memory, and Cognition, vol. 17, no. 3 (1991): 398–415. Cited against the sentence it follows: "retrieval is an important component of transfer, and one that solvers have difficulty executing on their own", so structural similarity between two problems does not establish that someone competent in one will recognise the other unaided. It supports only the difficulty of unaided retrieval and does not study the two cases named here. The claim that the skeleton and the diagnostics move between substrates is this entry's own. registry ↩

[13] Jurafsky, Daniel, and James H. Martin. "Words and Tokens". Chapter 2 of Speech and Language Processing, 3^rd edition draft, 2026. States that whether a capitalized and an uncapitalized string count as the same word type depends on the task, so the type count over a fixed text moves with the criterion while the count of running words does not. registry ↩

[14] U.S. Federal Aviation Administration. "14 CFR Part 39, Airworthiness Directives". Code of Federal Regulations, eCFR current edition, 2026. Section 39.5 issues a directive only where an unsafe condition exists in the product and is likely to exist or develop in other products of the same type design, which is precisely the survival test separating a type-level from a unit-level fault. registry ↩