{ "model": { "rank": 8874, "code": "thing-q117879", "model_id": "vr.tr.floating-point", "name": "floating point", "purpose": "Let an agent explain floating-point representation and its formats, relay the IEEE 754 standard, rounding and error behaviour from computing references, describe reduced-precision formats used in machine learning, and distinguish floating point from fixed point, integers, decimal arithmetic and arbitrary precision.", "family": "Thing Registry", "category": "Cross-cutting context", "status": "research-draft", "kind": "thing", "plane": "XCT", "domain": "XCT.QLT", "industry": "", "version": "", "url": "/models/thing/q117879/", "tier": 2, "score": 49, "payload": { "layer": "wikidata", "aliases": [ "double-precision floating-point format", "single-precision floating-point format", "FP6", "block floating-point", "minifloat", "binary integer decimal", "decimal128 floating-point format", "decimal32 floating-point format", "decimal64 floating-point format", "decimal floating point", "extended precision", "normal floating-point number", "NVFP4" ], "aliasCount": 13, "merged": 13, "knownIn": 49, "facets": null, "markers": [], "lexicalClass": "", "senseRank": null, "alsoRegisteredAs": null, "source": { "dataset": "wikidata", "item": "Q117879", "url": "https://www.wikidata.org/wiki/Q117879", "license": "CC0 1.0" } }, "research": { "vercy": "1.0-draft", "publication": { "status": "research-draft", "adjudicationStatus": "unreviewed", "publishableCanonical": false, "generatedAt": "2026-09-13T12:48:10Z", "providers": [ "Claude" ], "breadth": "written by Claude from model knowledge without web access - no source was read, every claim is a lead to verify", "pass": 2, "wave": 4, "engine": "claude" }, "metaModel": { "id": "THING-Q117879", "registryId": "vr.tr.floating-point", "name": "floating point", "version": "0.2.0-wave.4", "entryKind": "thing", "family": "Thing Registry", "domain": [ "XCT.QLT" ], "status": "research-draft" }, "canonicalUrl": "https://ver.cy/models/thing/q117879/", "model": { "registry_id": "vr.tr.floating-point", "name": "floating point", "purpose": "Let an agent explain floating-point representation and its formats, relay the IEEE 754 standard, rounding and error behaviour from computing references, describe reduced-precision formats used in machine learning, and distinguish floating point from fixed point, integers, decimal arithmetic and arbitrary precision.", "definition": "A method of representing real numbers in computers with a significand, a base and an exponent so that the radix point can float, standardised by IEEE 754 in single-precision 32-bit and double-precision 64-bit binary formats and in decimal formats including binary integer decimal encoding, with smaller formats such as minifloats and FP6 used in machine learning and block floating-point sharing one exponent across several values; floating point trades exact representation for range and is the basis of most scientific and graphics computing.", "what_it_is_for": "Representing real numbers in computing.", "affordances": [ "explain representation and formats", "relay the standard and errors", "describe reduced-precision formats", "distinguish related representations" ], "distinguishing_features": [ "Floating radix point", "Standardised formats", "Rounding error", "Special values" ], "appearance": "Not a visible object; a binary encoding.", "visual_identification": [ "Sign, exponent and significand encoding", "Single precision, double precision, minifloat, FP6, block floating-point, binary integer decimal", "Fixed point has a fixed radix; integers have no fraction; arbitrary precision grows as needed" ], "physical_properties": [ { "quantity": "IEEE 754 first published", "typical_range": "1985", "unit": "year", "note": "revised 2008 and 2019" }, { "quantity": "single precision", "typical_range": "32", "unit": "bits", "note": "24-bit significand" }, { "quantity": "double precision", "typical_range": "64", "unit": "bits", "note": "53-bit significand" }, { "quantity": "decimal digits, double", "typical_range": "about 15-17", "unit": "count", "note": "" } ], "families_and_kinds": [ "binary formats: half, single, double and quadruple precision", "decimal formats with binary integer decimal and densely packed decimal encodings", "reduced-precision formats such as bfloat16, FP8, FP6 and minifloats", "block floating-point", "extended and non-IEEE formats" ], "related_models": [ { "relation": "is a kind of", "target": "computer numbering format", "why": "in registry terms" }, { "relation": "is a kind of", "target": "number data type", "why": "in registry terms" }, { "relation": "is standardised by", "target": "IEEE 754", "why": "the floating-point standard" }, { "relation": "is contrasted with", "target": "fixed-point arithmetic", "why": "with a fixed radix" } ], "identifiers": [], "standards_and_regulation": [ "IEEE 754-2019", "ISO/IEC 60559", "Language standards specifying floating-point behaviour" ], "failure_modes_and_hazards": [ "Rounding and cancellation errors", "Comparing floats for exact equality", "Overflow, underflow and NaN propagation" ], "in_scope": [], "out_of_scope": [], "characteristics": [] }, "sources": [], "structure": { "bundles": [ { "id": "understand", "name": "Understand", "description": "What floating point is.", "rationale": "Science.", "layers": [ { "id": "definition", "name": "Definition", "description": "Definition and encoding.", "findings": [ { "id": "definition-finding", "name": "Definition", "description": "Definition.", "questions": [ { "text": "What is floating-point representation, and how do sign, exponent and significand encode a number?", "kind": "definition" }, { "text": "Is the question about the concept, a format, numerical error or a programming language?", "kind": "boundary" } ] } ] }, { "id": "formats", "name": "Formats", "description": "Formats.", "findings": [ { "id": "formats-finding", "name": "Formats", "description": "Formats.", "questions": [ { "text": "What are single and double precision, decimal formats, minifloats, FP6 and block floating-point?", "kind": "definition" }, { "text": "Which entry fits the specific format?", "kind": "action" } ] } ] } ] }, { "id": "standard", "name": "Standard", "description": "The standard.", "rationale": "Regulation.", "layers": [ { "id": "ieee", "name": "IEEE 754", "description": "IEEE 754.", "findings": [ { "id": "ieee-finding", "name": "IEEE 754", "description": "IEEE 754.", "questions": [ { "text": "What does IEEE 754 specify about formats, rounding modes, exceptions and special values?", "kind": "provenance" }, { "text": "Which references are standard?", "kind": "provenance" } ] } ] }, { "id": "history", "name": "History", "description": "History.", "findings": [ { "id": "history-finding", "name": "History", "description": "History.", "questions": [ { "text": "How did floating point develop from early machines to the standard, with Kahan s role attributed?", "kind": "provenance" }, { "text": "Which sources are cited?", "kind": "provenance" } ] } ] } ] }, { "id": "use", "name": "Use", "description": "Numerical practice.", "rationale": "Practice.", "layers": [ { "id": "errors", "name": "Errors", "description": "Errors and pitfalls.", "findings": [ { "id": "errors-finding", "name": "Errors", "description": "Errors.", "questions": [ { "text": "How do rounding, cancellation and accumulation errors arise, and how are they managed?", "kind": "action" }, { "text": "Which entry fits numerical analysis?", "kind": "action" } ] } ] }, { "id": "ml", "name": "Machine learning", "description": "Reduced precision.", "findings": [ { "id": "ml-finding", "name": "Machine learning", "description": "Machine learning.", "questions": [ { "text": "Why do machine learning systems use bfloat16, FP8, FP6 and block floating-point?", "kind": "provenance" }, { "text": "Which entry fits mixed-precision training?", "kind": "action" } ] } ] } ] }, { "id": "context", "name": "Context", "description": "Hardware and alternatives.", "rationale": "Context.", "layers": [ { "id": "hardware", "name": "Hardware", "description": "Hardware.", "findings": [ { "id": "hardware-finding", "name": "Hardware", "description": "Hardware.", "questions": [ { "text": "How do processors and GPUs implement floating-point units?", "kind": "provenance" }, { "text": "Which entry fits floating-point unit?", "kind": "action" } ] } ] }, { "id": "alternatives", "name": "Alternatives", "description": "Alternatives.", "findings": [ { "id": "alternatives-finding", "name": "Alternatives", "description": "Alternatives.", "questions": [ { "text": "When are fixed point, decimal, rational or arbitrary precision arithmetic preferred?", "kind": "provenance" }, { "text": "Which entry fits arbitrary-precision arithmetic?", "kind": "action" } ] } ] } ] } ] }, "openQuestions": [ "Should IEEE 754, double precision and bfloat16 be separate primary entries?", "How should computing references be linked?", "The registry entry has merged aliases naming specific formats; should they be split off?" ], "statistics": { "bundles": 4, "layers": 8, "findings": 8, "questions": 16 } }, "draft": { "generator": "vr.draft.v3", "status": "draft-generated", "researched": false, "archetype": "abstract concept", "method": "Written from the archetype playbook - what this kind of thing needs beyond identity and provenance - and from the structure that recurred across 6,333 models already researched by two engines. Applied to this entry by rule. No source was read for this thing and no claim here is researched. This entry carries no facets of its own, so they were inferred from its domain - a guess about a whole domain applied to one thing.", "facetsInferred": true, "nextPass": "A researcher replaces this draft with a sourced specification. Treat every sentence below as a proposal to argue with.", "purpose": "Give an agent a durable, checkable way to recognise a floating point, record what state it is in, and decide what may be done with it.", "whatItIs": "Let an agent explain floating-point representation and its formats, relay the IEEE 754 standard, rounding and error behaviour from computing references, describe reduced-precision formats used in machine learning, and distinguish floating point from fixed point, integers, decimal arithmetic and arbitrary precision.", "characteristics": { "substance": "abstract", "origin": "conceptual", "agency": "inert" }, "whatYouCanDoWithIt": [ "observed and measured" ], "distinguishingFeatures": [ "Names folded into this entry, which a task may need to split apart again: double-precision floating-point format, single-precision floating-point format, FP6, block floating-point, minifloat, binary integer decimal, decimal128 floating-point format, decimal32 floating-point format, decimal64 floating-point format, decimal floating point, extended precision, normal floating-point number.", "13 finer distinctions are held as aliases rather than separate entries, because telling them apart needs a task that asks for it.", "Described in 49 Wikipedia languages, which is a measure of how widely the thing is known, not of how important it is." ], "openQuestionsForResearch": [ "Which of the bundles below does a real task actually need, and which are ceremony?", "What does this thing have that the facets do not capture at all?", "Which neighbouring kind is most often confused with a floating point, and on what evidence are they told apart?" ], "whatItIsMadeOf": "an abstraction with no physical instance", "physicalCharacter": [ "Does nothing on its own; everything it does, something else did to it.", "These come from the domain this entry sits in rather than from the entry itself, so treat them as a first guess about the whole domain applied to one thing." ], "whatCanBeDoneWithIt": [ "observe it, measure it, record its state" ], "howItIsRecognised": [ "Nothing to see. What is recognised is an instance of it, and which instances count is exactly what is argued about." ], "relatedModels": [ { "relation": "covers", "note": "Finer kinds folded into this entry because telling them apart needs a task that asks for it. Each is a model waiting to be split out when one does.", "targets": [ "double-precision floating-point format", "single-precision floating-point format", "FP6", "block floating-point", "minifloat", "binary integer decimal", "decimal128 floating-point format", "decimal32 floating-point format", "decimal64 floating-point format", "decimal floating point", "extended precision", "normal floating-point number" ] } ], "standing": "Described in 49 Wikipedia languages, which measures how widely it is written about rather than how important or how common it is. 13 finer distinctions are held inside this entry as names rather than as separate models.", "structure": { "bundles": [ { "id": "identity-and-classification", "name": "Identity, naming and classification", "description": "How an agent tells one floating point from another, and a floating point from things that resemble it.", "rationale": "Recognition comes before every other claim. Without stable identity nothing else in the model can be trusted to be about the same thing twice.", "layers": [ { "id": "naming-and-identifiers", "name": "Names and identifiers", "description": "The names this thing goes by and the identifiers that survive translation and time.", "findings": [ { "id": "preferred-name-and-aliases", "name": "Preferred name, aliases and local names", "description": "Which name to use, which names mean the same thing, and which merely sound similar.", "questions": [ { "id": "preferred-name-and-aliases-q01", "text": "What identifies and describes the name of a floating point, and in what units or vocabulary?", "kind": "definition", "answer_data": [ "identifiers", "types and classes", "values with units", "explicit unknowns" ] }, { "id": "preferred-name-and-aliases-q02", "text": "Who or what asserted this about the name of a floating point, by which method, and when was it true?", "kind": "provenance", "answer_data": [ "authority", "method", "evidence", "event time", "knowledge time" ] }, { "id": "preferred-name-and-aliases-q03", "text": "What may an agent decide or do once the name of a floating point is known, and what must it refuse?", "kind": "action", "answer_data": [ "permitted actions", "preconditions", "refusals", "escalation" ] } ] }, { "id": "stable-identifiers", "name": "Stable identifiers and external keys", "description": "Identifiers that keep pointing at this kind of thing across systems and languages.", "questions": [ { "id": "stable-identifiers-q01", "text": "What identifies and describes an identifier for a floating point, and in what units or vocabulary?", "kind": "definition", "answer_data": [ "identifiers", "types and classes", "values with units", "explicit unknowns" ] }, { "id": "stable-identifiers-q02", "text": "Who or what asserted this about an identifier for a floating point, by which method, and when was it true?", "kind": "provenance", "answer_data": [ "authority", "method", "evidence", "event time", "knowledge time" ] }, { "id": "stable-identifiers-q03", "text": "What may an agent decide or do once an identifier for a floating point is known, and what must it refuse?", "kind": "action", "answer_data": [ "permitted actions", "preconditions", "refusals", "escalation" ] } ] } ] }, { "id": "classification-and-granularity", "name": "Classification and granularity", "description": "Where a floating point sits among kinds, and how finely a task needs to cut it.", "findings": [ { "id": "kind-and-parents", "name": "Kind, parents and neighbouring kinds", "description": "The classes this thing belongs to and the ones it is next to.", "questions": [ { "id": "kind-and-parents-q01", "text": "What identifies and describes the kind of a floating point, and in what units or vocabulary?", "kind": "definition", "answer_data": [ "identifiers", "types and classes", "values with units", "explicit unknowns" ] }, { "id": "kind-and-parents-q02", "text": "Who or what asserted this about the kind of a floating point, by which method, and when was it true?", "kind": "provenance", "answer_data": [ "authority", "method", "evidence", "event time", "knowledge time" ] }, { "id": "kind-and-parents-q03", "text": "What may an agent decide or do once the kind of a floating point is known, and what must it refuse?", "kind": "action", "answer_data": [ "permitted actions", "preconditions", "refusals", "escalation" ] } ] }, { "id": "distinguishing-features", "name": "Distinguishing features", "description": "What separates a floating point from the things most often confused with it.", "questions": [ { "id": "distinguishing-features-q01", "text": "What identifies and describes what distinguishes a floating point, and in what units or vocabulary?", "kind": "definition", "answer_data": [ "identifiers", "types and classes", "values with units", "explicit unknowns" ] }, { "id": "distinguishing-features-q02", "text": "Who or what asserted this about what distinguishes a floating point, by which method, and when was it true?", "kind": "provenance", "answer_data": [ "authority", "method", "evidence", "event time", "knowledge time" ] }, { "id": "distinguishing-features-q03", "text": "What may an agent decide or do once what distinguishes a floating point is known, and what must it refuse?", "kind": "action", "answer_data": [ "permitted actions", "preconditions", "refusals", "escalation" ] } ] } ] } ] }, { "id": "state-and-lifecycle", "name": "State and lifecycle", "description": "The states a floating point passes through and the events that move it between them.", "rationale": "Most decisions about a thing depend on what state it is in now, which is a claim with a time on it, not a property.", "layers": [ { "id": "lifecycle-stages", "name": "Lifecycle stages", "description": "From coming into existence to ceasing to be one of these.", "findings": [ { "id": "stages-and-transitions", "name": "Stages and transitions", "description": "The stages worth naming and what moves a floating point between them.", "questions": [ { "id": "stages-and-transitions-q01", "text": "What identifies and describes the lifecycle of a floating point, and in what units or vocabulary?", "kind": "definition", "answer_data": [ "identifiers", "types and classes", "values with units", "explicit unknowns" ] }, { "id": "stages-and-transitions-q02", "text": "Who or what asserted this about the lifecycle of a floating point, by which method, and when was it true?", "kind": "provenance", "answer_data": [ "authority", "method", "evidence", "event time", "knowledge time" ] }, { "id": "stages-and-transitions-q03", "text": "What may an agent decide or do once the lifecycle of a floating point is known, and what must it refuse?", "kind": "action", "answer_data": [ "permitted actions", "preconditions", "refusals", "escalation" ] } ] } ] }, { "id": "observations-and-status", "name": "Observations and current status", "description": "What is observed about a floating point, how often and by whom.", "findings": [ { "id": "observation-record", "name": "Observation record", "description": "How an observation of a floating point is recorded so that it can be superseded rather than overwritten.", "questions": [ { "id": "observation-record-q01", "text": "What identifies and describes an observation of a floating point, and in what units or vocabulary?", "kind": "definition", "answer_data": [ "identifiers", "types and classes", "values with units", "explicit unknowns" ] }, { "id": "observation-record-q02", "text": "Who or what asserted this about an observation of a floating point, by which method, and when was it true?", "kind": "provenance", "answer_data": [ "authority", "method", "evidence", "event time", "knowledge time" ] }, { "id": "observation-record-q03", "text": "What may an agent decide or do once an observation of a floating point is known, and what must it refuse?", "kind": "action", "answer_data": [ "permitted actions", "preconditions", "refusals", "escalation" ] } ] } ] } ] }, { "id": "definitions-in-contest", "name": "Definitions and who holds them", "description": "What floating point is taken to mean, and by whom.", "rationale": "When a field disagrees about a concept, the disagreement is the content. A model that picks one definition silently destroys the information.", "layers": [ { "id": "competing-definitions", "name": "Competing definitions", "description": "The main readings and the traditions behind them.", "findings": [ { "id": "definition-map", "name": "Definitions and their holders", "description": "Each definition with the school or body that holds it.", "questions": [ { "id": "definition-map-q01", "text": "Which definitions of floating point are in use, and which tradition or body holds each?", "kind": "definition" }, { "id": "definition-map-q02", "text": "What turns on the difference between them in practice?", "kind": "boundary" } ] } ] }, { "id": "operationalisation", "name": "Operationalisation", "description": "How it is measured or applied when it has to be.", "findings": [ { "id": "operational-record", "name": "Measures and proxies", "description": "Instruments and indicators used to stand in for it.", "questions": [ { "id": "operational-record-q01", "text": "How is floating point operationalised or measured in practice, and by what instrument?", "kind": "measurement" }, { "id": "operational-record-q02", "text": "What does that operationalisation leave out, and when does that matter?", "kind": "boundary" } ] } ] } ] }, { "id": "instances-and-use", "name": "Instances, use and consequence", "description": "What counts as an instance of floating point and what follows from calling something that.", "rationale": "Applying a concept is an act with consequences, so a model must say what the label licenses and what it does not.", "layers": [ { "id": "instances", "name": "What counts as an instance", "description": "Clear cases, borderline cases and non-cases.", "findings": [ { "id": "instance-tests", "name": "Tests for an instance", "description": "What would settle whether something falls under it.", "questions": [ { "id": "instance-tests-q01", "text": "What would settle whether something is an instance of floating point?", "kind": "boundary" }, { "id": "instance-tests-q02", "text": "Which borderline cases are argued about, and on what grounds?", "kind": "definition" } ] } ] }, { "id": "consequence", "name": "Consequence of application", "description": "Rights, duties or decisions that follow from the label.", "findings": [ { "id": "consequence-record", "name": "What the label licenses", "description": "What an agent may do once something is classified this way.", "questions": [ { "id": "consequence-record-q01", "text": "What follows practically once something is treated as floating point?", "kind": "action" }, { "id": "consequence-record-q02", "text": "What must an agent not infer from the label alone?", "kind": "action" } ] } ] } ] }, { "id": "provenance-and-evidence", "name": "Provenance, evidence and time", "description": "Where every claim about a floating point came from and when it held.", "rationale": "A claim without a source and a time cannot be superseded, only overwritten, and an agent that overwrites loses the ability to explain itself.", "layers": [ { "id": "source-and-authority", "name": "Source and authority", "description": "Who said it, on what evidence, and how strongly.", "findings": [ { "id": "claim-provenance", "name": "Claim provenance and confidence", "description": "The authority behind each claim about a floating point and how confident it is.", "questions": [ { "id": "claim-provenance-q01", "text": "What identifies and describes a claim about a floating point, and in what units or vocabulary?", "kind": "definition", "answer_data": [ "identifiers", "types and classes", "values with units", "explicit unknowns" ] }, { "id": "claim-provenance-q02", "text": "Who or what asserted this about a claim about a floating point, by which method, and when was it true?", "kind": "provenance", "answer_data": [ "authority", "method", "evidence", "event time", "knowledge time" ] }, { "id": "claim-provenance-q03", "text": "What may an agent decide or do once a claim about a floating point is known, and what must it refuse?", "kind": "action", "answer_data": [ "permitted actions", "preconditions", "refusals", "escalation" ] } ] } ] }, { "id": "time-and-versions", "name": "Time, versions and supersession", "description": "When a claim was true, when it was learnt, and what replaced it.", "findings": [ { "id": "validity-and-supersession", "name": "Validity period and supersession", "description": "How an old claim about a floating point is retired without being erased.", "questions": [ { "id": "validity-and-supersession-q01", "text": "What identifies and describes the validity of a claim about a floating point, and in what units or vocabulary?", "kind": "definition", "answer_data": [ "identifiers", "types and classes", "values with units", "explicit unknowns" ] }, { "id": "validity-and-supersession-q02", "text": "Who or what asserted this about the validity of a claim about a floating point, by which method, and when was it true?", "kind": "provenance", "answer_data": [ "authority", "method", "evidence", "event time", "knowledge time" ] }, { "id": "validity-and-supersession-q03", "text": "What may an agent decide or do once the validity of a claim about a floating point is known, and what must it refuse?", "kind": "action", "answer_data": [ "permitted actions", "preconditions", "refusals", "escalation" ] } ] } ] } ] } ] }, "statistics": { "bundles": 5, "layers": 10, "findings": 12, "questions": 32 } } } }