{ "vercy": "1.0-draft", "publication": { "status": "research-draft", "adjudicationStatus": "unreviewed", "publishableCanonical": false, "generatedAt": "2026-09-07T13:44:01Z", "providers": [ "Codex", "Grok" ], "missingProviders": [], "pass": 2, "cost": { "grok": { "usd": 0.00530026, "turns": 1, "seconds": 16.3, "error": null }, "codex": { "seconds": 64.0, "error": "Reading additional input from stdin...\nOpenAI Codex v0.153.3\n--------\nworkdir: R:\\02_PROJECTS\\02_Meta_Models_Platforms\\Ver.cy\\current\\thing-registry-backlog\nmodel: gpt-6-astra\nprovider: openai\napproval: never\nsandbox: read-only\nreasoning effort: none\nreasoning summaries: none\nsession id: 01a07c1b-978d-7022-8ac1-b2a9e0634deb\n--------\nuser\nYou are drafting a Vercy meta-model for one registered thing. Answer as JSON only, no prose around it.\n\nThing: numeral system\nRegistry id: vr.tr.numeral-system\nPlane / domain: INF / INF.MED\nRegistry definition: (none recorded)\nNames folded into this entry: (no" } }, "enrichment": { "pass": 3, "engine": "claude", "producedAt": "2026-10-06T12:00:00Z", "ingestedAt": "2026-10-06T08:04:40+00:00", "fields": [ "agent_conduct", "ethics", "failure_modes_and_hazards", "owners", "standards_and_regulation" ] }, "gate": { "passed": true, "version": "1.0", "at": "2026-10-07T10:10:25+00:00", "evidence": [ "completeness 1.00", "sense: Wikidata description", "2 live sources", "review by codex: pass" ] } }, "metaModel": { "id": "THING-Q122653", "registryId": "vr.tr.numeral-system", "name": "numeral system", "version": "0.1.0-research.1", "entryKind": "thing", "family": "Thing Registry", "domain": [ "INF.MED" ], "status": "research-draft" }, "canonicalUrl": "https://ver.cy/models/thing/q122653/", "model": { "registry_id": "vr.tr.numeral-system", "name": "numeral system", "purpose": "Enable an AI agent to recognise a numeral system, assess whether a representation is valid and interpretable under its rules, and determine which reading, writing, comparison or conversion actions are justified.", "definition": "A numeral system is a conventional mapping from written or spoken numeral tokens to abstract numbers, together with the composition rules that determine how those tokens combine to denote a value.", "scope_statement": "This model owns the conventions that make signs and their arrangement representations of numbers, including their interpretation, representational limits, variants and conditions for reliable use.", "in_scope": [ "Numeral signs, their numerical roles and accepted variants", "Composition rules, including positional, additive, subtractive or combined mechanisms", "Interpretation of numerals and the range of numbers expressible", "Validity, ambiguity and preferred representation conventions", "Conditions for reading, generating, normalising and converting numerals" ], "out_of_scope": [ "Numbers and number structures independently of their representation", "General writing systems, typography and character encoding standards", "Natural-language number names and grammatical number", "Measurement units, currencies and quantity semantics", "Arithmetic algorithms and calculating devices beyond their numeral interpretation requirements" ], "distinguishing_features": [ "It supplies conventions connecting signs and arrangements to numbers; a number itself is independent of those conventions.", "It governs numerical representation; a font or character encoding alone does not determine numerical value.", "Its scope is expressing numbers; a mathematical notation may additionally express operations, relations and propositions.", "A string using numeral signs may instead be an identifier: preserving leading zeros or forbidding arithmetic can indicate identifier use rather than a numerical interpretation.", "A shared digit inventory does not establish a shared system: positional weights, grouping rules or value assignments must also agree." ], "characteristics": [ { "name": "Representation mechanism", "kind": "category", "unit_or_values": "Positional, additive, subtractive, multiplicative-additive, other documented mechanism, or combination", "why_it_matters": "Determines how component signs contribute to the represented number." }, { "name": "Radix or position-weight rule", "kind": "category", "unit_or_values": "Fixed radix with specified value; mixed radix with specified sequence; other weight rule; not applicable; unresolved", "why_it_matters": "Prevents an agent from assuming decimal interpretation or uniform position weights." }, { "name": "Sign inventory", "kind": "relation", "unit_or_values": "Links to recognised signs, value assignments, modifiers and accepted visual variants", "why_it_matters": "Supports recognition while distinguishing numerical roles from appearance." }, { "name": "Representable number domain", "kind": "category", "unit_or_values": "Explicitly described number classes, bounds and exclusions", "why_it_matters": "Establishes whether a requested number can be expressed under the selected conventions." }, { "name": "Zero convention", "kind": "category", "unit_or_values": "Zero numeral, positional placeholder, both, neither, or context-dependent", "why_it_matters": "Distinguishes representing zero from preserving an empty position." }, { "name": "Interpretation determinacy", "kind": "state", "unit_or_values": "Unique under selected conventions; context-dependent; ambiguous; unresolved", "why_it_matters": "Determines whether automatic reading is justified." }, { "name": "Representation preference", "kind": "state", "unit_or_values": "Unique normal form; multiple preferred forms; accepted forms without preference; unresolved", "why_it_matters": "Controls whether rewriting an equivalent numeral is warranted." }, { "name": "Applicable convention profile", "kind": "relation", "unit_or_values": "Links to documented historical, regional, disciplinary or implementation conventions", "why_it_matters": "Keeps an agent from combining incompatible rules." } ], "affordances": [ "Identify candidate numeral systems for a representation and request context when identification is ambiguous.", "Validate a numeral against a selected convention profile and explain rule violations.", "Interpret a numeral or generate a representation for a supported number.", "Compare numerical values while preserving distinctions between written forms.", "Normalise or convert a numeral when equivalence is established, recording any approximation or lost representational information." ], "agent_conduct": { "may": [ "Convert between numeral systems and explain their rules.", "Name the numeral system used when presenting numbers." ], "must_not": [ "Misread numbers between systems, such as treating a binary or hexadecimal string as decimal.", "Present one culture's numeral system as superior or primitive.", "Hide a change of numeral system in data that others rely on.", "Mix grouping conventions in a way that alters amounts." ], "requires_human": [ "Changing the numeral format in shared financial or medical records." ] }, "ethics": { "considerations": [ "Confusion between systems causes costly errors.", "Numeral systems are cultural heritage, not a ranking of peoples." ], "affected_parties": [ "Users of data", "Students", "Communities with their own numerals" ] }, "owners": { "steward": "Nobody owns them; they are held in common by the communities that use them.", "master_systems": [] }, "failure_modes_and_hazards": [ "Misreading base or digit grouping alters amounts and doses.", "Leading zeros or prefixes misinterpreted by software." ], "standards_and_regulation": [ "The Unicode Standard, Unicode Consortium, which encodes digits of many numeral systems." ], "what_it_is_for": [ "Numeral systems are used in writing, speech, education and computing to represent numerical values.", "Their rules allow people and agents to interpret, compare and transform representations across systems such as decimal, binary and Roman numerals.", "Correct interpretation requires knowing the symbol values and any positional or compositional conventions." ], "facets_not_applicable": { "recognition": "A numeral system is an abstract set of representation rules whose identity cannot be established from visual appearance alone." } }, "sources": [ { "id": "src-wp-numeral-system", "title": "Numeral system", "url": "https://en.wikipedia.org/wiki/Numeral_system", "what_it_supports": "Core definition distinguishing numeral systems from numbers, and the main practical kinds (positional, additive, hybrid, unary).", "url_status": "live" }, { "id": "wikidata", "title": "Wikidata item Q122653: numeral system", "url": "https://www.wikidata.org/wiki/Q122653", "url_status": "live", "what_it_supports": "identity and sense of the item", "checked_by": "wikidata-api" } ], "structure": { "bundles": [ { "id": "system-identity-and-variants", "name": "System identity and variants", "description": "Establishes which numerical representation conventions the agent is applying.", "rationale": "The same signs can receive different interpretations across systems and convention profiles.", "layers": [ { "id": "identifying-conventions", "name": "Identifying conventions", "description": "Records the features that distinguish this system from plausible alternatives.", "findings": [ { "id": "system-recognition", "name": "System recognition", "description": "Records diagnostic combinations of signs, composition rules and contextual evidence.", "questions": [ { "text": "Which combination of signs and composition rules identifies this numeral system rather than a look-alike?", "kind": "definition", "id": "system-recognition-q01" }, { "text": "What additional context is required when a numeral is valid in several systems?", "kind": "boundary", "id": "system-recognition-q02" } ] } ] }, { "id": "convention-profiles", "name": "Convention profiles", "description": "Separates documented variants without assuming they are independent registry things.", "findings": [ { "id": "profile-applicability", "name": "Profile applicability", "description": "Records where particular numerical conventions apply and the evidence supporting that selection.", "questions": [ { "text": "Which sources establish the rules of each historical, regional or specialised profile?", "kind": "provenance", "id": "profile-applicability-q01" }, { "text": "Which differences change numerical interpretation, and which merely change the written appearance?", "kind": "boundary", "id": "profile-applicability-q02" } ] } ] } ] }, { "id": "signs-and-composition", "name": "Signs and composition", "description": "Captures the elements of numerals and the rules for combining them.", "rationale": "Recognising individual symbols is insufficient to determine whether their arrangement forms a numeral.", "layers": [ { "id": "numerical-signs", "name": "Numerical signs", "description": "Distinguishes value-bearing signs, placeholders, modifiers and separators.", "findings": [ { "id": "sign-roles", "name": "Sign roles", "description": "Records each recognised sign's contribution and its dependence on surrounding signs.", "questions": [ { "text": "Which signs carry values, mark empty positions, modify other signs or separate numeral components?", "kind": "definition", "id": "sign-roles-q01" }, { "text": "Which visually similar or alternate signs may be treated as equivalent under this profile?", "kind": "boundary", "id": "sign-roles-q02" } ] } ] }, { "id": "assembly-rules", "name": "Assembly rules", "description": "Records how order, repetition, grouping and spatial arrangement construct a numeral.", "findings": [ { "id": "numeral-formation", "name": "Numeral formation", "description": "Makes permitted combinations and structurally meaningful layout explicit.", "questions": [ { "text": "What ordering, repetition, grouping and spatial rules determine whether signs form an admissible numeral?", "kind": "definition", "id": "numeral-formation-q01" }, { "text": "Which changes to spacing, orientation or layout preserve a numeral, and which change or destroy its interpretation?", "kind": "boundary", "id": "numeral-formation-q02" } ] } ] } ] }, { "id": "value-and-expressibility", "name": "Value and expressibility", "description": "Connects admissible numerals to numbers and establishes representation limits.", "rationale": "An agent must know both how a numeral obtains its value and whether a requested value is expressible.", "layers": [ { "id": "evaluation-rules", "name": "Evaluation rules", "description": "Records how signs, positions and modifiers jointly determine numerical value.", "findings": [ { "id": "value-assignment", "name": "Value assignment", "description": "Specifies the applicable interpretation mechanism without assuming a positional system.", "questions": [ { "text": "How do sign values combine through positional weights, addition, subtraction, multiplication or other documented rules?", "kind": "definition", "id": "value-assignment-q01" }, { "text": "If position contributes value, what radix or weight sequence applies and how is the reference position established?", "kind": "definition", "id": "value-assignment-q02" } ] } ] }, { "id": "representation-domain", "name": "Representation domain", "description": "Records which numbers can be expressed and which extensions are required.", "findings": [ { "id": "expressibility-limits", "name": "Expressibility limits", "description": "Distinguishes core capabilities from optional conventions for zero, signs, fractions and extended forms.", "questions": [ { "text": "Can the selected profile express zero, negative numbers and non-integers, and which rules or extensions enable each?", "kind": "boundary", "id": "expressibility-limits-q01" }, { "text": "Which values have exact finite representations, and what bounds or non-finite representation conventions apply?", "kind": "boundary", "id": "expressibility-limits-q02" } ] } ] } ] }, { "id": "validity-and-equivalence", "name": "Validity and equivalence", "description": "Supports judgments about admissibility, ambiguity and alternative forms of the same number.", "rationale": "Readable, valid and preferred numerals need not be the same set.", "layers": [ { "id": "interpretation-status", "name": "Interpretation status", "description": "Separates rule compliance from an agent's ability to infer an intended value.", "findings": [ { "id": "validity-and-ambiguity", "name": "Validity and ambiguity", "description": "Records how to assess malformed, incomplete or multiply interpretable representations.", "questions": [ { "text": "Which rule violations make a numeral invalid even when its intended value appears recoverable?", "kind": "boundary", "id": "validity-and-ambiguity-q01" }, { "text": "When a representation is incomplete or admits multiple readings, what evidence must an agent obtain before assigning a value?", "kind": "action", "id": "validity-and-ambiguity-q02" } ] } ] }, { "id": "equivalent-forms", "name": "Equivalent forms", "description": "Records value equivalence and any documented preference among alternate numerals.", "findings": [ { "id": "normalisation-permission", "name": "Normalisation permission", "description": "Determines when a numeral can be rewritten while preserving its value and relevant source information.", "questions": [ { "text": "Which distinct admissible numerals represent the same number, and is a preferred form documented?", "kind": "definition", "id": "normalisation-permission-q01" }, { "text": "When may an agent normalise leading placeholders, repeated signs or alternate constructions, and what original-form information must it retain?", "kind": "action", "id": "normalisation-permission-q02" } ] } ] } ] }, { "id": "reading-writing-and-conversion", "name": "Reading, writing and conversion", "description": "Defines conditions for applying the system to concrete representations.", "rationale": "Successful numerical interpretation does not by itself justify rewriting a source or converting it to another system.", "layers": [ { "id": "contextual-use", "name": "Contextual use", "description": "Determines whether a sign sequence is being used numerically and whether an output is suitable for its destination.", "findings": [ { "id": "use-sensitive-actions", "name": "Use-sensitive actions", "description": "Records prerequisites for reading and generating numerals in their actual context.", "questions": [ { "text": "What evidence distinguishes a numeral expressing a number from the same signs used as a code, label or identifier?", "kind": "boundary", "id": "use-sensitive-actions-q01" }, { "text": "Before generating a numeral, which convention profile, representable domain and required layout must the agent establish?", "kind": "action", "id": "use-sensitive-actions-q02" } ] } ] }, { "id": "cross-system-conversion", "name": "Cross-system conversion", "description": "Records whether another numeral system can preserve the interpreted value and relevant representation properties.", "findings": [ { "id": "conversion-fidelity", "name": "Conversion fidelity", "description": "Distinguishes exact value conversion from approximation and loss of written-form information.", "questions": [ { "text": "Can the target system express the interpreted number exactly under its permitted representation conventions?", "kind": "boundary", "id": "conversion-fidelity-q01" }, { "text": "If conversion requires approximation or discards meaningful source-form information, what authorisation and accompanying record are required?", "kind": "action", "id": "conversion-fidelity-q02" } ] } ] } ] }, { "id": "evidence-and-external-alignment", "name": "Evidence and external alignment", "description": "What the world already says about this thing, gathered so the model can be checked against it.", "rationale": "A model that cannot be lined up against existing standards, identifiers and practice cannot be adopted by anyone who already uses them.", "layers": [ { "id": "reported-evidence", "name": "Reported evidence", "description": "Findings from the breadth pass, kept separate from the structural claims.", "findings": [ { "id": "evidence-kinds", "name": "Kinds and varieties", "description": "Reported by the breadth pass; each item needs checking against its source before it becomes normative.", "evidence": [ "positional (place-value) systems", "additive (sign-value) systems", "hybrid / multiplicative-additive systems", "unary / tally systems", "bijective numeration", "signed-digit / balanced systems", "factoradic and mixed-radix systems", "spoken / linguistic numeral systems" ], "questions": [ { "id": "evidence-kinds-q01", "text": "Which of these kinds and varieties hold for the sense of numeral system this model covers, and on what evidence?", "kind": "provenance" } ] } ] } ] } ] }, "openQuestions": [ "With no registry definition recorded, does this entry include spoken, signed and tactile numeral systems, or only written numerical notation?", "Which authoritative sources should establish the representation mechanisms and convention profiles covered by the model?", "Where should the boundary fall between a numeral system's core rules and extensions for fractions, exponents, repeating forms or special values?", "How should the model distinguish a variant of one numeral system from a separate system while respecting registry granularity?", "Which documented communities of use recognise preferred forms, tolerate irregular numerals or require preservation of original notation?" ], "statistics": { "bundles": 6, "layers": 11, "findings": 11, "questions": 21 } }