{ "vercy": "1.0-draft", "publication": { "status": "research-draft", "adjudicationStatus": "unreviewed", "publishableCanonical": false, "generatedAt": "2026-09-06T21:34:00Z", "providers": [ "Codex" ], "missingProviders": [ "Grok" ], "pass": 2, "cost": { "grok": { "usd": null, "turns": null, "seconds": 2.4, "error": "Error: Internal error: {\n \"message\": \"API error (status 402 Payment Required): Grok Build usage balance exhausted\",\n \"http_status\": 402\n}", "retried": true }, "codex": { "seconds": 49.2, "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: 01a078a3-be3d-7e03-af78-35b881c84160\n--------\nuser\nYou are drafting a Vercy meta-model for one registered thing. Answer as JSON only, no prose around it.\n\nThing: division\nRegistry id: vr.tr.division\nPlane / domain: XCT / XCT.REL\nRegistry definition: (none recorded)\nNames folded into this entry: (none)\n\nA Vercy" } }, "enrichment": { "pass": 3, "engine": "claude", "producedAt": "2026-10-06T11:00:00Z", "ingestedAt": "2026-10-06T08:02:03+00:00", "fields": [ "agent_conduct", "ethics", "failure_modes_and_hazards", "owners" ] }, "revisions": [ { "at": "2026-10-08T18:46:33+00:00", "engine": "codex", "fields": [ "agent_conduct", "definition", "distinguishing_features", "ethics", "failure_modes_and_hazards", "in_scope", "out_of_scope", "owners", "purpose", "scope_statement" ], "answering_review": "a3f1177c444d7b23da6cad0aa511c11eb65c00df8dea132f67955e8e9b8d3b1b" } ], "gate": { "passed": true, "version": "1.0", "at": "2026-10-08T18:54:35+00:00", "evidence": [ "completeness 1.00", "sense: Wikidata description", "2 live sources", "review by codex: pass" ] } }, "metaModel": { "id": "THING-Q1226939", "registryId": "vr.tr.division", "name": "division", "version": "0.1.0-research.1", "entryKind": "thing", "family": "Thing Registry", "domain": [ "XCT.REL" ], "status": "research-draft" }, "canonicalUrl": "https://ver.cy/models/thing/q1226939/", "model": { "registry_id": "vr.tr.division", "name": "division", "purpose": "Enable an AI agent to explain arithmetic division, interpret quotients and remainders, assess numerical results and recognise when division is undefined.", "definition": "Division is one of the four basic arithmetic operations and determines a quotient from a dividend and a nonzero divisor, expressing the number that, when multiplied by the divisor, gives the dividend; division of natural numbers may instead be expressed as a whole-number quotient with a remainder.", "scope_statement": "This model owns arithmetic division, including dividends, divisors, quotients, remainders, numerical domains and the conditions under which results are defined.", "in_scope": [ "The dividend, divisor and quotient define a division expression.", "Division is related to multiplication as an inverse operation when the divisor is nonzero.", "Natural-number division may produce a whole-number quotient and a remainder.", "The numerical domain determines which quotients can be represented within it.", "Exactness, approximation and rounding affect how a quotient is represented.", "Division by zero is undefined in ordinary arithmetic." ], "out_of_scope": [ "An organisational division is outside this arithmetic sense.", "Physical or conceptual partitioning without a numerical division relationship is outside this model.", "General classification systems and social groupings are outside this model.", "Resource allocation policies and ownership decisions are outside this model.", "Detailed computational implementations are outside this model." ], "distinguishing_features": [ "Division relates a dividend and a nonzero divisor to a quotient.", "Changing the order of dividend and divisor generally changes the result.", "An exact quotient multiplied by the divisor equals the dividend.", "For natural-number division with a positive divisor, the remainder is nonnegative and smaller than the divisor.", "Equal sharing and counting equal groups are interpretations of arithmetic division." ], "characteristics": [ { "name": "Divided whole", "kind": "relation", "unit_or_values": "Identified whole, including the version, extent or time interval to which the division applies", "why_it_matters": "A division cannot be assessed without knowing what its parts are intended to divide." }, { "name": "Dividing criterion", "kind": "category", "unit_or_values": "Explicit predicate, threshold, boundary, grouping rule or negotiated distinction", "why_it_matters": "Makes membership decisions explainable and exposes inconsistent application." }, { "name": "Resulting parts", "kind": "relation", "unit_or_values": "Identified parts linked to the whole through this division", "why_it_matters": "Distinguishes alternative divisions of the same whole." }, { "name": "Part count", "kind": "measurement", "unit_or_values": "Integer count of declared parts; unknown if unresolved", "why_it_matters": "Distinguishes binary divisions from divisions into multiple parts and detects changes in structure." }, { "name": "Coverage", "kind": "state", "unit_or_values": "Complete, partial, disputed or unknown; proportion only when a suitable measure exists", "why_it_matters": "Shows whether anything in the whole remains outside the declared parts." }, { "name": "Exclusivity", "kind": "state", "unit_or_values": "Mutually exclusive, overlapping, disputed or unknown", "why_it_matters": "Determines whether the division behaves as a strict partition and whether duplicate membership needs handling." }, { "name": "Boundary determination", "kind": "state", "unit_or_values": "Determinate, ambiguous, contested or unknown", "why_it_matters": "Identifies cases in which an agent cannot confidently assign membership." }, { "name": "Division status", "kind": "state", "unit_or_values": "Proposed, in use, superseded or withdrawn", "why_it_matters": "Prevents a proposed or obsolete division from being treated as currently applicable." } ], "affordances": [ "Determine which part contains a given element, location or interval under the stated criterion.", "Check for uncovered portions, overlapping parts and inconsistent boundary decisions.", "Compare alternative divisions of the same whole and explain where their memberships differ.", "Identify which downstream decisions depend on a particular division.", "Propose boundary revisions, refinement into smaller parts or consolidation of parts subject to stated authority.", "Suspend application where the whole, criterion or boundary is unresolved." ], "agent_conduct": { "may": [ "Explain arithmetic division and its relationship to multiplication.", "Calculate and report quotients and remainders for authorised tasks.", "State the numerical domain and any rounding assumptions." ], "must_not": [ "Present division by zero as a defined operation in ordinary arithmetic.", "Silently discard a remainder or present an approximation as exact.", "Treat a numerical quotient as sufficient justification for an allocation decision." ], "requires_human": [ "Approving consequential decisions that use division results to allocate rights or resources." ] }, "ethics": { "considerations": [ "Transparent assumptions and rounding help prevent misleading numerical claims.", "Arithmetic correctness alone does not establish the fairness of an allocation." ], "affected_parties": [ "Learners depend on accurate explanations of arithmetic.", "Users of calculated results depend on clear treatment of precision and remainders.", "People affected by numerical allocations depend on accountable decisions." ] }, "owners": { "steward": "Nobody owns the arithmetic operation; the mathematical community maintains its description.", "master_systems": [] }, "failure_modes_and_hazards": [ "Division by zero can produce undefined expressions or invalid computational results.", "Confusing the dividend and divisor changes the intended calculation.", "Confusing integer division with exact division can discard a remainder.", "Unstated rounding or numerical precision can misrepresent a quotient." ], "what_it_is_for": [ "Arithmetic division is used to calculate equal shares, determine how many groups fit into a quantity and express ratios or rates.", "It occurs in everyday calculations, mathematics, science and software.", "The number domain determines whether the result is expressed as an exact quotient, a quotient with a remainder or an approximation." ], "standards_and_regulation": [ "ISO 80000-2, issued by the International Organization for Standardization, specifies mathematical signs and symbols including notation for division." ], "facets_not_applicable": { "recognition": "Division is an abstract arithmetic operation rather than a visually identifiable physical thing." } }, "sources": [ { "id": "wikidata", "title": "Wikidata item Q1226939: division", "url": "https://www.wikidata.org/wiki/Q1226939", "url_status": "live", "what_it_supports": "identity and sense of the item", "checked_by": "wikidata-api" }, { "id": "wikipedia-en", "title": "Wikipedia: Division (mathematics)", "url": "https://en.wikipedia.org/wiki/Division_%28mathematics%29", "url_status": "live", "what_it_supports": "general description of the item", "checked_by": "wikidata-api sitelink" } ], "structure": { "bundles": [ { "id": "whole-and-parts", "name": "Whole and parts", "description": "Establishes what is divided and what counts as a result of this division.", "rationale": "Without a bounded whole and identifiable parts, an agent cannot distinguish division from an unrelated collection.", "layers": [ { "id": "whole-delimitation", "name": "Whole delimitation", "description": "Locates the extent within which the division makes claims.", "findings": [ { "id": "whole-reference", "name": "Whole reference", "description": "Record the whole and the extent or version used when assessing its parts.", "questions": [ { "text": "What whole is being divided, and what fixes its extent?", "kind": "definition", "id": "whole-reference-q01" }, { "text": "Which changes to the whole would require reassessing this division?", "kind": "boundary", "id": "whole-reference-q02" } ] } ] }, { "id": "resulting-parts", "name": "Resulting parts", "description": "Identifies the parts produced or recognised by the division.", "findings": [ { "id": "part-identification", "name": "Part identification", "description": "Record each part's identity and whether it already existed or was established through this division.", "questions": [ { "text": "Which distinguishable parts or sides constitute this division?", "kind": "definition", "id": "part-identification-q01" }, { "text": "What evidence establishes each part's relationship to the whole?", "kind": "provenance", "id": "part-identification-q02" } ] } ] } ] }, { "id": "criterion-and-boundaries", "name": "Criterion and boundaries", "description": "Explains how the division separates its parts and resolves membership.", "rationale": "The criterion distinguishes this division from other ways of dividing the same whole.", "layers": [ { "id": "dividing-rule", "name": "Dividing rule", "description": "Captures the distinction used to establish the parts.", "findings": [ { "id": "criterion-application", "name": "Criterion application", "description": "Record the rule and the observations or decisions needed to apply it.", "questions": [ { "text": "What predicate, threshold, boundary or agreement separates one part from another?", "kind": "definition", "id": "criterion-application-q01" }, { "text": "What evidence or decision established this criterion for this whole?", "kind": "provenance", "id": "criterion-application-q02" } ] } ] }, { "id": "boundary-cases", "name": "Boundary cases", "description": "Handles elements that lie on, cross or cannot be placed against a dividing boundary.", "findings": [ { "id": "membership-resolution", "name": "Membership resolution", "description": "Record boundary conventions, unresolved memberships and permitted ways to resolve them.", "questions": [ { "text": "How are items exactly on a threshold, spanning a boundary or lacking required evidence treated?", "kind": "boundary", "id": "membership-resolution-q01" }, { "text": "When membership is ambiguous or contested, may the agent assign it, retain multiple possibilities or defer to a named decision-maker?", "kind": "action", "id": "membership-resolution-q02" } ] } ] } ] }, { "id": "coverage-and-separation", "name": "Coverage and separation", "description": "Assesses whether the declared parts account for the whole and remain distinct.", "rationale": "Missing portions and overlapping membership can invalidate uses that require a complete, exclusive partition.", "layers": [ { "id": "whole-coverage", "name": "Whole coverage", "description": "Determines whether the parts exhaust the specified whole.", "findings": [ { "id": "remainder-accounting", "name": "Remainder accounting", "description": "Record uncovered portions and distinguish deliberate exclusions from unresolved or accidental gaps.", "questions": [ { "text": "Do the parts collectively cover the whole, and what evidence or measure supports that assessment?", "kind": "measurement", "id": "remainder-accounting-q01" }, { "text": "Is any remainder an explicit part, an allowed omission or evidence that the division is incomplete?", "kind": "boundary", "id": "remainder-accounting-q02" } ] } ] }, { "id": "part-exclusivity", "name": "Part exclusivity", "description": "Determines whether membership in more than one part is possible or permitted.", "findings": [ { "id": "overlap-assessment", "name": "Overlap assessment", "description": "Record intersections between parts and whether they comply with the intended meaning of this division.", "questions": [ { "text": "Which parts overlap, and how can the extent of their overlap be established?", "kind": "measurement", "id": "overlap-assessment-q01" }, { "text": "Does the intended use permit shared membership, or does it require mutually exclusive parts?", "kind": "boundary", "id": "overlap-assessment-q02" } ] } ] } ] }, { "id": "application-and-revision", "name": "Application and revision", "description": "Establishes when the division may guide decisions and how it may change.", "rationale": "An agent must distinguish recognising a boundary from having authority to impose or revise it.", "layers": [ { "id": "applicability", "name": "Applicability", "description": "Connects the division's status and justification to its permitted uses.", "findings": [ { "id": "use-conditions", "name": "Use conditions", "description": "Record whether the division is descriptive or prescriptive, its current status and the decisions for which it is accepted.", "questions": [ { "text": "Does this division describe observed separation, prescribe a separation or propose one?", "kind": "definition", "id": "use-conditions-q01" }, { "text": "For which decisions may the agent apply this division, and what acceptance or authority is required?", "kind": "action", "id": "use-conditions-q02" } ] } ] }, { "id": "revision-consequences", "name": "Revision consequences", "description": "Tracks how boundary changes, refinement or consolidation affect the division and its dependants.", "findings": [ { "id": "permitted-transformations", "name": "Permitted transformations", "description": "Record permitted changes and whether they revise this division or establish an alternative division of the same whole.", "questions": [ { "text": "Who may move boundaries, subdivide parts, consolidate parts or withdraw the division?", "kind": "action", "id": "permitted-transformations-q01" }, { "text": "Which membership assignments and dependent decisions must be reassessed after each permitted change?", "kind": "action", "id": "permitted-transformations-q02" } ] } ] } ] } ] }, "openQuestions": [ "Does vr.tr.division in XCT.REL mean division of a whole into parts, social separation, an organisational unit or another sense? No registry definition was supplied.", "Does the registry require divisions to be exhaustive and mutually exclusive, or does it admit partial and overlapping divisions?", "How should this entry be bounded against neighbouring concepts such as partition, decomposition, separation and distinction?", "Does the registered thing denote the dividing act, the resulting relationship or both, and what determines continuity across revisions?", "Which existing Vercy world model, if any, already owns this concept and should serve as its single source of truth?" ], "statistics": { "bundles": 4, "layers": 8, "findings": 8, "questions": 16 } }