{ "vercy": "1.0-draft", "publication": { "status": "research-draft", "adjudicationStatus": "unreviewed", "publishableCanonical": false, "generatedAt": "2026-09-12T08:30:25Z", "providers": [ "Codex" ], "breadth": "recalled by Codex without web access - no source was read", "missingProviders": [], "pass": 2, "cost": { "grok": { "seconds": 16.6, "error": "Reading additional input from stdin...\nOpenAI Codex v0.153.4\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: 01a094bc-6529-7032-b5ef-5df33483dbdf\n--------\nuser\nDescribe what is already known about one registered thing. Answer as JSON only, no prose around it.\n\nThing: center\nSense to describe: (none recorded)\nDomain code: XCT.QTY\nAlso known as: (none)\n\n\nContext for this batch of 1001 things:\n# Batch 043: 1001 register", "usd": 0.0, "recall": true }, "codex": { "seconds": 56.4, "error": "Reading additional input from stdin...\nOpenAI Codex v0.153.4\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: 01a094bc-652e-7fb2-8489-cabb9ebc19fc\n--------\nuser\nYou are drafting a Vercy meta-model for one registered thing. Answer as JSON only, no prose around it.\n\nThing: center\nRegistry id: vr.tr.center\nPlane / domain: XCT / XCT.QTY\nRegistry definition: (none recorded)\nNames folded into this entry: (none)\n\n\nContext fo" } }, "enrichment": { "pass": 3, "engine": "claude", "producedAt": "2026-10-06T11:00:00Z", "ingestedAt": "2026-10-06T08:08:35+00:00", "fields": [ "agent_conduct", "ethics", "failure_modes_and_hazards", "owners", "visual_identification" ] } }, "metaModel": { "id": "THING-Q191169", "registryId": "vr.tr.center", "name": "center", "version": "0.1.0-research.1", "entryKind": "thing", "family": "Thing Registry", "domain": [ "XCT.QTY" ], "status": "research-draft" }, "canonicalUrl": "https://ver.cy/models/thing/q191169/", "model": { "registry_id": "vr.tr.center", "name": "center", "purpose": "Enable an agent to identify, determine and use a center relative to a specified object, space and centering rule while preserving ambiguity and uncertainty.", "definition": "In geometry and quantitative modelling, a center is a point designated as central to an object or distribution by a specified criterion, such as symmetry, balance, or distance, and need not exist or be unique.", "scope_statement": "This model owns center as an abstract positional or structural relation, provisionally interpreting XCT / XCT.QTY as mathematical or quantitative context; it does not assume that every object has one unique center.", "in_scope": [ "The object, region, distribution or structure whose center is sought", "The definition of centrality and conditions under which it applies", "A center expressed as a point, element, set or explicitly unresolved result", "Dependence on geometry, distance, weighting and reference frame", "Existence, uniqueness, uncertainty and permitted uses of the result" ], "out_of_scope": [ "Institutions, facilities or settlements named a center, including immigration detention centers", "Units of measurement and the quantities they measure", "Complete models of the objects or distributions being centered", "General ranking or network centrality scores without a specified center-selection rule", "Specialized algebraic centers pending confirmation of the registry sense" ], "distinguishing_features": [ "A center must be attributable to a specified referent and centering rule; a position alone is insufficient.", "A center is not a measurement unit: coordinates may use units, but center itself supplies no unit definition.", "Midpoint, centroid, center of mass and circumcenter are interchangeable only when their defining conditions make them coincide.", "A center need not belong to the object being centered; membership must be checked separately.", "The word center in a facility name does not establish the abstract centering relation modeled here." ], "characteristics": [ { "name": "Centered referent", "kind": "relation", "unit_or_values": "Identified segment, figure, region, distribution, point set or other explicitly supported structure", "why_it_matters": "Determines what the center belongs to and which inputs define it." }, { "name": "Centering rule", "kind": "category", "unit_or_values": "Midpoint, centroid, center of mass, circumcenter, incenter, symmetry center, optimization-defined center or another explicit definition", "why_it_matters": "Different rules can produce different centers for the same referent." }, { "name": "Ambient space and distance", "kind": "relation", "unit_or_values": "Specified space, dimensionality and metric where applicable", "why_it_matters": "Distance and averaging operations depend on the space in which they are defined." }, { "name": "Weighting basis", "kind": "category", "unit_or_values": "Unweighted elements, length, area, volume, mass, probability or explicitly defined weights", "why_it_matters": "Identifies which contributions govern a weighted center." }, { "name": "Center representation", "kind": "measurement", "unit_or_values": "Coordinates with frame and axis units where applicable; otherwise an identified element or set", "why_it_matters": "Makes the result interpretable without forcing every center into Euclidean coordinates." }, { "name": "Existence and multiplicity", "kind": "state", "unit_or_values": "Not assessed, nonexistent under the rule, unique, multiple or unresolved", "why_it_matters": "Prevents an agent from presenting a single point when no unique result is justified." }, { "name": "Membership in referent", "kind": "state", "unit_or_values": "Interior, boundary, exterior, member, nonmember, not applicable or unknown", "why_it_matters": "Controls whether the center can serve as a location within the centered object." }, { "name": "Result uncertainty", "kind": "measurement", "unit_or_values": "Error bound or uncertainty region in declared units, with method; exact or unassessed where appropriate", "why_it_matters": "Separates a mathematically defined center from its estimated or numerically approximated location." } ], "affordances": [ "Select a centering rule appropriate to a stated task and referent.", "Compute or identify candidate centers when the rule's prerequisites are satisfied.", "Compare centers produced by different definitions without silently substituting one for another.", "Transform a center's representation between compatible reference frames.", "Check uniqueness, membership and uncertainty before using a center for alignment, placement or distance measurement.", "Reassess a center when the referent, weights or geometry change." ], "agent_conduct": { "may": [ "Compute a center by a stated criterion, such as centroid, circumcenter or median.", "State which criterion was used and whether the center lies inside the object." ], "must_not": [ "Report a center without saying which definition of center was used.", "Treat the center of a distribution as typical of every member, such as each person in a population.", "Confuse a geometric center with an institution or facility named a center." ], "requires_human": [ "Choosing which center to use when the result drives a decision about people, such as siting a service." ] }, "ethics": { "considerations": [ "Choice of center, mean or median, can make a group look better or worse off than it is." ], "affected_parties": [ "People described by statistics", "Users of analyses" ] }, "owners": { "steward": "Nobody owns the concept; the analyst answers for the criterion chosen.", "master_systems": [] }, "visual_identification": [ "Usually marked as a labelled point, often O or C, at a symmetry or balance position.", "Different centers of the same triangle appear as distinct points, which coincide only in special cases." ], "failure_modes_and_hazards": [ "A centroid can lie outside a non-convex shape, misleading placement decisions.", "Means pulled by outliers misrepresent the center of skewed data." ], "what_it_is_for": [ "In chess, the center comprises the four squares d4, d5, e4 and e5.", "Players and analytical systems use this region to discuss piece activity, pawn structure and control of central routes." ], "standards_and_regulation": [ "The Laws of Chess, issued by the International Chess Federation, define the board and algebraic square notation used to identify d4, d5, e4 and e5." ] }, "sources": [ { "id": "wikidata", "title": "Wikidata item Q191169: center", "url": "https://www.wikidata.org/wiki/Q191169", "url_status": "live", "what_it_supports": "identity and sense of the item", "checked_by": "wikidata-api" }, { "id": "wikipedia-de", "title": "Wikipedia (de): Zentrum (Schach)", "url": "https://de.wikipedia.org/wiki/Zentrum_%28Schach%29", "url_status": "live", "checked_by": "wikidata-api sitelink", "what_it_supports": "general description of the item" } ], "structure": { "bundles": [ { "id": "center-meaning", "name": "Center meaning", "description": "Establishes what is being centered and what center means in this instance.", "rationale": "The bare name does not distinguish several incompatible center definitions.", "layers": [ { "id": "centered-referent", "name": "Centered referent", "description": "Identifies the object and extent to which the centering relation applies.", "findings": [ { "id": "referent-extent", "name": "Referent extent", "description": "A center must be tied to a specified whole, subset or distribution.", "questions": [ { "text": "What exact object, subset or distribution is being centered?", "kind": "definition", "id": "referent-extent-q01" }, { "text": "Does the referent include its interior, only its boundary or only selected observations?", "kind": "boundary", "id": "referent-extent-q02" } ] } ] }, { "id": "centering-definition", "name": "Centering definition", "description": "Distinguishes the selected center concept from neighboring concepts.", "findings": [ { "id": "defining-rule", "name": "Defining rule", "description": "The result is governed by an explicit construction, symmetry condition or optimization criterion.", "questions": [ { "text": "Which mathematical rule defines this center?", "kind": "definition", "id": "defining-rule-q01" }, { "text": "What source or task requirement establishes that this is the intended rule?", "kind": "provenance", "id": "defining-rule-q02" } ] } ] } ] }, { "id": "geometry-and-contributions", "name": "Geometry and contributions", "description": "Records the space, distances and contributions that determine the center.", "rationale": "A center can change when the geometry or weighting changes even if the named referent stays the same.", "layers": [ { "id": "space-and-metric", "name": "Space and metric", "description": "Establishes the setting in which location, distance and admissible constructions are interpreted.", "findings": [ { "id": "geometric-assumptions", "name": "Geometric assumptions", "description": "The centering rule must be meaningful in the declared ambient space.", "questions": [ { "text": "In what space and dimension is the referent represented, and what distance rule applies?", "kind": "definition", "id": "geometric-assumptions-q01" }, { "text": "Would curvature, periodic coordinates or a change of metric alter this center?", "kind": "boundary", "id": "geometric-assumptions-q02" } ] } ] }, { "id": "weights-and-measure", "name": "Weights and measure", "description": "Identifies how parts of the referent contribute to the result.", "findings": [ { "id": "contribution-basis", "name": "Contribution basis", "description": "Boundary, area, volume, mass and sample weighting must not be treated as equivalent without justification.", "questions": [ { "text": "Which measure or weights govern the center, or does the rule require none?", "kind": "measurement", "id": "contribution-basis-q01" }, { "text": "Are those contributions observed, specified or assumed, and where is that basis documented?", "kind": "provenance", "id": "contribution-basis-q02" } ] } ] } ] }, { "id": "existence-and-determination", "name": "Existence and determination", "description": "Determines whether the rule yields a center and how the result is established.", "rationale": "An agent must distinguish a valid unique center from degeneracy, multiple candidates and computational failure.", "layers": [ { "id": "existence-and-uniqueness", "name": "Existence and uniqueness", "description": "Checks the prerequisites and possible multiplicity of the selected center.", "findings": [ { "id": "admissible-center-set", "name": "Admissible center set", "description": "The outcome may be one center, multiple centers or no center under the chosen definition.", "questions": [ { "text": "Does the referent satisfy the selected rule's existence conditions?", "kind": "boundary", "id": "admissible-center-set-q01" }, { "text": "Is the center unique, and if not, what identifies the full candidate set?", "kind": "definition", "id": "admissible-center-set-q02" } ] } ] }, { "id": "calculation-and-error", "name": "Calculation and error", "description": "Connects the reported center to a construction or calculation and its limitations.", "findings": [ { "id": "determination-evidence", "name": "Determination evidence", "description": "A reported location needs a reproducible basis and a distinction between input uncertainty and approximation error.", "questions": [ { "text": "Which construction, algorithm or observation produced the center from the stated inputs?", "kind": "provenance", "id": "determination-evidence-q01" }, { "text": "What uncertainty or numerical error applies to the result, and how was it assessed?", "kind": "measurement", "id": "determination-evidence-q02" } ] } ] } ] }, { "id": "representation-and-use", "name": "Representation and use", "description": "Makes a determined center usable for a particular operation.", "rationale": "A valid mathematical center can still be unsuitable for an operation requiring an interior, accessible or stable location.", "layers": [ { "id": "location-and-membership", "name": "Location and membership", "description": "Expresses the center and checks its relationship to the referent's extent.", "findings": [ { "id": "usable-location", "name": "Usable location", "description": "The result must carry sufficient positional context and must not imply membership merely by being called a center.", "questions": [ { "text": "How is the center represented, including coordinate frame and units where applicable?", "kind": "measurement", "id": "usable-location-q01" }, { "text": "Does the center lie inside, on or outside the referent, and does the intended operation permit that relationship?", "kind": "action", "id": "usable-location-q02" } ] } ] }, { "id": "change-and-substitution", "name": "Change and substitution", "description": "Controls reuse after changes and replacement by a differently defined center.", "findings": [ { "id": "reuse-conditions", "name": "Reuse conditions", "description": "Reusing a center requires checking whether its defining inputs and task requirements still hold.", "questions": [ { "text": "After a change to shape, membership, weights or frame, can this center be transformed directly or must it be recomputed?", "kind": "action", "id": "reuse-conditions-q01" }, { "text": "What evidence and tolerance justify substituting another type of center for this task?", "kind": "action", "id": "reuse-conditions-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-confidence-notes", "name": "Check these first", "description": "Recalled without web access and unsourced; every item is a lead to verify.", "evidence": [ "No sense is recorded; the geometric interpretation is provisional and should be checked against the originating registry record.", "Under this interpretation, center is neither a measurement unit nor a quantity with a universal dimension or conversion factor.", "A publication should specify the applicable geometry, weighting, and defining criterion before asserting existence, uniqueness, or location." ], "questions": [ { "id": "evidence-confidence-notes-q01", "text": "Which of these check these first hold for the sense of center this model covers, and on what evidence?", "kind": "provenance" } ] }, { "id": "evidence-kinds", "name": "Kinds and varieties", "description": "Recalled without web access and unsourced; every item is a lead to verify.", "evidence": [ "Center of symmetry", "Centroid", "Center of mass", "Circumcenter", "Incenter" ], "questions": [ { "id": "evidence-kinds-q01", "text": "Which of these kinds and varieties hold for the sense of center this model covers, and on what evidence?", "kind": "provenance" } ] }, { "id": "evidence-real-world-use", "name": "Real-world use", "description": "Recalled without web access and unsourced; every item is a lead to verify.", "evidence": [ "Locating reference points in geometric construction and computer-aided design", "Determining mass balance in mechanics", "Summarizing the spatial position of a collection of points", "Positioning inscribed or circumscribed circles in triangle geometry" ], "questions": [ { "id": "evidence-real-world-use-q01", "text": "Which of these real-world use hold for the sense of center this model covers, and on what evidence?", "kind": "provenance" } ] }, { "id": "evidence-failure-modes-and-hazards", "name": "Failure modes and hazards", "description": "Recalled without web access and unsourced; every item is a lead to verify.", "evidence": [ "Using a center without specifying the defining criterion", "Assuming that the centroid and center of mass coincide when density is nonuniform", "Assuming every object has a unique center of symmetry", "Assuming a center must lie within the object" ], "questions": [ { "id": "evidence-failure-modes-and-hazards-q01", "text": "Which of these failure modes and hazards hold for the sense of center this model covers, and on what evidence?", "kind": "provenance" } ] }, { "id": "evidence-regional-variation", "name": "Regional variation", "description": "Recalled without web access and unsourced; every item is a lead to verify.", "evidence": [ "\"Center\" is the usual American English spelling; \"centre\" is usual in British English." ], "questions": [ { "id": "evidence-regional-variation-q01", "text": "Which of these regional variation hold for the sense of center this model covers, and on what evidence?", "kind": "provenance" } ] }, { "id": "evidence-neighbours", "name": "Neighbouring kinds and how to tell them apart", "description": "Recalled without web access and unsourced; every item is a lead to verify.", "evidence": [ { "name": "midpoint", "difference": "A midpoint bisects a line segment; a center applies to a broader object or distribution under a specified criterion." }, { "name": "origin", "difference": "An origin is the chosen zero point of a coordinate system and need not coincide with an object's center." }, { "name": "central tendency", "difference": "Central tendency summarizes typical values in a distribution; a geometric center designates a spatial point." }, { "name": "immigration detention center", "difference": "This names a detention facility, using the institutional or building sense of center rather than the geometric sense." } ], "questions": [ { "id": "evidence-neighbours-q01", "text": "Which of these neighbouring kinds and how to tell them apart hold for the sense of center this model covers, and on what evidence?", "kind": "provenance" } ] } ] } ] } ] }, "openQuestions": [ "Does vr.tr.center denote a geometric center, a broader mathematical concept or another sense, given the missing registry definition?", "Which center definitions are intended to be covered by this entry, and which already have authoritative neighboring models?", "Should graph centers and specialized algebraic centers be included, linked as related concepts or excluded?", "Does XCT.QTY indicate a deliberate quantitative classification, or does the registry classification require review?", "Which authoritative references should establish the supported definitions and their existence, uniqueness and transformation conditions?" ], "statistics": { "bundles": 5, "layers": 9, "findings": 14, "questions": 22 } }