{ "vercy": "1.0-draft", "publication": { "status": "research-draft", "adjudicationStatus": "unreviewed", "publishableCanonical": false, "generatedAt": "2026-09-12T11:02:35Z", "providers": [ "Codex" ], "breadth": "recalled by Codex without web access - no source was read", "missingProviders": [], "pass": 2, "cost": { "grok": { "seconds": 17.8, "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: 01a09547-561f-7d11-9aa8-95ec533acc35\n--------\nuser\nDescribe what is already known about one registered thing. Answer as JSON only, no prose around it.\n\nThing: loop\nSense to describe: (none recorded)\nDomain code: XCT.QLT\nAlso known as: (none)\n\n\nContext for this batch of 1001 things:\n# Batch 044: 1001 registered", "usd": 0.0, "recall": true }, "codex": { "seconds": 81.0, "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: 01a09547-5610-7570-a348-630ddea37ea0\n--------\nuser\nYou are drafting a Vercy meta-model for one registered thing. Answer as JSON only, no prose around it.\n\nThing: loop\nRegistry id: vr.tr.loop-q4558786\nPlane / domain: XCT / XCT.QLT\nRegistry definition: (none recorded)\nNames folded into this entry: (none)\n\n\nConte" } }, "enrichment": { "pass": 3, "engine": "claude", "producedAt": "2026-10-06T12:00:00Z", "ingestedAt": "2026-10-06T08:46:50+00:00", "fields": [ "agent_conduct", "ethics", "owners" ] }, "gate": { "passed": true, "version": "1.0", "at": "2026-10-07T10:10:31+00:00", "evidence": [ "completeness 1.00", "sense: Wikidata description", "2 live sources", "review by codex: pass" ] } }, "metaModel": { "id": "THING-Q4558786", "registryId": "vr.tr.loop-q4558786", "name": "loop", "version": "0.1.0-research.1", "entryKind": "thing", "family": "Thing Registry", "domain": [ "XCT.QLT" ], "status": "research-draft" }, "canonicalUrl": "https://ver.cy/models/thing/q4558786/", "model": { "registry_id": "vr.tr.loop-q4558786", "name": "loop", "purpose": "Enable an agent to recognise a topological loop, assess evidence about its continuity and deformation class, and choose valid transformations within its ambient space.", "definition": "In a geometric or topological sense, a loop is a continuous path whose endpoint coincides with its starting point.", "scope_statement": "This model owns loop as a continuous map γ:[0,1]→X with γ(0)=γ(1), matching vr.tr.loop-q4558786; it records the map, ambient space, basepoint convention and conditions governing comparison and transformation. Registry sense: [Wikidata Q4558786](https://www.wikidata.org/wiki/Q4558786).", "in_scope": [ "Continuous closed paths, including constant loops and paths with repeated points", "Ambient topology, excluded regions and endpoint identification", "Parameterisation, traversal direction and distinctions between a map and its image", "Based homotopy, null-homotopy and the boundary with free-loop conventions", "Loop concatenation, reversal and applicable invariants" ], "out_of_scope": [ "Programming loops, feedback loops and recurring processes", "Algebraic loops defined by a binary operation", "Graph self-edges and closed walks except through an explicit topological realisation", "Knots and links as embedded objects with isotopy constraints", "The full structure of fundamental groups and loop spaces", "Physical circuits, ropes and tracks independently of their topological abstraction" ], "distinguishing_features": [ "The candidate supplies a continuous path whose endpoints coincide in X; visual proximity alone does not establish closure.", "Self-intersections, retracing and constant maps are permitted, so being a simple closed curve is not required.", "Traversal data matters: two maps can have the same image while traversing it in different directions or different numbers of times.", "A fixed basepoint must be distinguished from a convention allowing that point to move during deformation.", "Closure does not establish null-homotopy; deformability must be assessed in the specified ambient space." ], "characteristics": [ { "name": "Ambient space", "kind": "relation", "unit_or_values": "Space X with topology, identifications and excluded subsets", "why_it_matters": "Determines continuity, endpoint equality and admissible deformations." }, { "name": "Loop representation", "kind": "category", "unit_or_values": "Formula; piecewise map; circle-domain map; certified polygonal path; sampled candidate", "why_it_matters": "Determines what can be verified directly and what requires reconstruction." }, { "name": "Closure and continuity evidence", "kind": "state", "unit_or_values": "Established; conditional; unverified; refuted, recorded separately", "why_it_matters": "Separates valid loops from incomplete or invalid candidates." }, { "name": "Basepoint convention", "kind": "category", "unit_or_values": "Distinguished fixed basepoint; basepoint forgotten for comparison; unspecified", "why_it_matters": "Controls which comparisons and compositions are meaningful." }, { "name": "Basepoint", "kind": "relation", "unit_or_values": "x0 = γ(0) = γ(1) in X", "why_it_matters": "Locates the common endpoint and permits compatibility checks." }, { "name": "Traversal structure", "kind": "category", "unit_or_values": "Constant; injective except at endpoints; repeated points; retracing; undetermined", "why_it_matters": "Prevents assumptions of simplicity or a single traversal." }, { "name": "Comparison relation", "kind": "category", "unit_or_values": "Map equality; image equality; specified reparameterisation; based homotopy; free homotopy", "why_it_matters": "Makes the meaning of two loops being equivalent explicit." }, { "name": "Null-homotopy status", "kind": "state", "unit_or_values": "Established; obstructed; unresolved, relative to X and the chosen convention", "why_it_matters": "Supports or rules out a proposed contraction." }, { "name": "Winding number", "kind": "measurement", "unit_or_values": "Integer, only with a suitable target, orientation and reference point", "why_it_matters": "Provides a conditional invariant without imposing a planar interpretation on every loop." } ], "affordances": [ "Validate a proposed loop against continuity, closure and ambient-space requirements.", "Compare loop representations using an explicitly selected equivalence relation.", "Concatenate loops after checking their common basepoint and traversal convention.", "Reverse or reparameterise a loop while recording the resulting map.", "Seek a contraction or another homotopy and verify its constraints.", "Compute applicable invariants and report what they establish or leave unresolved." ], "agent_conduct": { "may": [ "Explain loops in geometry and topology from mathematics sources.", "Compute or visualize loops and their properties for learners." ], "must_not": [ "Confuse a loop with a closed curve that is not continuous or with a cycle in a graph without saying so.", "Present incorrect proofs or definitions as established.", "Misattribute results in topology to the wrong mathematicians.", "Present homework answers as a student's own work for assessment." ], "requires_human": [ "Certifying a proof for publication or assessment." ] }, "ethics": { "considerations": [ "Accurate definitions matter in teaching and in fields that build on topology.", "Credit for mathematical discoveries matters to researchers." ], "affected_parties": [ "Students", "Mathematicians" ] }, "owners": { "steward": "Nobody owns the concept; it belongs to the mathematical commons.", "master_systems": [] }, "what_it_is_for": [ "Loops are studied in topology and geometry to describe continuous paths that return to their starting point.", "They are used to investigate holes, fundamental groups and whether paths can be continuously deformed within a specified space." ], "failure_modes_and_hazards": [ "Confusing a closed path with a simple closed curve can invalidate arguments because a loop may intersect itself.", "Assuming every loop can contract to a point can produce incorrect conclusions about the topology of its ambient space." ], "facets_not_applicable": { "interfaces": "No generally applicable official standard, law or classification governs a loop as a mathematical object.", "recognition": "A topological loop is an abstract mathematical object whose defining properties cannot be established by visual appearance alone." } }, "sources": [ { "id": "wikidata", "title": "Wikidata item Q4558786: loop", "url": "https://www.wikidata.org/wiki/Q4558786", "url_status": "live", "what_it_supports": "identity and sense of the item", "checked_by": "wikidata-api" }, { "id": "wikipedia-en", "title": "Wikipedia: Loop (topology)", "url": "https://en.wikipedia.org/wiki/Loop_%28topology%29", "url_status": "live", "what_it_supports": "general description of the item", "checked_by": "wikidata-api sitelink" } ], "structure": { "bundles": [ { "id": "loop-definition", "name": "Loop definition", "description": "Establish the mathematical sense and membership conditions.", "rationale": "The name is ambiguous, while a drawing of a closed shape does not specify a continuous map.", "layers": [ { "id": "defining-convention", "name": "Defining convention", "description": "Record the definition used by the relevant mathematical source or application.", "findings": [ { "id": "closed-path-convention", "name": "Closed path convention", "description": "Use continuity and coincident endpoints as the entry test; record whether a basepoint is distinguished. Reference: [Hatcher, Algebraic Topology, §1.1](https://pi.math.cornell.edu/~hatcher/AT/ATch1.pdf).", "questions": [ { "text": "Which source or application supplies the loop definition and basepoint convention?", "kind": "provenance", "id": "closed-path-convention-q01" }, { "text": "Is the object represented as an interval-domain map with equal endpoints or as a circle-domain map?", "kind": "definition", "id": "closed-path-convention-q02" } ] } ] }, { "id": "membership-evidence", "name": "Membership evidence", "description": "Check the particular candidate against the chosen definition.", "findings": [ { "id": "continuity-and-closure", "name": "Continuity and closure", "description": "Record separate evidence for continuity and endpoint equality.", "questions": [ { "text": "What establishes continuity, including at every piecewise join?", "kind": "definition", "id": "continuity-and-closure-q01" }, { "text": "Do the endpoints coincide in X itself, including any quotient identifications?", "kind": "boundary", "id": "continuity-and-closure-q02" }, { "text": "If the evidence consists of samples, what interpolation and error assumptions remain unverified?", "kind": "measurement", "id": "continuity-and-closure-q03" } ] } ] } ] }, { "id": "ambient-space-and-basepoint", "name": "Ambient space and basepoint", "description": "Specify where the loop lives and which point anchors it.", "rationale": "Loop properties and permissible operations depend on the target space and anchoring convention.", "layers": [ { "id": "target-space", "name": "Target space", "description": "Identify topology, identifications and obstacles relevant to the loop.", "findings": [ { "id": "ambient-constraints", "name": "Ambient constraints", "description": "Record the exact target rather than inferring it from a plot.", "questions": [ { "text": "What is X, and which topology or quotient construction defines it?", "kind": "definition", "id": "ambient-constraints-q01" }, { "text": "Which removed points, forbidden subsets or boundary restrictions constrain the loop and its deformations?", "kind": "boundary", "id": "ambient-constraints-q02" } ] } ] }, { "id": "anchoring", "name": "Anchoring", "description": "Specify the common endpoint and its role in subsequent operations.", "findings": [ { "id": "basepoint-commitment", "name": "Basepoint commitment", "description": "Record whether the selected basepoint must remain fixed.", "questions": [ { "text": "Which point is x0, and how is it identified in the representation of X?", "kind": "definition", "id": "basepoint-commitment-q01" }, { "text": "Must every intermediate loop retain x0 during the intended deformation?", "kind": "boundary", "id": "basepoint-commitment-q02" }, { "text": "If changing basepoints is required, which connecting path and transport convention will be used?", "kind": "action", "id": "basepoint-commitment-q03" } ] } ] } ] }, { "id": "representation-and-traversal", "name": "Representation and traversal", "description": "Preserve the distinction between a loop map, its parameterisation and its visible trace.", "rationale": "Image-only descriptions can erase reversal, repeated traversal and retracing.", "layers": [ { "id": "map-versus-image", "name": "Map versus image", "description": "Identify what the supplied representation retains.", "findings": [ { "id": "traversal-information", "name": "Traversal information", "description": "Record ordered traversal and the policy for treating reparameterisations.", "questions": [ { "text": "Does the input determine γ, or only the subset γ([0,1])?", "kind": "definition", "id": "traversal-information-q01" }, { "text": "Which direction, repeated traversals and pauses does the representation retain?", "kind": "measurement", "id": "traversal-information-q02" }, { "text": "Which parameter changes, if any, count as preserving the same represented object?", "kind": "boundary", "id": "traversal-information-q03" } ] } ] }, { "id": "regularity-and-simplicity", "name": "Regularity and simplicity", "description": "Separate optional geometric restrictions from loop membership.", "findings": [ { "id": "additional-curve-properties", "name": "Additional curve properties", "description": "Record constant behaviour, repeated points and any extra smoothness or embedding requirements.", "questions": [ { "text": "Is the loop constant, simple, self-intersecting or retracing, and what establishes that assessment?", "kind": "measurement", "id": "additional-curve-properties-q01" }, { "text": "Does the intended operation require differentiability, rectifiability or an embedding beyond continuity?", "kind": "boundary", "id": "additional-curve-properties-q02" } ] } ] } ] }, { "id": "deformation-and-classification", "name": "Deformation and classification", "description": "Assess loop equivalence and contraction with explicit constraints and evidence.", "rationale": "A proposed deformation needs more than visual resemblance, and an invariant may provide only partial information.", "layers": [ { "id": "homotopy-contract", "name": "Homotopy contract", "description": "Specify what a permitted deformation must preserve.", "findings": [ { "id": "homotopy-witness", "name": "Homotopy witness", "description": "Require a continuous family in X with the chosen endpoint constraints. Reference: [Hatcher, Algebraic Topology, §1.1](https://pi.math.cornell.edu/~hatcher/AT/ATch1.pdf).", "questions": [ { "text": "Is the requested comparison based homotopy, free homotopy or a stronger relation such as isotopy?", "kind": "definition", "id": "homotopy-witness-q01" }, { "text": "What explicit deformation or theorem establishes the claimed relation?", "kind": "provenance", "id": "homotopy-witness-q02" }, { "text": "Does the entire deformation remain in X and satisfy the selected anchoring and intersection constraints?", "kind": "boundary", "id": "homotopy-witness-q03" } ] } ] }, { "id": "obstructions-and-invariants", "name": "Obstructions and invariants", "description": "Track evidence supporting or obstructing contraction and comparison.", "findings": [ { "id": "classification-evidence", "name": "Classification evidence", "description": "Attach assumptions and evidential limits to each invariant or class assignment.", "questions": [ { "text": "Which invariant is defined for this X and loop, and what choices are required to compute it?", "kind": "measurement", "id": "classification-evidence-q01" }, { "text": "Does the result decide the proposed equivalence or supply only a necessary condition?", "kind": "boundary", "id": "classification-evidence-q02" }, { "text": "Is contraction established by a witness, ruled out by an obstruction or still unresolved?", "kind": "action", "id": "classification-evidence-q03" } ] } ] } ] }, { "id": "loop-operations", "name": "Loop operations", "description": "Determine which constructions are valid and what their results mean.", "rationale": "Operations on representative maps must be distinguished from algebraic operations on homotopy classes.", "layers": [ { "id": "composition-and-reversal", "name": "Composition and reversal", "description": "Check compatibility and traversal conventions before constructing another loop.", "findings": [ { "id": "operation-preconditions", "name": "Operation preconditions", "description": "Record operands, basepoint compatibility and the formula governing the constructed map.", "questions": [ { "text": "Do the loops to be concatenated share the required basepoint in the same X?", "kind": "boundary", "id": "operation-preconditions-q01" }, { "text": "Which factor is traversed first, and how is the parameter interval allocated?", "kind": "action", "id": "operation-preconditions-q02" }, { "text": "Is reversal being applied to the map, or is an inverse being asserted for its homotopy class?", "kind": "definition", "id": "operation-preconditions-q03" } ] } ] }, { "id": "transformation-validation", "name": "Transformation validation", "description": "Verify what survives a construction or change of representation.", "findings": [ { "id": "result-and-preservation", "name": "Result and preservation", "description": "Record the resulting loop and justify each claimed preservation property.", "questions": [ { "text": "After simplification or reparameterisation, what establishes continuity, closure and the claimed equivalence?", "kind": "action", "id": "result-and-preservation-q01" }, { "text": "If a continuous map X→Y transports the loop, what is its new basepoint and which class information may be lost?", "kind": "action", "id": "result-and-preservation-q02" }, { "text": "Are identity, inverse or associativity claims about literal maps or about equivalence classes?", "kind": "boundary", "id": "result-and-preservation-q03" } ] } ] } ] }, { "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 and topological interpretation used here is provisional.", "The registry's meaning of XCT.QLT should be checked before excluding computational, feedback, graph-theoretic, or algebraic senses.", "This is recalled knowledge, not source-verified research." ], "questions": [ { "id": "evidence-confidence-notes-q01", "text": "Which of these check these first hold for the sense of loop 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": [ "Simple loop, with no self-intersections apart from closure", "Self-intersecting loop", "Based loop, with a specified starting and ending point", "Free loop, without a fixed basepoint", "Contractible loop", "Noncontractible loop" ], "questions": [ { "id": "evidence-kinds-q01", "text": "Which of these kinds and varieties hold for the sense of loop 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": [ "Representing closed routes in geometric models", "Studying spaces through fundamental groups and homotopy", "Describing closed contours in computer graphics", "Defining paths for contour integration" ], "questions": [ { "id": "evidence-real-world-use-q01", "text": "Which of these real-world use hold for the sense of loop 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": [ "Assuming every loop is simple and therefore has no self-intersections", "Assuming every loop can be continuously contracted to a point within its ambient space", "Assuming every continuous loop has a finite, well-defined arc length", "Confusing a parameterized loop with its geometric image" ], "questions": [ { "id": "evidence-failure-modes-and-hazards-q01", "text": "Which of these failure modes and hazards hold for the sense of loop 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": "path", "difference": "A path need not have coincident starting and ending points; a loop does." }, { "name": "circle", "difference": "A Euclidean circle has constant distance from a center; a loop need not be circular." }, { "name": "simple closed curve", "difference": "A simple closed curve has no self-intersections; a general loop may intersect itself or retrace its path." }, { "name": "graph self-loop", "difference": "In graph theory, a self-loop is a single edge incident to the same vertex at both ends." }, { "name": "programming loop", "difference": "A programming loop is a control structure for repeated execution, rather than a continuous closed path." }, { "name": "algebraic loop", "difference": "In abstract algebra, a loop is a quasigroup with an identity element; closure of a path is not its defining property." } ], "questions": [ { "id": "evidence-neighbours-q01", "text": "Which of these neighbouring kinds and how to tell them apart hold for the sense of loop this model covers, and on what evidence?", "kind": "provenance" } ] } ] } ] } ] }, "openQuestions": [ "Does Vercy intend this entry to require a distinguished basepoint, given that the linked registry item distinguishes free loops while also treating closed curve as an equivalent name?", "Does an existing world-model publication already own topological loops or closed paths, requiring this entry to link to it?", "Which representation families must the model support first: symbolic maps, combinatorial realisations, geometric paths or sampled observations?", "What evidence standard should distinguish certified continuity and homotopy from numerical or visual indications?", "Which ambient-space families warrant specialised invariant extensions, without implying that winding number classifies arbitrary loops?" ], "statistics": { "bundles": 6, "layers": 11, "findings": 15, "questions": 32 } }