{ "model": { "rank": 4120, "code": "thing-q200227", "model_id": "vr.tr.negative-real-number", "name": "negative real number", "purpose": "Enable an agent to recognise a real number strictly below zero, establish its magnitude and ordering, and determine which mathematical operations preserve its value or remain defined.", "family": "Thing Registry", "category": "Cross-cutting context", "status": "research-draft", "kind": "thing", "plane": "XCT", "domain": "XCT.QLT", "industry": "", "version": "", "url": "/models/thing/q200227/", "tier": 2, "score": 78, "payload": { "layer": "wikidata", "aliases": [ "negative integer", "negative exponent" ], "aliasCount": 2, "merged": 2, "knownIn": 78, "facets": null, "markers": [], "lexicalClass": "", "senseRank": null, "alsoRegisteredAs": null, "source": { "dataset": "wikidata", "item": "Q200227", "url": "https://www.wikidata.org/wiki/Q200227", "license": "CC0 1.0" } }, "research": { "vercy": "1.0-draft", "publication": { "status": "research-draft", "adjudicationStatus": "unreviewed", "publishableCanonical": false, "generatedAt": "2026-09-09T19:30:54Z", "providers": [ "Codex" ], "breadth": "recalled by Codex without web access - no source was read", "missingProviders": [], "pass": 2, "cost": { "grok": { "seconds": 19.6, "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: 01a087a5-fea4-7540-b553-e47c233b2438\n--------\nuser\nDescribe what is already known about one registered thing. Answer as JSON only, no prose around it.\n\nThing: negative real number\nSense to describe: (none recorded)\nDomain code: XCT.QLT\nAlso known as: (none)\n\n\nContext for this batch of 695 things:\n# Batch 004: ", "usd": 0, "recall": true }, "codex": { "seconds": 56.9, "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: 01a087a5-fe95-7ed2-9c54-65d5b4558462\n--------\nuser\nYou are drafting a Vercy meta-model for one registered thing. Answer as JSON only, no prose around it.\n\nThing: negative real number\nRegistry id: vr.tr.negative-real-number\nPlane / domain: XCT / XCT.QLT\nRegistry definition: (none recorded)\nNames folded into thi" } } }, "metaModel": { "id": "THING-Q200227", "registryId": "vr.tr.negative-real-number", "name": "negative real number", "version": "0.1.0-research.1", "entryKind": "thing", "family": "Thing Registry", "domain": [ "XCT.QLT" ], "status": "research-draft" }, "canonicalUrl": "https://ver.cy/models/thing/q200227/", "model": { "registry_id": "vr.tr.negative-real-number", "name": "negative real number", "purpose": "Enable an agent to recognise a real number strictly below zero, establish its magnitude and ordering, and determine which mathematical operations preserve its value or remain defined.", "definition": "A negative real number is an element x of the ordered field of real numbers satisfying x < 0.", "scope_statement": "This model owns the properties and permitted mathematical treatment specific to an individual negative real number x < 0, specialising the broader real-number concept without duplicating its construction.", "in_scope": [ "Strict negativity within the standard order on the real numbers", "Magnitude, additive inverse and position relative to zero and other real numbers", "Exact and approximate representations of a negative real value", "Arithmetic sign rules and closure conditions involving negative real operands", "Domain restrictions for real-valued functions applied to negative arguments" ], "out_of_scope": [ "Construction and general completeness properties of the real-number system", "Zero, positive real numbers and the broader class of nonpositive real numbers", "Non-real complex numbers and choices of complex function branches", "Negative infinity as an extended-real element", "Physical units, debts, temperatures and other interpretations of signed quantities", "Machine signed-zero semantics and floating-point implementation details" ], "distinguishing_features": [ "Membership requires both x ∈ ℝ and x < 0; a minus sign in an expression alone does not establish membership.", "Zero fails the strict inequality, so a nonpositive value is not necessarily a negative real number.", "For a negative real number, |x| = -x > 0; magnitude alone cannot distinguish x from its positive additive inverse.", "Negative integers, negative noninteger rationals and negative irrationals all qualify; integrality and rationality are not defining requirements.", "Every negative real number is finite; negative infinity is excluded, and machine -0 denotes mathematical zero rather than a negative real value." ], "characteristics": [ { "name": "Real value", "kind": "measurement", "unit_or_values": "Dimensionless x ∈ (-∞, 0), expressed exactly or through a justified approximation", "why_it_matters": "Identifies the mathematical value to which comparisons and operations apply." }, { "name": "Negativity verification", "kind": "state", "unit_or_values": "Proved negative | unresolved from available information | disproved", "why_it_matters": "Distinguishes confirmed membership from a candidate whose displayed approximation or symbolic expression is insufficient." }, { "name": "Magnitude", "kind": "measurement", "unit_or_values": "|x| = -x ∈ (0, ∞), dimensionless", "why_it_matters": "Records distance from zero and prevents confusion between greater magnitude and greater numerical value." }, { "name": "Arithmetic subclass", "kind": "category", "unit_or_values": "Negative integer | negative noninteger rational | negative irrational | not established", "why_it_matters": "Supports exact representation choices and checks that require rationality or integrality." }, { "name": "Additive inverse", "kind": "relation", "unit_or_values": "Unique positive real y = -x with x + y = 0", "why_it_matters": "Connects the value to its positive counterpart without treating the two as interchangeable." }, { "name": "Certified enclosure", "kind": "measurement", "unit_or_values": "Interval I ⊆ ℝ containing x, with explicit endpoint inclusion and error guarantees", "why_it_matters": "An enclosure contained in (-∞, 0) certifies negativity; one containing zero may leave the sign unresolved." }, { "name": "Order relative to a comparator", "kind": "relation", "unit_or_values": "For specified real y: x < y | x = y | x > y | comparison unresolved", "why_it_matters": "Supports ranking and inequality reasoning, including reversal of magnitude order between negative values." } ], "affordances": [ "Verify or reject strict negativity using an exact expression, proof or certified bound.", "Convert between equivalent representations while preserving the value and any approximation guarantees.", "Compute magnitude, additive inverse and reciprocal with their correct signs.", "Compare negative values and transform inequalities with the required order reversals.", "Determine the sign of arithmetic results and whether they remain negative real numbers.", "Check real-domain admissibility before evaluating logarithms, roots or powers." ] }, "sources": [], "structure": { "bundles": [ { "id": "strict-negative-membership", "name": "Strict negative membership", "description": "Establishes that the candidate denotes a real value strictly below zero.", "rationale": "The defining boundary is a strict order condition, which notation and approximate displays can obscure.", "layers": [ { "id": "real-domain-and-zero-boundary", "name": "Real domain and zero boundary", "description": "Separates negative real values from zero and values outside the real domain.", "findings": [ { "id": "strict-order-membership", "name": "Strict order membership", "description": "A value qualifies exactly when it is real and strictly less than zero; zero and negative infinity do not qualify.", "questions": [ { "text": "Does the candidate denote an element of ℝ, rather than an extended-real element or a non-real complex value?", "kind": "boundary", "id": "strict-order-membership-q01" }, { "text": "What establishes x < 0 and excludes x = 0?", "kind": "definition", "id": "strict-order-membership-q02" } ] } ] }, { "id": "expression-and-subclass", "name": "Expression and subclass", "description": "Distinguishes the denoted value from its written sign and identifies relevant arithmetic specialisations.", "findings": [ { "id": "semantic-sign-and-subclass", "name": "Semantic sign and subclass", "description": "An expression such as -a is negative only when a > 0. Negative real values include integers, noninteger rationals and irrationals.", "questions": [ { "text": "Which assumptions on symbols make the expression strictly negative?", "kind": "definition", "id": "semantic-sign-and-subclass-q01" }, { "text": "Is the value an integer, a noninteger rational or an irrational, and what establishes that classification?", "kind": "boundary", "id": "semantic-sign-and-subclass-q02" } ] } ] } ] }, { "id": "magnitude-and-order", "name": "Magnitude and order", "description": "Records how a negative value relates to zero, its positive counterpart and other real values.", "rationale": "Agents must distinguish numerical order from magnitude order when reasoning about negative numbers.", "layers": [ { "id": "distance-and-reflection", "name": "Distance and reflection", "description": "Connects negativity to positive magnitude and additive inversion.", "findings": [ { "id": "positive-magnitude", "name": "Positive magnitude", "description": "For x < 0, the distance from zero is |x| = -x > 0, and -x is the unique additive inverse of x.", "questions": [ { "text": "What is |x|, and is it known exactly or only within bounds?", "kind": "measurement", "id": "positive-magnitude-q01" }, { "text": "Does the requested transformation require the original negative value, its magnitude or its positive additive inverse?", "kind": "action", "id": "positive-magnitude-q02" } ] } ] }, { "id": "comparison-and-local-order", "name": "Comparison and local order", "description": "Handles comparisons between negative values and the absence of adjacent negative real numbers.", "findings": [ { "id": "reversed-magnitude-order", "name": "Reversed magnitude order", "description": "For negative x and y, x < y exactly when |x| > |y|. There is no greatest negative real number: x < x/2 < 0 for every x < 0.", "questions": [ { "text": "Is the comparison about numerical value or distance from zero?", "kind": "measurement", "id": "reversed-magnitude-order-q01" }, { "text": "Does a request for the negative real closest to zero mistakenly assume that a greatest negative real exists?", "kind": "boundary", "id": "reversed-magnitude-order-q02" } ] } ] } ] }, { "id": "representation-and-sign-evidence", "name": "Representation and sign evidence", "description": "Connects exact expressions and numerical approximations to justified claims about a negative value.", "rationale": "An agent must preserve mathematical identity and avoid assigning a sign that the available precision does not establish.", "layers": [ { "id": "exact-denotation", "name": "Exact denotation", "description": "Records exact representations and the assumptions needed to interpret them.", "findings": [ { "id": "equivalent-negative-expressions", "name": "Equivalent negative expressions", "description": "Different expressions may denote the same negative real number. A finite decimal interpreted exactly is rational; a rounded decimal may represent an approximation to another value.", "questions": [ { "text": "Is the supplied decimal or symbolic expression an exact value or an approximation?", "kind": "definition", "id": "equivalent-negative-expressions-q01" }, { "text": "What derivation or input specification supports the claimed equivalence between representations?", "kind": "provenance", "id": "equivalent-negative-expressions-q02" } ] } ] }, { "id": "approximation-near-zero", "name": "Approximation near zero", "description": "Assesses whether error bounds establish strict negativity.", "findings": [ { "id": "certified-negative-enclosure", "name": "Certified negative enclosure", "description": "A valid enclosure wholly contained in (-∞, 0) proves negativity. An enclosure containing both negative values and zero cannot by itself prove strict negativity.", "questions": [ { "text": "What error bound or interval, including endpoint inclusion, is guaranteed to contain the exact value?", "kind": "measurement", "id": "certified-negative-enclosure-q01" }, { "text": "Is that enclosure wholly negative, or must the agent refine the approximation or obtain a symbolic sign proof?", "kind": "action", "id": "certified-negative-enclosure-q02" } ] } ] } ] }, { "id": "arithmetic-and-real-domain-actions", "name": "Arithmetic and real-domain actions", "description": "Determines result signs, inequality effects and real-domain restrictions for operations involving negative values.", "rationale": "Negativity changes which operations preserve membership and which function evaluations are admissible over the reals.", "layers": [ { "id": "arithmetic-sign-and-order-effects", "name": "Arithmetic sign and order effects", "description": "Tracks signs and ordering under elementary arithmetic.", "findings": [ { "id": "closure-and-inequality-reversal", "name": "Closure and inequality reversal", "description": "The sum of two negative reals is negative; their product and quotient are positive; their difference may have any sign. The reciprocal of a negative real is negative. Multiplying or dividing an inequality by a negative value reverses its direction.", "questions": [ { "text": "Given the operand signs and values, is the result negative, zero or positive?", "kind": "action", "id": "closure-and-inequality-reversal-q01" }, { "text": "Does the inequality transformation multiply or divide by a known negative value, requiring reversal of the comparison?", "kind": "action", "id": "closure-and-inequality-reversal-q02" } ] } ] }, { "id": "roots-powers-and-logarithms", "name": "Roots, powers and logarithms", "description": "Checks domains before applying functions whose real-valued definitions restrict negative arguments.", "findings": [ { "id": "negative-argument-domain-checks", "name": "Negative argument domain checks", "description": "A negative real has a unique real odd root and no real even root, and its real logarithm is undefined. Under the real-root convention, x^(p/q) for x < 0 and coprime integers p and q with q > 0 is real when q is odd; arbitrary real exponents require an explicit domain check.", "questions": [ { "text": "Does the requested logarithm, root or power admit this negative argument within the specified real domain and exponent convention?", "kind": "boundary", "id": "negative-argument-domain-checks-q01" }, { "text": "For a rational exponent, has p/q been reduced to lowest terms before checking denominator parity and determining the result's sign?", "kind": "action", "id": "negative-argument-domain-checks-q02" }, { "text": "If the operation has no real result, should the agent report it as undefined in this domain or hand the task to a complex-number model?", "kind": "action", "id": "negative-argument-domain-checks-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": [ "The definition is standard in ordinary real analysis; no competing definition is needed for this sense.", "Notation such as ℝ− varies between authors in whether it includes zero; an explicit inequality or interval avoids ambiguity.", "This account is recalled mathematical knowledge, not a researched source review." ], "questions": [ { "id": "evidence-confidence-notes-q01", "text": "Which of these check these first hold for the sense of negative real number 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": [ "Negative integers", "Negative rational numbers that are not integers", "Negative algebraic irrational numbers", "Negative transcendental numbers" ], "questions": [ { "id": "evidence-kinds-q01", "text": "Which of these kinds and varieties hold for the sense of negative real number this model covers, and on what evidence?", "kind": "provenance" } ] }, { "id": "evidence-identifiers", "name": "Identifiers and schemes", "description": "Recalled without web access and unsourced; every item is a lead to verify.", "evidence": [ { "scheme": "Mathematical set notation", "value_or_pattern": "{x ∈ ℝ : x < 0} = (−∞, 0)", "note": "Denotes the set of all negative real numbers; neither zero nor negative infinity is a member." } ], "questions": [ { "id": "evidence-identifiers-q01", "text": "Which of these identifiers and schemes hold for the sense of negative real number 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 balances below zero under a specified accounting convention.", "Expressing coordinates and displacements opposite a chosen positive direction.", "Expressing temperatures below zero on Celsius or Fahrenheit scales.", "Representing decreases through negative changes or rates of change.", "Representing quantities below a chosen reference level." ], "questions": [ { "id": "evidence-real-world-use-q01", "text": "Which of these real-world use hold for the sense of negative real number this model covers, and on what evidence?", "kind": "provenance" } ] }, { "id": "evidence-measurements", "name": "Typical measurements", "description": "Recalled without web access and unsourced; every item is a lead to verify.", "evidence": [ { "quantity": "Numerical value x", "typical_range": "Exactly x ∈ (−∞, 0); no smallest member and no member closest to zero.", "unit": "None intrinsically; applications may attach units." }, { "quantity": "Absolute value |x|", "typical_range": "(0, ∞)", "unit": "None intrinsically; inherits the unit in an application." } ], "questions": [ { "id": "evidence-measurements-q01", "text": "Which of these typical measurements hold for the sense of negative real number 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": [ "Including zero confuses negative with nonpositive.", "Failing to reverse an inequality when multiplying or dividing both sides by a negative number.", "Assuming that a negative number with greater absolute value is greater in the usual order.", "Treating the square root or real logarithm of a negative real number as real-valued.", "Confusing floating-point negative zero with a strictly negative real number; mathematically, −0 = 0." ], "questions": [ { "id": "evidence-failure-modes-and-hazards-q01", "text": "Which of these failure modes and hazards hold for the sense of negative real number 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": "Real number", "difference": "Negative real numbers are precisely those real numbers strictly less than zero." }, { "name": "Nonpositive real number", "difference": "Nonpositive real numbers include zero; negative real numbers exclude it." }, { "name": "Negative integer", "difference": "A negative integer is a negative real number with no fractional part; many negative real numbers are not integers." }, { "name": "Positive real number", "difference": "A positive real number is strictly greater than zero." }, { "name": "Non-real complex number", "difference": "A non-real complex number has a nonzero imaginary part and is not classified as negative by the usual real ordering." }, { "name": "Negative infinity", "difference": "Negative infinity is an added element in the extended real number system, not a real number." } ], "questions": [ { "id": "evidence-neighbours-q01", "text": "Which of these neighbouring kinds and how to tell them apart hold for the sense of negative real number this model covers, and on what evidence?", "kind": "provenance" } ] } ] } ] } ] }, "openQuestions": [ "Which existing Vercy real-number model should supply the inherited definitions of equality, order and exact representation?", "Which authoritative mathematical references should ground the researched publication, particularly its convention for rational powers of negative bases?", "What proof or certified-error evidence should Vercy require before classifying a numerically supplied candidate as strictly negative?", "Which neighbouring model should own the interpretation of machine signed zero and rounded displays when those are supplied as inputs?", "How should unresolved sign conditions on symbolic parameters be represented while withholding confirmed membership?" ], "statistics": { "bundles": 5, "layers": 9, "findings": 15, "questions": 24 } }, "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 negative real number, record what state it is in, and decide what may be done with it.", "whatItIs": "Enable an agent to recognise a real number strictly below zero, establish its magnitude and ordering, and determine which mathematical operations preserve its value or remain defined.", "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: negative integer, negative exponent.", "2 finer distinctions are held as aliases rather than separate entries, because telling them apart needs a task that asks for it.", "Described in 78 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 negative real number, 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": [ "negative integer", "negative exponent" ] } ], "standing": "Described in 78 Wikipedia languages, which measures how widely it is written about rather than how important or how common it is. 2 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 negative real number from another, and a negative real number 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 negative real number, 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 negative real number, 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 negative real number 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 negative real number, 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 negative real number, 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 negative real number 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 negative real number 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 negative real number, 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 negative real number, 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 negative real number 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 negative real number from the things most often confused with it.", "questions": [ { "id": "distinguishing-features-q01", "text": "What identifies and describes what distinguishes a negative real number, 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 negative real number, 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 negative real number 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 negative real number 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 negative real number between them.", "questions": [ { "id": "stages-and-transitions-q01", "text": "What identifies and describes the lifecycle of a negative real number, 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 negative real number, 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 negative real number 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 negative real number, how often and by whom.", "findings": [ { "id": "observation-record", "name": "Observation record", "description": "How an observation of a negative real number 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 negative real number, 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 negative real number, 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 negative real number 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 negative real number 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 negative real number 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 negative real number 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 negative real number 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 negative real number?", "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 negative real number?", "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 negative real number 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 negative real number and how confident it is.", "questions": [ { "id": "claim-provenance-q01", "text": "What identifies and describes a claim about a negative real number, 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 negative real number, 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 negative real number 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 negative real number is retired without being erased.", "questions": [ { "id": "validity-and-supersession-q01", "text": "What identifies and describes the validity of a claim about a negative real number, 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 negative real number, 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 negative real number 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 } } } }