{ "model": { "rank": 7123, "code": "thing-q218005", "model_id": "vr.tr.sum", "name": "sum", "purpose": "Let an agent compute and explain sums, use summation notation and rules, evaluate series and Riemann sums, and support learning across levels.", "family": "Thing Registry", "category": "Cross-cutting context", "status": "research-draft", "kind": "thing", "plane": "XCT", "domain": "XCT.QLT", "industry": "", "version": "", "url": "/models/thing/q218005/", "tier": 2, "score": 57, "payload": { "layer": "wikidata", "aliases": [ "Riemann sum", "partial sum", "Positive element", "digit sum", "Sums of powers", "empty sum", "telescoping sum", "aliquot sum", "double sum", "algebraic sum", "exponential sum", "character sum", "debit", "Delta-v budget", "sums of three cubes", "sum of normally distributed random variables", "growing-degree day", "sum of a series", "sum of decimal digits", "Weyl sums", "Kloosterman sum", "net debit required", "Baskerville-Emin GDD" ], "aliasCount": 23, "merged": 23, "knownIn": 57, "facets": null, "markers": [], "lexicalClass": "", "senseRank": null, "alsoRegisteredAs": "vr.tr.sum-artifact", "source": { "dataset": "wikidata", "item": "Q218005", "url": "https://www.wikidata.org/wiki/Q218005", "license": "CC0 1.0" } }, "research": { "vercy": "1.0-draft", "publication": { "status": "research-draft", "adjudicationStatus": "unreviewed", "publishableCanonical": false, "generatedAt": "2026-09-11T21:59:31Z", "providers": [ "Claude" ], "breadth": "written by Claude from model knowledge without web access - no source was read, every claim is a lead to verify", "pass": 2, "wave": 2, "engine": "claude" }, "metaModel": { "id": "THING-Q218005", "registryId": "vr.tr.sum", "name": "sum", "version": "0.2.0-wave.2", "entryKind": "thing", "family": "Thing Registry", "domain": [ "XCT.QLT" ], "status": "research-draft" }, "canonicalUrl": "https://ver.cy/models/thing/q218005/", "model": { "registry_id": "vr.tr.sum", "name": "sum", "purpose": "Let an agent compute and explain sums, use summation notation and rules, evaluate series and Riemann sums, and support learning across levels.", "definition": "The result of adding numbers, quantities or other addable objects together, from simple arithmetic sums and digit sums to partial sums of series, Riemann sums approximating integrals, sums of powers, weighted sums and the empty sum equal to zero; summation is notated with the sigma symbol and underlies arithmetic, algebra, analysis and statistics.", "what_it_is_for": "Results of addition.", "affordances": [ "compute sums", "explain summation notation and rules", "evaluate series and Riemann sums", "support learning" ], "distinguishing_features": [ "Additive", "Finite or infinite", "Notated with sigma", "Foundational" ], "appearance": "Not physical; numbers and expressions with the sigma symbol.", "visual_identification": [ "Result of adding", "Sigma notation", "A product is the result of multiplying" ], "physical_properties": [], "families_and_kinds": [ "finite arithmetic sums", "digit sums and sums of powers", "partial sums and series", "Riemann sums", "weighted sums and the empty sum" ], "related_models": [ { "relation": "is a kind of", "target": "operation result", "why": "category" }, { "relation": "is a kind of", "target": "weighted sum", "why": "category" }, { "relation": "is related to", "target": "calculation", "why": "computing sums" }, { "relation": "is related to", "target": "amicable numbers", "why": "divisor sums" } ], "identifiers": [], "standards_and_regulation": [ "Mathematical notation conventions" ], "failure_modes_and_hazards": [ "Off-by-one errors in index ranges", "Misusing divergent series", "Floating point accumulation error" ], "in_scope": [], "out_of_scope": [], "characteristics": [] }, "sources": [], "structure": { "bundles": [ { "id": "compute", "name": "Compute", "description": "Working out sums.", "rationale": "Arithmetic.", "layers": [ { "id": "basic", "name": "Basic", "description": "Basic sums.", "findings": [ { "id": "basic-finding", "name": "Basic", "description": "Basic sums.", "questions": [ { "text": "What is the sum of these numbers, and how can it be checked?", "kind": "action" }, { "text": "What is a digit sum, and how is it used in checks?", "kind": "definition" } ] } ] }, { "id": "formulas", "name": "Formulas", "description": "Closed forms.", "findings": [ { "id": "formulas-finding", "name": "Formulas", "description": "Closed forms.", "questions": [ { "text": "Which closed-form formulas give sums of arithmetic and geometric progressions and sums of powers?", "kind": "definition" }, { "text": "How are they proved?", "kind": "definition" } ] } ] } ] }, { "id": "notation", "name": "Notation", "description": "Sigma notation.", "rationale": "Rules.", "layers": [ { "id": "sigma", "name": "Sigma", "description": "Reading and writing sums.", "findings": [ { "id": "sigma-finding", "name": "Sigma", "description": "Sigma notation.", "questions": [ { "text": "How is sigma notation read and written, including index ranges and the empty sum?", "kind": "definition" }, { "text": "How are sums manipulated by linearity, reindexing and splitting?", "kind": "definition" } ] } ] }, { "id": "weighted", "name": "Weighted", "description": "Weighted sums.", "findings": [ { "id": "weighted-finding", "name": "Weighted", "description": "Weighted sums.", "questions": [ { "text": "What are weighted sums, and how do averages, expectations and dot products use them?", "kind": "definition" }, { "text": "How is a weighted sum computed here?", "kind": "action" } ] } ] } ] }, { "id": "analysis", "name": "Analysis", "description": "Series and integrals.", "rationale": "Advanced.", "layers": [ { "id": "series", "name": "Series", "description": "Partial sums and series.", "findings": [ { "id": "series-finding", "name": "Series", "description": "Series.", "questions": [ { "text": "What are partial sums, and when does an infinite series converge?", "kind": "definition" }, { "text": "Which tests decide convergence?", "kind": "definition" } ] } ] }, { "id": "riemann", "name": "Riemann", "description": "Riemann sums.", "findings": [ { "id": "riemann-finding", "name": "Riemann", "description": "Riemann sums.", "questions": [ { "text": "How do Riemann sums approximate integrals, and how does the approximation improve?", "kind": "definition" }, { "text": "How is a Riemann sum computed for this function?", "kind": "action" } ] } ] } ] }, { "id": "learn", "name": "Learn", "description": "Teaching and computing.", "rationale": "Education.", "layers": [ { "id": "teach", "name": "Teach", "description": "Teaching sums.", "findings": [ { "id": "teach-finding", "name": "Teach", "description": "Teaching.", "questions": [ { "text": "How can summation be taught from arithmetic to sigma notation?", "kind": "action" }, { "text": "Which misconceptions arise?", "kind": "provenance" } ] } ] }, { "id": "numeric", "name": "Numeric", "description": "Numerical summation.", "findings": [ { "id": "numeric-finding", "name": "Numeric", "description": "Numerical summation.", "questions": [ { "text": "How can floating point summation error be reduced, such as by compensated summation?", "kind": "action" }, { "text": "Which entry fits numerical methods?", "kind": "action" } ] } ] } ] } ] }, "openQuestions": [ "Should series be a separate entry?", "How should notation guides be linked?", "How should numerical methods be linked?" ], "statistics": { "bundles": 4, "layers": 8, "findings": 8, "questions": 16 } }, "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 sum, record what state it is in, and decide what may be done with it.", "whatItIs": "Let an agent compute and explain sums, use summation notation and rules, evaluate series and Riemann sums, and support learning across levels.", "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: Riemann sum, partial sum, Positive element, digit sum, Sums of powers, empty sum, telescoping sum, aliquot sum, double sum, algebraic sum, exponential sum, character sum.", "23 finer distinctions are held as aliases rather than separate entries, because telling them apart needs a task that asks for it.", "Described in 57 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 sum, 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": [ "Riemann sum", "partial sum", "Positive element", "digit sum", "Sums of powers", "empty sum", "telescoping sum", "aliquot sum", "double sum", "algebraic sum", "exponential sum", "character sum" ] } ], "standing": "Described in 57 Wikipedia languages, which measures how widely it is written about rather than how important or how common it is. 23 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 sum from another, and a sum 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 sum, 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 sum, 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 sum 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 sum, 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 sum, 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 sum 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 sum 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 sum, 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 sum, 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 sum 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 sum from the things most often confused with it.", "questions": [ { "id": "distinguishing-features-q01", "text": "What identifies and describes what distinguishes a sum, 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 sum, 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 sum 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 sum 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 sum between them.", "questions": [ { "id": "stages-and-transitions-q01", "text": "What identifies and describes the lifecycle of a sum, 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 sum, 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 sum 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 sum, how often and by whom.", "findings": [ { "id": "observation-record", "name": "Observation record", "description": "How an observation of a sum 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 sum, 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 sum, 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 sum 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 sum 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 sum 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 sum 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 sum 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 sum?", "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 sum?", "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 sum 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 sum and how confident it is.", "questions": [ { "id": "claim-provenance-q01", "text": "What identifies and describes a claim about a sum, 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 sum, 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 sum 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 sum is retired without being erased.", "questions": [ { "id": "validity-and-supersession-q01", "text": "What identifies and describes the validity of a claim about a sum, 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 sum, 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 sum 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 } } } }