Topics — What a work is about. Nucleation holds whatever reading the owner files here, whether or not an Anthology of the SOTA topic could also hold it; instruction for ML practice belongs to the anthology (ADR-048). The words are seeded from the clusters the reading-time triage of 2026-09-25 found, and grow by decision.
Contextuality — whether outcomes can be explained without reference to the context of measurement — Kochen–Specker and Bell contextuality and their sheaf-theoretic form, generalized (Spekkens) contextuality, noncontextual models and their limits, and contextuality outside physics.
37 of 547 CLAIM documents. Back to the full index.
| # | Title | Summary | Status |
|---|---|---|---|
| CLAIM-001 | The conditional-diffusion literature already covers directed transport between observational scenarios, including changing covers | The owner at U34, quoting A93’s research opportunity: “I think conditional diffusion literature has us covered here.” Accepted for compositional conditioning and transport between distributions; never shown for changing covers, and limited by A97 itself. | Proposed |
| CLAIM-009 | Pragmatic judgements may be formally contextual: their context-relative distributions may admit no global extension once direct context effects are accounted for | A24’s “contextuality hypothesis, which remains open”, and A30’s H2. The manuscript keeps it as a possibility its empirical programme tests (§3, §9, §10) and disclaims any presumption that it holds. | Proposed |
| CLAIM-037 v4 | Formal contextuality is a failure of global extension, distinct from ordinary context dependence, and needs Contextuality-by-Default when marginals shift with context | The manuscript’s §3 and §9. It separates three things: context dependence, stochastic noncommutativity, and contextuality as an obstruction to a global section. Its note of 2026-10-29 names the version it should cite: CbD 2.0 (LIT-831). | Proposed |
| CLAIM-038 v3 | A communicative object is a context-indexed system of empirical constraints over a cover of contexts, and these need not extend to one globally realizable interpretation | A78, after the owner’s U29 pointer to this record’s sheaf- contextuality readings, which the assistant said it “couldn’t reopen”. The manuscript §3: “an empirical model can remain well-defined even without a global hidden meaning state.” | Active |
| CLAIM-041 v2 | Context-sensitive interpretation, order effects and noncommuting framing operations do not by themselves establish nonclassical probability or quantum contextuality | Built over A21–A30, against the assistant’s quantum move and then the owner’s U13. The manuscript §9 states it. Its strongest ground, the record’s THEORY-013, is not cited in the manuscript. | Active |
| CLAIM-044 v2 | Ambiguity and contextuality are different phenomena: an ambiguous utterance admits several compatible global assignments, a contextual one admits none | A81 §3.4 and A82 §8.7, recovered. The manuscript keeps the contrast between context sensitivity and contextuality but not this one, between too many global readings and none. Dropped at C6 without critique. | Proposed |
| CLAIM-069 v3 | The 2016 Contextuality-by-Default criterion was being replaced by multimaximal couplings as it appeared, and the change matters for observables in more than two contexts | From the reading of Dzhafarov and Kujala 2016 (NOTE-600). The manuscript cites the 2016 paper; its general observational covers need the later version. | Superseded — by ARG-022 |
| CLAIM-070 | Transport induced by one global stochastic kernel carries a global extension of the source model to a global extension of the target model | Proposition II of A84, Proposition B2 of C6, the manuscript’s Proposition 2. Without a common global kernel preservation is not automatic, which leaves open whether transport can create or destroy contextuality. | Active |
| CLAIM-071 | Conditional generation shares a mathematical vocabulary with translation, not a mechanism: denoising time is not telephone-game time, and a generative failure is not a proof of sheaf contextuality | A97’s own two limits, which the manuscript §7 keeps. They became the whole of the claim once generation was demoted from realization to analogue. | Active |
| CLAIM-073 | Demonstrating that interpretive framings do not commute establishes that the judgements cannot be described by one ordinary joint probability distribution | The owner at U13, answering A24. Granted for projective measurements, refuted for operations by a classical counterexample (A30) that the owner never contested, so Rejected; what replaced it is pragmatic noncommutativity, which the manuscript keeps. | Rejected — by CLAIM-052 |
| CLAIM-100 | Sheaf-theoretic contextuality has to be extended to directed transport between observational scenarios whose covers change, and that extension is the theory’s open mathematical problem | A93 §1’s “Research opportunity” and A94’s bridge question, which the owner quoted at U34. The manuscript concedes the gap (“cover-changing or incompatible maps demand separate analysis”, §6) without posing it. | Superseded — by CLAIM-125 |
| CLAIM-105 v4 | In documented reconstruction chains, steps that keep most local judgements commonly change their global compatibility: translation preserves local meanings while changing the global structure of meaning | A78’s thesis for the paper, “potentially the most interesting connection we’ve found”, with Δ_CF, the change in contextual fraction along a chain, as its measure. The manuscript keeps the thesis as its Abstract’s last sentence but drops the measure and the worked examples (at C6, per the chunk-5 reader). | Proposed |
| CLAIM-109 | In translation the pragmatic frame does not merely select a description of meaning but participates in determining which meaning becomes actual | A21’s “preferred formulation”, reached by the quantum-cognition analogy. Withdrawn over A24–A30 as the inference was undercut, and replaced by a hypothesis held open for test. | Superseded — by CLAIM-009 |
| CLAIM-121 | A transport whose local kernels commute with restriction maps overlap-consistent source models to overlap-consistent target models | Proposition I of A84, Proposition B1 of C6, the manuscript’s Proposition 1. It concerns marginal consistency, not global noncontextuality. | Active |
| CLAIM-124 | Communicative objects are characterized through overlapping constraints on observables at partially ordered levels; translation transports these locally constrained structures, and repeated reconstruction changes both local interpretations and their global compatibility | The thesis of proposal v5 (A81–A83, under U30), which put observational structure first: “a global communicative object is no longer stipulated in advance.” Revised at U31 into the selective preservation of decision-relevant information. | Superseded — by CLAIM-026 |
| CLAIM-125 v4 | Directed transport between empirical models whose covers change has two open problems: when it preserves decision-relevant information, and how it extends to signalling data | CLAIM-100 narrowed. Simulations between empirical models already give directed stochastic transport between scenarios whose covers change, and settle when it preserves global compatibility. What is left open is decision-relevant information and signalling data. | Active |
| CLAIM-127 v3 | Conditioning on a communicative situation, intervening on it and intervening on what the interpreter is told are three different operations, so a framing intervention should index the empirical model, e_C^a = P(Y_C | do(a)), not enter its cover as one more context | The owner’s do() move at U41, formalized at A129 §1 and §5 and restated in the review relayed the same day. A129 keeps three operations apart: conditioning on the situation, intervening on it, and intervening on what the interpreter is told. It keeps one cover, with the empirical laws indexed by intervention. The link to signalling is the record’s extrapolation, and A129’s own graph gives a second route to it. | Proposed |
| CLAIM-131 | A compatible family of sections of the event sheaf always glues, so where a communicative object lacks a global realization the obstruction lies in its supports or distributions, not in the event sheaf | The assistant at A125 §2 and A129 §2, after the owner’s U41 “double click on this”. It is the standard sheaf property of E(U) = ∏ O_x (Abramsky and Brandenburger). Granted, because it is elementary; it is used against TERM-002’s wording, not against CLAIM-038’s thesis, which version 2 restates to agree with it. | Active |
| CLAIM-141 v2 | Causal-loop consistency and sheaf contextuality are both local-to-global problems, but passing to distributions affects them oppositely: a loop with no deterministic solution has a distributional fixed point, while a model with no global section in its supports has no global distribution either | A161, after the owner’s U46, sharpened. A161 saw that a causal loop and a contextual model are “not the same”, but not that they run in opposite directions under passage to distributions, or why. Its parity pattern is LIT-278’s identification of Liar cycles with contextual support tables, which the record holds and has read (NOTE-251). A173 and A178 kept the three kinds of global consistency apart; A218 Ch10.9 keeps the feedback case. | Active |
| CLAIM-143 v3 | Local descriptions that disagree are not thereby incompatible: whether there is an obstruction can be assessed only relative to a specified class of admissible correspondences between their observations, independently validated and not admitted because they remove the disagreement | A164, after the owner’s U47, restated by A173, A178, A203, A214 and A218. Three classes of disagreement (coordinate difference, structural transformation, global obstruction) and an order of tests: fix and validate the correspondence, then ask whether the descriptions extend jointly. A173 proposed it as a design principle; it is a thesis of the line. The relativity example motivates it and is not evidence for it. | Active |
| CLAIM-197 | Sections over contexts that do not overlap always glue, so a sense that differs between disjoint contexts is not a gluing failure: a failure needs an overlap carrying sections that disagree, and which families count as covers decides whether anything glues | Dual-filed from MOM-CLM-088 (ADR-037). The sheaf condition says a family of sections that agree on overlaps glues to one global section. Where two contexts do not overlap, agreement is vacuous and they glue. So “tall”, which takes one threshold for people and another for trees, is one global section with the comparison class part of the meaning, not a failure of gluing. A failure needs contexts that overlap and carry sections that disagree there. Which families count as covering is the piece that decides whether anything glues, and a sheaf picture of meaning that does not state it has decided nothing. | Active |
| CLAIM-201 | Over a fixed scenario, a change of global compatibility at small local distortion needs contextual judgements, which the behavioural data read so far lack; the form of the headline those data leave open is a change of cover, in which a rendering makes some of the source’s questions undecidable for its readers and decides others the source left open | The record’s narrowing, on 2026-10-10, of CLAIM-105 after CLAIM-219. It concedes that the record’s reading of LIT-264 finds no contextual behavioural data, so the fixed-scenario form of “Translation may preserve local meanings while changing the global structure of meaning” has no case but a constructed one. It shows why the fixed-scenario form is sharp and why it needs contextuality. It keeps the form the record already names: “Only a change of scenario can make it jump” (CLAIM-105), and manuscript §11’s “A transport may preserve overlaps but change the available measurement cover”. A proposal; its test is the discriminating study. | Proposed |
| CLAIM-207 | The transports of Propositions 1–2 and of D_obs act on judgement outcomes, not texts, and for any one source–target pair a constant kernel transports any overlap-consistent target, so they constrain a translation only once one kernel family is fixed across many utterances and derived from the text channel | Found in the record’s audit of the line on 2026-10-10 (formal lens); no turn of the exchange raises it. The manuscript’s kernels K_C map readers’ judgements to readers’ judgements, while a translation is a channel on texts, T(v | u), and TERM-008 records that the two levels are never formally related. For one source and any overlap-consistent target, the constant kernel makes D_obs zero and satisfies naturality. Granted, because it is elementary. It does not say CLAIM-121 or CLAIM-070 is false; it bears on what they are used to support. | Active |
| CLAIM-219 v4 | A change in the global compatibility of a fixed scenario is either a change in contextuality proper, which the behavioural data read show none of, or a change in overlap consistency, which is ordinary context dependence and moves by at most 2ε when each context moves by ε | Found in the record’s audit of the line on 2026-10-10 (structure lens); no turn of the exchange raises it. Dzhafarov, Zhang and Kujala (LIT-264) find no contextuality in five kinds of behavioural data, and CLAIM-125 reports that 34 of 90 language systems signal too much to be contextual. If pragmatic data are noncontextual as a rule, CLAIM-105’s defeat condition is met by default; what is left to change is overlap consistency, which is the “trivial sense of contextuality” and is fixed by the local distributions. The only instance of the headline is the stipulated CASE-037. Among the claims LIT-264 is cited only by CLAIM-041, not by CLAIM-105. The objection is open; it does not say a contextual pragmatic data set cannot exist. | Active |
| CLAIM-235 v3 | The line’s proposed quantities have no finite-data estimators: plug-in signalling from one or a few occurrences per context is positive in expectation when the true marginals agree, so the contextual fraction is undefined on raw tables, and deficiency over text-valued renderings has no estimator | Found in the record’s audit of the line on 2026-10-10 (formal and empirical lenses); no turn of the exchange raises it. The plug-in signalling of two empirical marginals is positive in expectation when the true marginals agree, so raw tables signal, and the contextual fraction is undefined on them. With one occurrence per context, a non-signalling rank-2 system gives Δ of 0, 2 or 4, with expectation 2: the values NOTE-654 finds in 51 of the 90 systems behind CLAIM-125’s “69 of the 90 systems signal”. The data are author-assigned corpus senses, not judgements. Deficiency over text-valued renderings has no estimator. It does not say signalling is rare in pragmatic judgements, where order effects are themselves signalling. | Active |
| CLAIM-237 v2 | The first open problem of directed transport is not yet posed: a contextual model is a menu of incompatible experiments, and under the natural order on menus any state-independent classical simulation is dominated automatically, so what is open is only the converse or a deficiency bound | Found in the record’s audit of the line on 2026-10-10 (formal lens); no turn of the exchange raises it. Blackwell’s order compares experiments, each a family of distributions over one parameter. An empirical model has no parameter, and if it is contextual it has no joint distribution, only one per context. Posing CLAIM-125’s first part needs models indexed by situations and an order on menus of experiments. Under the natural order, the preservation direction is automatic for a classical simulation that does not depend on the situation. Granted, because the argument is elementary. It narrows what is open; it does not close it. | Active |
| CLAIM-245 | Under Contextuality-by-Default, a deterministic context-wise recoding can make a noncontextual signalling source maximally contextual, or turn a contextual source into pure signalling, so per-content signalling is not monotone under such maps and the quantity to bound is joint overlap discrepancy | Found in the record’s audit of the line on 2026-10-10 (formal lens); no turn of the exchange raises it. Two worked rank-2 systems answer NOTE-654’s open question negatively: THEORY-177’s per-content signalling can rise under deterministic recodings, once the source signals, and CbD contextuality can be created or removed by them. By data processing, the joint overlap discrepancy cannot rise, so that is the quantity CLAIM-125’s second part should name. Granted, because the examples are elementary. It does not say THEORY-174 is wrong, which is about no-signalling models. | Active |
| CLAIM-251 v2 | A change in which questions a receiver population can answer determinately is not by itself a change of cover in the sheaf sense: the cover belongs to the measurement scenario and the responses are an empirical model on it, so such a change is a change of empirical model, which can create or remove a gluing obstruction on a fixed cover but does not change what the cover is, and the operational notion needs its own name until a functorial link is shown | From the interlocutor’s reading of PR #121 and its reconciliation, relayed by the owner on 2026-10-12, on the open tension between CLAIM-197 with CASE-048 and the operational cover of CLAIM-201. It keeps the empirical notion and denies it the sheaf-theoretic name. Open. | Proposed |
| CLAIM-265 v3 | Local descriptions that disagree are not thereby incompatible: whether they obstruct a joint description is decided only relative to a specified class of admissible correspondences between their observations, and a correspondence admitted only because it removes the disagreement decides nothing | The general content of CLAIM-143, filed alone under ADR-040 so that the order of tests does not rest on CLAIM-011, CLAIM-004 and CLAIM-035, which are about translation. Disagreement between local descriptions sorts into a coordinate difference, a structural transformation or a global obstruction, and the sort cannot be made until a class of admissible transition maps is given. Inertial frames (CASE-039) show disagreement with no obstruction once the maps are known. | Active |
| CLAIM-310 v2 | Sorting schemes over objects with determinate properties never conflict as descriptions, since the product of any sortings refines them all; they conflict as arrangements, since a fixed number of bins realizes one partition when each item is stored once, and which costs least depends on what is searched for and on what stands out within a bin | What is directionally right in the owner’s LEGO monograph, as Mathematics of Meaning graded it. Its contextuality claim is empty: any sortings of bricks share a joint refinement (MOM-CLM-137), and the events they generate stay Boolean (MOM-ARG-047). Its intuition that builders cannot share a sorting is true of arrangements. One set of bins realizes one partition, the product may need more bins than there are, and the cheapest choice depends on what each builder searches for and on what stands out within a bin (CASE-095). The disagreement is a trade, not a failure of global truth. Sorting on one attribute also turns a search for a combination of features into a search for one feature within each bin, which Treisman and Gelade (LIT-1082, read) show is the difference between a serial scan and one found at a glance. | Active |
| CLAIM-319 | Over a scenario of n contexts in an odd cycle, changing the support of one context takes the contextual fraction from 1 to 0 while the other n − 1 contexts and every marginal are kept exactly, at a weighted observational distortion of 1/n, so within a scenario the fraction’s Lipschitz constant against that distortion is at least n; and any change of global extension needs a contextual model on one side | Split from CLAIM-201 under ADR-043: the derivation that claim called “decisive and checkable”, stated on its own. For odd n, an n-cycle of ±1 observables in which every context anticorrelates is strongly contextual; making one context correlate gives a model with a global distribution. The two agree on n − 1 contexts and on every marginal, differ by total variation 1 in the last, and so lie at weighted D_obs = 1/n with contextual fractions 1 and 0. For n = 3 it is CASE-037 with one observable relabelled. It answers how small the local change can be; it says nothing about whether any data are contextual. | Active |
| CLAIM-320 | Within one fixed measurement scenario, two no-signalling empirical models can agree on all but one of their contexts and on every single-observable marginal while their contextual fractions are 1 and 0, so keeping most local judgement distributions does not fix their global compatibility | Split from CLAIM-105 under ADR-043: the possibility that claim’s headline needs, shown by the pair it lost and recovered in CASE-037. On the cover {AB, BC, AC} with binary outcomes, the parity triangle at 1/2 per allowed outcome is no-signalling and strongly contextual, with contextual fraction 1. Change only S_AC to {(0,0), (1,1)}: two contexts and every marginal are unchanged, and the model now extends to a global distribution, with fraction 0. It is an existence result by construction, and the weights are stipulated. It does not say reconstruction chains do this, which is CLAIM-105’s thesis and interpretive, and the context that changes moves by a total-variation distance of 1. | Active |
| CLAIM-325 | The behavioural data the record has read show no contextuality proper: none of the five kinds of data Dzhafarov, Zhang and Kujala re-analyse is contextual, Wang et al. test none of their 90 language systems for it, and no documented test of pragmatic or meaning judgements finds it at adequate power | Split from CLAIM-219 under ADR-043: the empirical premise of that objection’s dilemma, which CLAIM-201 conceded. Dzhafarov, Zhang and Kujala (LIT-264, read in NOTE-235) find none of five kinds of behavioural data contextual, two of them previously published as contextual; Wang, Sadrzadeh, Abramsky and Cervantes (LIT-851) report signalling in 69 of 90 language systems and test none for contextuality; CASE-053 collects the documented tests on elicited judgements and finds no contextual pragmatic data. It is scoped: CASE-053 records a reliable positive result on instructed matching, so “none in behavioural data” is too broad, and the absence is LIT-264’s working hypothesis, not a proof that such data cannot exist. | Active |
| CLAIM-372 | Within a fixed measurement scenario, the contextual fraction is a piecewise-linear and Lipschitz-continuous function of the empirical model’s probability table, with a constant that depends only on the scenario | The record’s own derivation, from the linear programme of Abramsky, Barbosa and Mansfield (LIT-265, Eq. 3), which THEORY-165 holds. The non-contextual fraction is the minimum of the dual objective over finitely many vertices, so it is concave and piecewise linear in the probability table, and the contextual fraction is Lipschitz in it. The constant is the largest ℓ₁ norm of a dual vertex, which depends only on the scenario and is not bounded here. Nothing here crosses scenarios or applies to signalling data. | Active |
| CLAIM-374 | On a consistently connected system, Contextuality-by-Default and the sheaf criterion agree: a maximally connected coupling exists exactly when a global law has the contexts’ laws as its marginals | The record’s derivation of what NOTE-600 marks as its own inference. In a consistently connected system, every observable has one distribution in all the contexts that contain it. Then each connection’s maximal coupling makes its copies equal with probability 1 (LIT-777, Theorem 3.3), so a maximally connected coupling is a joint law of one variable per observable, which is a global section in Abramsky and Brandenburger’s sense (LIT-016, THEORY-012). Conversely, a global section gives such a coupling. The two criteria come apart only when marginals shift with context. | Active |
| CLAIM-471 v5 | Physical interconnection can generate effective constraints on joint behaviour; measurement can estimate correspondences among local descriptions; and adaptive apparatuses can revise those correspondences; gluing expresses compatibility under specified relations, but neither the relations’ physical generation nor their adequacy follows from gluing alone | The owner’s U20 of the exchange of 2026-10-27, “interactions generate constraints that manifest as gluing conditions between intertial frames”, restated at the owner’s review. The readings found the correspondence maps given, measured or designed in nearly every formalism the exchange cited, and changed by interaction only in one constructed model whose authors call the result “learning to lie”. So the claim separates three mechanisms. Physical interconnection changes what joint behaviour is admissible, and only it bears on the strong thesis that interaction generates constraints. Measurement estimates correspondences that already held. Adaptation revises an apparatus’s own rules of comparison. The open question is QUESTION-282: when interaction changes the physically operative correspondence structure, rather than revealing or redescribing it. | Active |
| CLAIM-510 | Measurement can establish, and not only estimate, a correspondence among local descriptions: some correspondences that measurement estimates can be checked against evidence the measurement did not itself produce | The clause CLAIM-471 dropped when the twenty-fourth status review narrowed “establish” to “estimate” (ADR-047, kind 2). It is the record’s own wording, and no source asserts it. CLAIM-143’s order of tests needs it to be possible, since the order asks for correspondences that are independently validated. No held case meets it yet. | Proposed |