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.
33 of 1352 THEORY documents. Back to the full index.
| # | Title | Summary | Status |
|---|---|---|---|
| THEORY-010 | Grangier and Auffèves’s contextual objectivity is an ontological postulate, not contextuality in either formal sense: its one argued consequence, unpredictability after a change of context, is reproduced by an epistemically restricted classical model | Places Grangier & Auffèves (2018), LIT-077, against the two formal notions (LIT-016, LIT-003) and against Spekkens’s epistricted models (LIT-007). The placement is the record’s, joining NOTE-044’s reading with LIT-007 and LIT-016; Grangier’s own derivations are not held. | Proposed |
| THEORY-011 v4 | Generalized contextuality is strictly broader than Kochen–Specker contextuality: a qubit already has no preparation-noncontextual model, though no Kochen–Specker argument with sharp measurements exists in dimension two | Spekkens (2005), LIT-266, §III and §IV, read in full in NOTE-748; restated in Budroni et al. (LIT-263, §IV.E, read in NOTE-844). Corrects the reading that contextuality needs dimension three. The dimension-two limit holds for sharp measurements only. | Active |
| THEORY-012 v8 | An empirical model is Kochen–Specker-noncontextual exactly when its context distributions glue to one global distribution, and since signed global sections always exist for no-signalling models, negative probability does not mark contextuality | Abramsky & Brandenburger (2011), LIT-016, Thm 8.1 with Prop 3.1, and Thms 5.4 and 5.9 — proved for finite measurement scenarios with no-signalling built into the definition. The graded version, the contextual fraction (LIT-265), is read (NOTE-236): CF = 0 exactly when this criterion holds. The review that places this formulation among its equivalents is read (NOTE-844); it asserts the equivalence with citations and does not show it. | Active |
| THEORY-013 v3 | Once context-dependent marginals are separated from contextuality, the behavioural, social and word-meaning data published as contextual show none | Dzhafarov, Zhang & Kujala (2015), LIT-264 — Contextuality-by-Default applied to five data sets, including primed word combinations from the quantum-cognition literature. Seeded, not yet read closely. The authors call general absence a working hypothesis, and later work in the same programme is reported to find behavioural contextuality. | Proposed |
| THEORY-014 v3 | In both formalisms of contextuality, classicality is the existence of a nonnegative version of a linear representation that always exists over the reals, so negativity is universal and only its unavoidability is nonclassical | An inference joining two proved results: LIT-016 Thms 5.4 and 5.9 with Thm 8.1, and LIT-003 Thm 2.8 with Cor 3.5. Each half is proved and read; the parallel is the record’s own, and LIT-003 attempts no comparison with LIT-016. | Active |
| THEORY-015 v3 | Kochen–Specker noncontextuality is measurement noncontextuality plus outcome determinism for sharp measurements, and preparation noncontextuality implies that determinism, so every Kochen–Specker proof refutes universal generalized noncontextuality while measurement noncontextuality alone is consistent with quantum theory | Spekkens (2005), LIT-266, §III, §VIII.A (Eqs. 77–88), §VIII.B, §IX — the bridge between the record’s two contextuality threads, which no held work states. Read in full in NOTE-748, which confirmed the §VIII.A proof and its need for the full preparation set. Joining it to the sheaf form (LIT-016) is the record’s inference. | Active |
| THEORY-016 v3 | An operational theory admits a generalized-noncontextual model exactly when its GPT admits a positive quasiprobability representation, and for a tomographically local theory any diagram-preserving such model is an exact frame with exactly as many ontic states as the GPT’s dimension | Schmid et al. (2020), LIT-003, Prop 3.2, Prop 3.4, Cor 3.5, Thm 4.1, Cor 4.2, Prop 4.3 — proved. Spekkens’s odd-d stabilizer Wigner representation (LIT-007) is a worked instance. The theorem gives no test for whether a positive representation exists. | Active |
| THEORY-020 | Every Boolean algebra is the clopen algebra of its Stone space of prime ideals, and a finite one is the power set of its atoms, so a single Boolean context always has two-valued valuations and the Kochen–Specker obstruction lies in how contexts overlap | Stone (1936, 1937), LIT-353 and LIT-358: every Boolean ring is isomorphic to the compact open sets of its prime-ideal space, a totally disconnected, locally compact Hausdorff space that is compact exactly when there is a unit, and every such space arises this way. Kochen & Specker (LIT-298, Thm 0) turn this into the criterion that a partial Boolean algebra embeds in a Boolean one iff its two-valued homomorphisms separate points. The joining of the two, that non-classicality needs more than one context, is the record’s. Neither Stone paper uses “ultrafilter” or states a duality of categories. | Active |
| THEORY-024 v2 | Classical Boolean logic is restored when a presheaf of contextual data acquires a global section or is sheafified | Ghose (2025), LIT-276 — asserts that the Heyting algebra of truth values “becomes Boolean” when the presheaf data collapse to a global section, and that sheaves encode Boolean reasoning. Both claims are asserted, not proved. The record’s readings refute them. The internal logic of a topos is fixed by the base category and its topology, not by whether one presheaf has a section (Isham–Butterfield, LIT-325, §6). Sheaf toposes such as Sh(ℝ) are not Boolean (NOTE-249). The contextuality criterion itself is untouched. | Rejected |
| THEORY-037 v3 | In the topos programme quantum propositions form a distributive Heyting algebra, not an orthocomplemented lattice, and its negation is a pseudo-complement under which excluded middle can fail | Döring & Isham (2007, II), LIT-335 — daseinisation maps each projector injectively to a clopen sub-object of the spectral presheaf, with δ(P∨Q) = δ(P)∨δ(Q) but only δ(P∧Q) ⪯ δ(P)∧δ(Q). The orthocomplement is carried to inner daseinisation, not to ¬δ(P). That Sub_cl(Σ) is Heyting (Thm 2.5) is sketched in the source, and the record re-derives it: each Σ_V is extremally disconnected, so Sub_cl(Σ) is a frame. Paper I (LIT-343) chooses intuitionistic deduction. Isham–Butterfield (LIT-325) state that the Heyting algebra is fixed by the base category. | Active |
| THEORY-165 v2 | Within a fixed measurement scenario, the non-contextual fraction is the value of a linear programme whose constraint vector is the empirical model’s probability table, and the contextual fraction is convex under mixing | From Abramsky, Barbosa & Mansfield (2017), LIT-265: the non-contextual fraction is the value of a linear programme whose constraint vector is the empirical model (Eq. 3), and convexity of CF under mixing is their Theorem 2. Piecewise linearity and the Lipschitz bound are the record’s own derivation, now CLAIM-372. The Lipschitz constant depends on the scenario and is not bounded here. Nothing here applies to signalling data, where CF is undefined. | Active |
| THEORY-168 v3 | In Contextuality-by-Default, whether a fixed set of measurements is contextual depends on how the system is represented: which couplings are imposed, and which dichotomizations of the variables are included | Dzhafarov, Cervantes & Kujala (2017), LIT-790, with Dzhafarov & Kujala’s CbD 2.0 (LIT-831) and CbD 1.0 (LIT-777). The same measurements can receive different verdicts. Maximal and multimaximal couplings can disagree when a content appears in three or more contexts (four, for binary variables), and the record’s worked case shows it. Multimaximal couplings of non-binary variables can be destroyed by coarse-graining. With every dichotomization kept, two content-sharing variables are contextual on their own unless one nominally dominates the other. The authors present the representation as the analyst’s choice, not as a defect. What the record does not get from these papers is any rule for choosing it. | Active |
| THEORY-171 v3 | When the causal constraints on events depend on context, deterministic assignments that are causal in each context can fail to glue into one causal assignment, so causal structure is itself a source of contextuality | From Gogioso & Pinzani’s trilogy: The Topology of Causality, LIT-808, read in NOTE-612, with the definitions of The Combinatorics of Causality, LIT-800 (NOTE-635). Over a space of input histories with the lowerset topology, causal functions form a separated presheaf, and on the space Θ₃ it is not a sheaf: two causal assignments on disjoint opens give one event two outputs on their common extension. That example was checked here, and it settles the claim. The source’s Theorem 2.34, that the presheaf is a sheaf exactly when no two contexts impose incompatible causal pasts on a common event, is reported as the source’s. Its proof was not read, and it is QUESTION-143. It does not say any physical or quantum data display the effect. | Active |
| THEORY-174 v3 | Classical simulations between no-signalling empirical models on different scenarios never create contextuality, and a convex map between two scenarios’ model sets is induced by a classical non-adaptive procedure exactly when some non-contextual model of the hom scenario that satisfies its predicate induces it | Karvonen (2018), LIT-846; Abramsky, Barbosa, Karvonen & Mansfield (2019), LIT-847; Barbosa, Karvonen & Mansfield (2021, v2 2024), LIT-845. A simulation answers each measurement of the target by a jointly measurable set of the source’s, with shared classical randomness, so the cover may change. Along any simulation the non-contextual fraction cannot fall; contextual models cannot be cloned; and which maps between model sets are classical non-adaptive procedures is a non-contextuality question on a hom scenario, re-derived here. No-signalling models only, and nothing about information preserved. | Active |
| THEORY-177 v2 | In a binary cyclic system, the Contextuality-by-Default measure of signalling is twice the sum, over contents, of the least direct influence of context that a canonical causal model of the data must place on each content, and each content’s least influence is the total-variation distance between its two marginals | Wang, Sadrzadeh, Abramsky & Cervantes (2021), LIT-851, Proposition 1. It joins CbD’s maximal couplings (LIT-777, Theorem 3.3) to Jones’s 2019 correspondence between couplings and canonical models, which the paper quotes and the record derives independently. The result measures signalling. Its minima are per content, each reached in its own model; one model reaches them all only if the system is noncontextual. It says nothing about contextuality beyond the bound that a rank-2 system with Δ ≥ 2 cannot be contextual, and identifies no particular causal model. | Active |
| THEORY-231 v3 | Within classical realism, a generalized-noncontextuality no-go refutes Leibnizian representations, not realist representations as such; it rests on a stronger assumption than a Bell-like no-go and so applies where none exists, as in prepare-measure scenarios, but only Leibnizianity implying noncontextuality is proved | Schmid, Selby and Spekkens (2020), LIT-945, §VI.C, §VIII (Eqs. 200, 214, 215), read in part in NOTE-737, which is Skimmed: §§II–IV and the proofs in Appendices C–G were not read. A Leibnizian classical realist representation implies a generalized-noncontextual one, so every noncontextuality no-go is a no-go for Leibnizian representations. The converse is Conjecture 1′, so a Leibnizianity failure is not shown to be a noncontextuality failure. The prepare-measure claim is stated, not derived, in the text read. | Active |
| THEORY-303 | A measurement scenario whose compatibility hypergraph is acyclic admits no contextuality: locally consistent context distributions always glue to a global one, so a contextual scenario needs an induced cycle of length at least four | Vorob’ev (1962), as stated in Budroni, Cabello, Gühne, Kleinmann & Larsson (2022), LIT-263, §V.B.2, Eq. 79, and App. A.6, read in NOTE-844. Distributions that agree on overlaps and sit on a hypergraph with the running-intersection property glue, step by step, to one joint distribution. For sharp measurements this means a chordal compatibility graph. So CHSH’s square and KCBS’s pentagon are the smallest contextual scenarios. Stated and illustrated in the review, not proved there. | Proposed |
| THEORY-309 v2 | If contexts are defined by joint measurability alone, every nondisturbing correlation, maximally contextual ones included, is realized by trivial measurements on a one-dimensional quantum system, so Kochen–Specker contextuality needs a stronger operational notion of context | Budroni, Cabello, Gühne, Kleinmann & Larsson (2022), LIT-263, §IV.B.2, Eqs. 27–28, adapting Fritz (2012), read in NOTE-844. For a nonsignalling p(ab|xy), the POVMs G^{xy}_{ab} = p(ab|xy)𝟙 on a one-dimensional space are jointly measurable for each pair and reproduce p. So contextuality relative to joint measurability alone is trivial, and the review requires contexts of repeatable, nondisturbing measurements. Liang, Spekkens & Wiseman’s sharpness parameter is the other known escape. | Active |
| THEORY-315 v2 | For a state whose four-state reflection orbit is realizable, generalized noncontextuality bounds two binary predictabilities by |⟨X⟩| + |⟨Z⟩| ≤ 1, so the form of a predictability trade-off, not its existence, can witness contextuality | Catani, Leifer, Scala, Schmid and Spekkens (2022), LIT-980, read in NOTE-825. Proved analytically, with a saturating model, for preparation noncontextuality and exact operational equivalence. The bound constrains a whole uncertainty relation only in a theory where every state has the orbit; the qubit’s circle violates it, and a classical theory without the symmetry escapes it. It needs no perfectly distinguishable states, and it is not a sheaf or Kochen–Specker criterion. | Active |
| THEORY-403 | The single-photon Mach–Zehnder phenomenology with balanced beamsplitters and phases 0 or π, including which-way detection, the bomb tester, delayed choice and the quantum eraser, is reproduced exactly by a local, deterministic classical field model with an epistemic restriction, so that slice of interference forces neither complementarity, nor observer-dependent reality, nor nonlocality | Catani, Leifer, Schmid & Spekkens (2021), LIT-019, read in full in NOTE-018. Each mode carries a binary occupation and a binary phase; an agent may know at most one of N, Φ, N⊕Φ; the beamsplitter swaps N_L with Φ_L⊕Φ_R. The model gives the quantum statistics for the phase shifter, which-way detection, the bomb tester (¼), delayed choice and the eraser. The existence proof holds for that fragment. The paper’s further claim, that the model is generalized-noncontextual and so classical by its preferred criterion, is asserted, not proved, and unbalanced beamsplitters already admit a no-go. | Active |
| THEORY-474 | Spekkens’ toy bit theory, restricted to maximal knowledge and post-selected measurements, has a universal, sound and complete ZX-style graphical calculus whose phase-free rules and symplectic check-matrix conditions are exactly those of pure qubit stabilizer theory; the two calculi differ in the phase group, the Klein four-group against Z₄ | Backens & Duman (2014), LIT-054, read in full in NOTE-066. A red–green spider calculus interpreted in the category of relations is universal and sound, and complete by Backens’ stabilizer route. A binary matrix is a valid toy state iff SᵀJS = 0, the stabilizer condition (Lemma 3). The phase-free rules coincide with stabilizer ZX. That the phase group is the only categorical difference is cited, not shown, and completeness leans on analogy for several steps. The paper does no ψ-epistemic analysis and says nothing about which operational difference the phase group carries. | Active |
| THEORY-516 | For any presheaf of propositions over a small category of contexts, a sieve-valued valuation satisfies the generalized functional-composition condition exactly when it is a subobject of that presheaf, and the construction runs unchanged in classical physics, where every microstate gives a global section yet truth values are still non-Boolean sieves; so the logic of the truth values is fixed by the base category, not by whether a presheaf has global sections | Butterfield & Isham (1998), LIT-381, read in full in NOTE-329: Theorem 4.1 proves that generalized FUNC is exactly naturality of ν : G → Ω, for any presheaf G of posets on any small category. In classical physics the value presheaf has a global section per microstate (3.6–3.7), yet the macrostate and microstate valuations are sieve-valued, and NOTE-329 shows excluded middle failing at a microstate. Isham & Butterfield (1999), LIT-389 (NOTE-334), adds that Ω is unique for a given topos and that a base with one arrow between any two objects gives two-valued logic. The choice of base, and so of the logic, remains free. | Active |
| THEORY-524 | On cyclic measurement scenarios, where the contexts’ overlaps form one chordless N-cycle, the ℤ/2 Čech obstruction computed on the (N−1)-th iterated joint model is exact for logical and strong contextuality, the bound N − 1 being tight; beyond cycles no such result is established, the published extension is false on its own example, and the completeness conjecture fails on a Kochen–Specker cover that is never detected at any level | Carù (2018), LIT-280, read in NOTE-253, and the same result republished as Thm IV.32 of Carù’s 2019 thesis, LIT-281, read in NOTE-254. The cyclic theorem is proved and was confirmed on Hardy, on the (2,2,4) counterexample and on 659 random contextual cycle models. The failures beyond cycles (Prop 8.2 / IV.34, the §8 cover, Conjecture 9.1 / IV.41) are the readers’ computations and a lifting lemma, not the author’s. The joint models grow exponentially; nothing analyses the cost. | Active |
| THEORY-526 | The Čech cohomology obstruction of a support section is a sound but incomplete witness of contextuality: it vanishes exactly when the section lies in a compatible family of integer combinations of support sections, so it is non-zero on every section of every All-vs-Nothing model, over any coefficient ring, on a connected cover, yet it misses the Hardy model entirely, part of a strongly contextual Kochen–Specker cover, and every section of a strongly contextual model on the fully symmetric (2,2,4) Bell cover | Abramsky, Mansfield & Barbosa (2011), LIT-277 (NOTE-250); Abramsky, Barbosa, Kishida, Lal & Mansfield (2015), LIT-278 (NOTE-251); Carù (2017), LIT-279 (NOTE-252). The criterion (Prop 4.2 / Prop 16) and the All-vs-Nothing theorem (Thm 21) are proved; the three failures are explicit models, which the readers re-computed exactly over ℤ and ℤ/2. Two steps are the readers’: that the §8 cover and the (2,2,4) model admit no All-vs-Nothing argument over any ring, by Thm 21 read contrapositively. The witness is possibilistic, so it cannot grade anything below strong contextuality. | Active |
| THEORY-553 | In the Döring–Isham topos representation of quantum theory a bounded physical quantity cannot take values in the topos’s real-number object; it is represented faithfully by an arrow from the spectral presheaf to a presheaf of monotone real functions over subcontexts, so its value at a context is a spread that widens as the context shrinks, and these values form only a commutative monoid, under which sums of daseinised quantities are not daseinisations of sums | Döring & Isham, paper III (2007/8), LIT-299 (NOTE-290), restated with additions in LIT-378 (NOTE-326). The Gel’fand transforms of daseinised operators grow as contexts shrink, so arrows into the constant presheaf ℝ are impossible (3.3–3.4). Each  gives a natural transformation δ̆^o(A) : Σ → ℝ^⪰ (Thm 3.1), and  ↦ δ̆^o(A) is injective, by de Groote’s results. ℝ^⪰ is a monoid, not a group; differences need a group completion, whose global elements are the functions of bounded variation on the context poset. No choice among the candidate value objects is made, and the state-dependent reading of the spread is cited, not proved. | Active |
| THEORY-559 | In Kolmogorovian probability, joint distributedness is transitive, so representing a measurement by one random variable in every context it occurs in already puts all measurements of a connected system on one probability space; within that representation a Kochen–Specker or Bell contradiction refutes the context-independent identification of measurements, not the existence of a joint distribution | Dzhafarov & Kujala (2017), LIT-836, read in full in NOTE-623. The transitivity step is an elementary proof; the reading of the reductio is an argument that rests on it. It binds the random-variable representation only: the sheaf account keeps one variable per measurement and asks whether marginals glue, and a reader who holds that view is not bound by it. The paper also proves that a coupling of a binary connection is multimaximal iff adjacent pairs, ordered by their means, are maximally coupled (Theorem II.3). | Active |
| THEORY-580 v2 | On any cover of a space of input histories, the empirical models compatible with a causal structure are exactly the points of a polytope cut from a product of simplices by linear causality equations, so how much of a model a causal structure can explain is a linear program; causal separability is relative to an assumed ambient structure, and the causally separable fraction is never less than the separable local fraction | Gogioso and Pinzani (2023), LIT-788, skimmed in NOTE-624, with the proofs of the causaltope theorems (2.18, 2.19, 2.25) and of the lower bound (2.29) read and checked on promotion (2026-10-20), against the definitions they take from The Topology of Causality. The proofs are short because the work is in the definitions; the one step left implicit closes. The quantum switches witness indefinite order only relative to an ambient space with known no-signalling constraints, not absolutely. | Active |
| THEORY-619 | Over the poset of commutative von Neumann subalgebras, coarse-graining a projector to a smaller subalgebra is exactly the direct image of its clopen region of the Gelfand spectrum under restriction, so the coarse-graining presheaf is the presheaf of clopen spectral regions; and a quantum state’s sieve-valued truth values are fixed by one coherent family of regions, its supports: a proposition is true at a subcontext exactly when the support there lies under the coarse-grained proposition | Butterfield & Isham (2001), “Topos Perspective on the Kochen-Specker Theorem: IV”, LIT-382, read in full in NOTE-328. §2.4 proves G ≅ CloΣ: restricting the characters of V₁ that make P̂ true gives exactly the characters of V₂ that make its coarse-graining true, via a cited state-extension theorem. Theorem 3.1 shows that any assignment defined by “support ≤ coarse-grained proposition”, with supports forming a global element of G, is a sieve-valued valuation obeying FUNC; a state’s supports qualify. Both theorems are close to definitional. Nothing here builds Heyting operations on clopen sub-objects. | Active |
| THEORY-623 | In the two tests of contextuality in language data that the record has read, the contextuality is put there by the experimenter or not secured: meaning-selection models of ambiguous phrases estimated from corpora are all signalling and their two Contextuality-by-Default verdicts are plausibly noncontextual by their own bootstrap, while BERT’s 52 million anaphora models have a support fixed by the sentence schema, so whether each counts as contextual depends only on how uncertain the model’s three referent choices are | Lo, Sadrzadeh & Mansfield (2024), LIT-844, read in NOTE-648, and Wang, Sadrzadeh, Abramsky & Cervantes (2021), LIT-842, read in NOTE-645. Both readings recomputed the criteria. That 71.1% CbD-contextual measures BERT’s uncertainty is NOTE-648’s derivation from the stipulated support (CNT1 = 2 − Δ). The only possibilistically contextual phrase model has hand-set supports. Neither study uses human judgements, so neither bears on whether people’s interpretations are contextual. | Active |
| THEORY-720 | Classical simulations between no-signalling empirical models on finite scenarios, which may change the cover, never create contextuality: a model is non-contextual exactly when the empty model simulates it, the non-contextual fraction cannot fall along a simulation, strong contextuality is reflected backwards, and only non-contextual models can be cloned | Karvonen (2018), LIT-846, Theorems 4.1, 4.3 and 4.5, read in NOTE-651; Abramsky, Barbosa, Karvonen & Mansfield (2019), LIT-847, Theorems 21 and 22, read in NOTE-647. A classical simulation answers each measurement of the target by a jointly measurable set of the source’s, with shared classical randomness, so the cover may change. Non-contextual models are exactly those the empty model simulates, NCF cannot fall along a simulation, strong contextuality is reflected backwards, and a model clones itself only if it is non-contextual. No-signalling models on finite scenarios only. Which maps are simulations is THEORY-174’s open half. | Active |
| THEORY-722 | In Contextuality-by-Default 2.0, whether a system of non-binary variables is contextual depends on which variables represent the measurements: coarse-graining can turn a noncontextual system into a contextual one, while for connections of two variables, and for consistently connected systems, CbD 1.0 and 2.0 agree | Dzhafarov & Kujala (2017), LIT-831, Examples 1–3 and Section 4, read in NOTE-643 (claims C4 and C6). Under multimaximal couplings, lumping values of non-binary variables can destroy every multimaximal coupling, so a noncontextual system becomes contextual. The verdict on a fixed set of measurements therefore depends on which variables represent them. For connections of two variables, hence cyclic systems, and for consistently connected systems, the 1.0 and 2.0 definitions agree. It does not say the coupling choice changes verdicts in larger connections, which is THEORY-168’s asserted part. | Active |
| THEORY-875 | Phenomenal binding of the parts of an experience can be modelled as agreement, on overlaps, of measured similarity structures assigned to the parts by a presheaf, and the broad quale is fixed by its parts exactly when that presheaf is a sheaf; a sheaf failure may mark disunity, as proposed for binocular rivalry, or context dependence within one unified experience, as in the Ebbinghaus illusion, and the framework does not yet say which | Lee-Youngzie, Tsuchiya, Robinson, Dietz & Monti (2026), LIT-1352, read in full in NOTE-1059. A hypothesis article with no data. It proposes the presheaf and two readings of its failure, disunity for rivalry and context dependence for the Ebbinghaus illusion, without a criterion between them. It does not identify unity with a global section, since it assumes unity always holds. Its global section is measured data, its worked topology example is malformed, and by its own definition of gluing the rivalry case is not a sheaf failure. It answers QUESTION-255 only by showing that a sheaf failure need not be disunity. | Proposed |
| THEORY-1170 | A convex map between two scenarios’ model sets is induced by a classical adaptive procedure exactly when some non-contextual model of the corresponding adaptive hom scenario induces it | The adaptive analogue of Theorem 44 that Barbosa, Karvonen and Mansfield assert in Closing Bell (LIT-845, §6.2) without proof, split from THEORY-174 when the fifteenth status review narrowed that entry to the non-adaptive procedures its re-derivation covers and promoted it (ADR-047, kind 1: a dropped clause the source asserts). The non-adaptive route does not transfer as it stands, since Lemma 39 fails for adaptive procedures. Proposed until a proof is read or re-derived. | Proposed |