contextuality.
47 of 1538 NOTE documents. Back to the full index.
| # | Title | Summary | Status |
|---|---|---|---|
| NOTE-013 v2 | Quasi-quantization | Take a classical statistical theory over a phase space Ω = R^{2n} or (Z_d)^{2n}, and allow only uniform distributions over V^⊥ + v, where V is an isotropic subspace (a Poisson-commuting set of linear “quadrature” variables) and v ∈ V gives their values. The result is operationally identical to the quadrature quantum subtheory (the stabilizer formalism for odd prime d) for continuous variables and for odd prime d; the proof is that the Wigner functions of that subtheory are exactly these distributions (§IV.A). For d = 2 the two theories are isomorphic element by element but make different predictions, because the qubit stabilizer subtheory is contextual (§IV.B). | Read |
| NOTE-016 v2 | The sheaf-theoretic structure of non-locality and contextuality | For finite measurement scenarios, an empirical model has a factorizable (local / non-contextual) hidden-variable realization iff its compatible family of distributions extends to a global section (Thm 8.1). Over the reals every no-signalling model has such a section (Thm 5.9: “negative-probability LHV” ⇔ no-signalling, because both span the same subspace, of dimension D = Σ_{U∈𝒰}(l−1)^{|U|}, Thm 5.4). Contextuality comes in three strictly nested strengths (probabilistic ⊋ possibilistic ⊋ strong), with the Bell, Hardy and GHZ(n≥3) models as witnesses of each level. | Read |
| NOTE-017 v2 | A structure theorem for generalized-noncontextual ontological models | Take a tomographically local GPT and any convex-linear, empirically adequate, diagram-preserving map M from it into FVect_R. Then M(T) = χ_B ∘ T ∘ χ_A⁻¹ for unique invertible linear maps χ_A (Thm 4.1). Consequences: - Every diagram-preserving quasiprobabilistic model is an exact (non-overcomplete) frame representation (Prop. 4.3). - Every diagram-preserving noncontextual ontological model has |Λ_A| = dim(A), the GPT dimension (Cor. 4.2, §4.3): exactly d² ontic states for a qudit and 4 for a qubit. - The paper also proves (Cor. 3.5) that three things are equivalent in arbitrary compositional scenarios, without needing tomographic locality: a noncontextual ontological model of the operational theory; an ontological model (simplex embedding) of its GPT; and a positive quasiprobabilistic model of its GPT. | Read |
| NOTE-018 v2 | Why interference phenomena do not capture the essence of quantum theory | The paper models each mode of the interferometer as a classical bit pair (occupation N ∈ Z_2, phase Φ ∈ Z_2). The agent may know only one of N, Φ or N⊕Φ and must be maximally ignorant of the rest. Under that restriction, local and deterministic dynamics (beamsplitter: swap N_L with Φ_L⊕Φ_R) reproduce exactly the 50-50, ϕ ∈ {0, π} Mach–Zehnder statistics (output port L with probability 1 or 0; ½/½ with a which-way detector). The same holds for the Elitzur–Vaidman bomb tester (success probability ¼), delayed choice and the quantum eraser (interference within each P_A outcome class, none within each Q_A class). So this “TRAP” slice of interference phenomenology cannot, on its own, force wave–particle complementarity, observer-dependence or nonlocal/retrocausal influence. The paper leaves aside the phenomenology it concedes is nonclassical (unbalanced beamsplitters, the functional form of the duality relation, Hardy’s interferometer). | Read |
| NOTE-044 v2 | Grangier & Auffèves, What is quantum in quantum randomness? | The paper argues informally, with no equations anywhere in it, that an “elementary” system with a fixed finite number N of exclusive modalities, placed in contexts that can change, must behave unpredictably when the context changes: a return to C1 after C2 cannot be certain, or there would be N² > N joint modalities (p. 4). It asserts that adding one condition, that the context can change continuously, makes the N×N modality-transition matrix unistochastic, i.e. Born-rule, but defers that proof to refs [14, 15] (p. 5). The anti-reductionist conclusion follows from Postulate 0, which declares contexts non-contextual by definition, not from an argument against decoherence. | Read |
| NOTE-235 v2 | Dzhafarov, Zhang & Kujala, contextuality in behaviour | Under Contextuality-by-Default, which separates context-dependent marginals (“inconsistent connectedness”) from contextuality, no behavioural or social data set re-analysed is contextual: 73 poll question-order pairs, Schröder staircases, conjoint choices, 23 primed word combinations and psychophysical matching. The quantum question model’s QQ equality implies noncontextuality, so a quantum model here predicts its absence. The worked Rose–Jackson example mislabels two marginals; its conclusion stands. | Read |
| NOTE-236 v2 | Abramsky, Barbosa & Mansfield, contextual fraction | For any no-signalling empirical model, the contextual fraction CF (one minus the largest weight of a noncontextual sub-model) is a linear programme. Its dual gives a Bell inequality whose normalised violation equals CF, and no Bell inequality is violated more (Theorem 1). CF is invariant under relabelling, non-increasing under translation of measurements, coarse-graining and mixing, and NCF is multiplicative under products (Theorem 2). It lower-bounds the failure probability of Z2-linear MBQC (Theorem 3) and of k-consistent games (Theorem 4). | Read |
| NOTE-237 v2 | Budroni et al., Kochen–Specker contextuality (RMP review) | A review that fixes a minimal definition of Kochen–Specker contextuality as the impossibility of a global joint distribution whose marginals are the context distributions (Fine’s theorem; the sheaf-theoretic framework is one of several equivalent formulations), and that treats Spekkens’s generalized contextuality as a different notion, covered only to mark the difference. | Superseded — by NOTE-844 |
| NOTE-238 v2 | Spekkens, generalized contextuality (2005) | Defines a noncontextual ontological model as one in which operationally equivalent procedures (preparations, measurements, transformations) get identical representations; shows the traditional Kochen–Specker notion is the special case of measurement noncontextuality for sharp measurements plus outcome determinism, proves that preparation noncontextuality implies that outcome determinism, and proves preparation contextuality already for a qubit. | Superseded — by NOTE-748 |
| NOTE-243 v2 | Identifying Quantum Structure in AI Language | Two findings are reported. First, prompted as test subjects on Aerts & Sozzo’s “The Animal Acts” concept-combination test, ChatGPT and Gemini give CHSH values above 2: 4 in a guided conversation, and 2.25 and 3.09 (ChatGPT) and 2.12 and 4 (Gemini) over 81 prompted repetitions, against 2.42 for the 81 humans in 2011. Second, the rank–frequency curve of one 2,861-word Gemini story fits a Bose–Einstein form with energy E_i=(i−1)^0.8 far better than a Maxwell–Boltzmann form. The authors take these as showing that LLM “code is structurally quantum” (§5). The CHSH analysis never checks the strongly context-dependent marginals in its own tables. One reported expectation value disagrees with its table. The Bose–Einstein fit is numerically a Zipf–Mandelbrot law. | Read |
| NOTE-249 v2 | Measurement as Sheafification: Context, Logic, and Truth after Quantum Mechanics | A programmatic essay, with no theorem, model or computation of its own. It restates Abramsky & Brandenburger’s criterion (contextuality and non-locality as the absence of a global section of a presheaf over measurement contexts) and adds three things. It declares measurement to be “sheafification” of that presheaf, without specifying a site, a topology or any sheafified object. It asserts that the Ghose–Patra seven-valued logic is a finite Heyting algebra, without giving an order or operations. It proposes that a quantum potential scaled by 0 ≤ λ ≤ 1 (λ = 1 quantum, λ = 0 classical Hamilton–Jacobi) carries the presheaf continuously to a sheaf, which is asserted, not modelled. Its one worked formula, v2’s Čech “obstruction class” [δs], is a coboundary and so is zero by construction. | Read |
| NOTE-250 v2 | The Cohomology of Non-Locality and Contextuality | For an empirical model e on a measurement cover 𝒰, a section s in the support of context C₁ gets a class γ(s) ∈ Ȟ¹(𝒰, F_{C̄₁}), relative Čech cohomology of the presheaf F = F_ℤ S_e of formal ℤ-linear combinations of support sections. γ(s) = 0 iff s belongs to a compatible family of such ℤ-combinations (Prop 4.2), so a non-vanishing γ(s) is a sufficient but not necessary witness of contextuality (Prop 4.3). γ is non-zero for every section of the PR box, GHZ, the triangle, the 18-vector Kochen–Specker set and the Peres–Mermin square, but it vanishes on the Hardy model and on one strongly contextual Kochen–Specker cover (§8). | Read |
| NOTE-251 | Contextuality, Cohomology and Paradox | For a model whose outcomes live in a commutative ring R, “All-vs-Nothing” (AvN_R) means the R-linear equations satisfied by every support section of every context have no global solution. Theorem 21 proves AvN_R(S) ⇒ SC(Aff S) ⇒ CSC_R(S) ⇒ CSC_ℤ(S) ⇒ SC(S), so every AvN model is strongly contextual with a non-vanishing Čech obstruction on every section. Theorem 4 shows that every state stabilised by an “AvN triple” of n-qubit Pauli operators yields such a model. The “paradox” half proves much less: an informal identification of Liar cycles with strongly contextual support tables, one exact case (the length-4 Liar cycle is the PR box), and the cohomology of paradox deferred to future work. | Read |
| NOTE-252 | On the Cohomology of Contextuality | Carù gives a possibilistic model on the two-party, two-setting, four-outcome Bell cover that is strongly contextual, yet whose Čech obstruction vanishes on all 22 support sections (Fig 4, Table 1). That refutes Abramsky–Mansfield–Barbosa’s Conjecture 8.1 for any symmetry or connectedness condition the Bell cover meets. I confirmed the refutation over ℤ and ℤ/2. The rest is weaker. Odd-degree “higher obstructions” form a hierarchy (Prop 5.5), but every level above the first is empty for every no-signalling model (Prop 5.6). Prop 6.3 restates the known torsor description of Ȟ¹. Prop 6.1 is false in the “only if” direction; the PR box refutes it. | Read |
| NOTE-253 | Towards a complete cohomology invariant for non-locality and contextuality | For cyclic scenarios, where the contexts’ intersection graph is a single chordless N-cycle, Carù proves that ℤ/2 Čech cohomology of the (N−1)-th iterated “joint model” is a complete invariant for logical and strong contextuality (Thm 7.7). I confirmed this on the Hardy model, on his own 2017 counterexample (detected on all 22 sections at level 3) and on 659 random contextual cycle models. The extension beyond cycles does not hold as stated. Prop 8.2 is false on the paper’s own Table 5 model. Worse, the one non-cyclic case the paper claims to repair, the §8 Kochen–Specker cover of Abramsky–Mansfield–Barbosa, is never detected at any level under the paper’s definitions (my proof and computation). That refutes the paper’s closing Conjecture 9.1. | Read |
| NOTE-254 | Logical and Topological Contextuality in Quantum Mechanics and Beyond | The thesis’s cohomology chapters republish the 2017 and 2018 papers with the “joint model” renamed the “line model”. The definitions, Thm IV.32 (complete on cyclic scenarios at level |M|−1), Prop IV.34, Thm IV.36 and Conjecture IV.41 carry over unchanged. So does every defect found in the preprint. Under the thesis’s own Def IV.26, the §8 Kochen–Specker cover of Abramsky–Mansfield–Barbosa is still detected on only 6 of 15 sections at levels 0–3 (my recomputation), and a lifted ℤ/2 family shows it is never fully detected at any level. The context-wise reading the worked examples use detects all 15 sections at level 2. The genuinely new material lies outside the cohomology programme: a probabilistic line-model construction (§IV.7), a valuation-algebra “theory of disagreement” with inference algorithms (Ch V, bound O(k^n·l^{k(n−1)+1}) on (n,k,l) scenarios), and the AvN-triple characterisation of stabiliser states (Ch VI). | Read |
| NOTE-271 | A topos perspective on the Kochen–Specker theorem: I. Quantum states as generalized valuations | Isham & Butterfield show that, for bounded self-adjoint operators with discrete spectrum, a global section of the spectral presheaf Σ(Â) = σ(Â) on the category O_d, whose arrows are functional relations B̂ = f(Â), is literally a valuation obeying the value rule and FUNC. A global section of the dual presheaf D(W) = Hom(W, {0,1}) on the poset W of Boolean subalgebras of projectors is literally a Kochen–Specker 0/1 assignment. The Kochen–Specker theorem (cited, not reproved) is therefore equivalent to “no global sections” when dim H > 2 (§§2.2–2.3). In place of the missing global valuations, they construct contextual truth values in the Heyting algebra of sieves: ν^ρ(A ∈ Δ) = {f: B̂ →  | tr(ρ Ê[B ∈ f(Δ)]) = 1}. For every density matrix these satisfy functional composition, null, monotonicity, exclusivity and unit conditions (§4.4, §5.3, Theorem 5.1). | Read |
| NOTE-277 v2 | A topos foundation for theories of physics: I. Formal languages for physics | The programme paper. Its contention is that a theory of a physical system S is a representation of a typed “local language” L(S) (ground types Σ and R, function symbols A : Σ → R) in a topos. Physical quantities become arrows Σ_φ → R_φ, and propositions become sub-objects of Σ_φ, which form a Heyting algebra. Classical physics is the representation in Sets. The paper proves nothing. Its one argument is that the axiom ¬(A ε Δ) ⇔ A ε ℝ∖Δ is not validated by non-Boolean Heyting representations (§3.2.1). | Read |
| NOTE-279 | The problem of hidden variables in quantum mechanics | Theorem 1 exhibits a finite partial Boolean algebra D, generated by 117 directions in E³, that admits no homomorphism onto Z₂. §4 embeds D in the projections of the spin-1 space of orthohelium’s 2³S₁ state, via α ↦ P J_α². So no assignment of 0/1 values to those quantum propositions respects all the Boolean relations within each commeasurable set. Theorem 0 makes the target precise: a partial Boolean algebra embeds in a Boolean algebra iff its Z₂-homomorphisms separate points. That is, hidden variables in the paper’s sense need enough “global valuations”, and quantum mechanics in dimension 3 has none. The same paper builds a classical hidden-variable model for spin ½ (§6). It argues that von Neumann’s no-go needed additivity on non-commuting observables (Theorem 3). | Read |
| NOTE-290 | A topos foundation for theories of physics: III. The representation of physical quantities with arrows δ̆°(A): Σ̲ → ℝ̲≽ | Each bounded self-adjoint  becomes an arrow δ̆^o(A) : Σ → ℝ^⪰, where ℝ^⪰ is the presheaf of real-valued order-reversing functions on ↓V. At λ ∈ Σ_V it sends V′ ⊆ V to λ(δ^o(Â)_{V′}), and δ^o(Â)_V is the spectral-order-least operator in V above Â. The map  ↦ δ̆^o(A) is injective, but ℝ^⪰ is only an additive monoid, not the real-number object. Its Grothendieck completion k(ℝ^⪰) is an abelian-group object whose global elements are exactly the functions of bounded variation on V(H). | Read |
| NOTE-292 v2 | A topos foundation for theories of physics: II. Daseinisation and the liberation of quantum theory | A projector P̂ is mapped to the clopen sub-object δ(P̂) of the spectral presheaf Σ over the poset V(H) of abelian von Neumann subalgebras, by “daseinisation” (de Groote’s V-support): δ(P̂)V = the least projector in V above P̂. The map is injective and preserves ∨, but only δ(P̂∧Q̂) ⪯ δ(P̂)∧δ(Q̂). This represents the propositional language PL(S) in the Heyting algebra Sub_cl(Σ). A pure state gives the truth object T^ψ, and “A ε Δ” gets the sieve-valued truth value {V′ ⊆ V | ⟨ψ|δ(Ê[A∈Δ]){V′}|ψ⟩ = 1}. | Read |
| NOTE-326 | ’What is a Thing?’: Topos Theory in the Foundations of Physics | The Döring–Isham programme in one volume. A theory of a system is a representation of a typed language L(S) in a topos. In quantum theory, presheaves over the abelian von Neumann subalgebras V(H), daseinisation sends projectors injectively to clopen sub-objects of the spectral presheaf Σ, preserving ∨ but not ∧. A pure state gives sieve-valued truth values. Every bounded self-adjoint  becomes an arrow Σ → ℝ^↔ whose value at a point is a pair of monotone functions, an interval that widens as contexts coarsen. Most of it reprints papers I–IV. New are the inverse-image corollary linking PL(S) and L(S), values in a pseudo-state, and the algebra of the quantity-value candidates. The Heyting structure on Sub_cl(Σ) is still only sketched. | Read |
| NOTE-327 | A Topos Perspective on the Kochen-Specker Theorem: III. Von Neumann Algebras as the Base Category | Hamilton, Isham & Butterfield move the series’ base category from operators (O) and Boolean subalgebras (W) to the poset V of commutative von Neumann subalgebras of B(H). There they restate Kochen–Specker as “the spectral presheaf Σ(V) = Gelfand spectrum of V has no global elements” (dim H > 2, cited, §2.2). They identify the coarse-graining presheaf G(V) = L(V), G(i)(P̂) = inf{Q̂ ∈ L(V₂) | P̂ ≤ Q̂} (Def. 3.1), with the presheaf CloΣ of clopen subsets of the spectra; the isomorphism is asserted, and part IV proves it. A state ρ yields the sieve-valued valuation ν^ρ_V(P̂) = {V′ ⊆ V | ρ(G(P̂)) = 1} (Def. 3.4) and the support projectors inf{P̂ ∈ L(V) | ρ(P̂) = 1}. These form a global element of G and hence an “interval valuation”, a subobject of Σ (§§4.2–4.4). The probability-r valuations give subobjects of G but not global elements. | Read |
| NOTE-328 | A Topos Perspective on the Kochen-Specker Theorem: IV. Interval Valuations | Butterfield & Isham show, over the poset V of commutative von Neumann subalgebras, that sieve-valued valuations and “interval valuations” (assignments of support projectors, or of subsets of Gelfand spectra) determine each other under stated conditions. If supports s(α, V) = inf{P̂ | α_V(P̂) = true_V} form a global element of the coarse-graining presheaf G, then α_{V₁}(P̂) = {V₂ ⊆ V₁ | G(s(α, V₁)) ≤ G(P̂)} is a sieve-valued valuation obeying FUNC (Theorem 3.1). There is an analogue for “tight” subobjects of Σ (Theorem 3.2). Both are satisfied by every state’s valuation ν^ρ. The ordering ≤ (or ⊆) is shown to be the natural relation securing sievehood, null, monotonicity, exclusivity and unit (§4). The review §2.4 also supplies the proof, via state extension, that G ≅ CloΣ: restricting the clopen set of P̂ to V₂ gives the clopen set of its coarse-graining. Part III had only asserted this. | Read |
| NOTE-329 | A Topos Perspective on the Kochen-Specker Theorem: II. Conceptual Aspects, and Classical Analogues | Butterfield & Isham argue that the sieve-valued “generalised valuations” of part I are not a quantum peculiarity but the natural valuations for any presheaf of propositions on any small category. Three supports are offered. (1) Classical physics: the value presheaf Υ(Ā) = Ā(S) on the category M of measurable functions has global sections (one per microstate, eq. 3.7), yet a macrostate R ⊆ S yields a sieve-valued valuation ν^R(A ∈ Δ) = {f_M | B̄(R) ⊆ f(Δ)} (eq. 3.10) with the same FUNC property as the quantum ν^ρ. (2) A proof that a sieve-valued valuation on any presheaf G obeys generalised FUNC, ν(B, G(f)(d)) = f*(ν(A, d)), iff it is a natural transformation G → Ω, i.e. a subobject of G (Theorem 4.1). (3) An informal argument, explicitly “not a genuine deduction” (§5.2), that if partial truth is fixed by which weakenings of a proposition are totally true, the truth value is a sieve. | Read |
| NOTE-333 | Topos Theory and Consistent Histories: The Internal Logic of the Set of All Consistent Sets | Isham takes the poset B of all Boolean subalgebras (“windows”) of the history orthoalgebra UP, ordered by coarse-graining, and shows that the presheaf A_d(W) = {α | some d-consistent W′ ⊇ W contains α} is a subobject of the constant presheaf ΔUP, whereas the naive “realisable in W” assignment is not a presheaf at all (§4.1–4.2). The probability claim ⟨α, p⟩ then gets the sieve-valued semantic value {W ⊆ W₀ | ∃ d-consistent W′ ⊇ W with α ∈ W′} if d(α, α) = p and ∅ otherwise (4.16), a global element 1 → Ω in Set^B, so the logic of “all consistent sets at once” is the distributive but non-Boolean Heyting algebra of sieves on B. | Read |
| NOTE-334 | Some Possible Roles for Topos Theory in Quantum Theory and Quantum Gravity | Isham & Butterfield argue, without proving anything new, that presheaf toposes over a base of “contexts” suit physics because the subobject classifier Ω is fixed by the base. They say this answers the objection that many-valued logics are arbitrary (§2.2), and that it keeps the logic distributive (§1.1). They then sketch seven applications. Five are speculative one-paragraph proposals (frames, observers, causal sets, TQFT, synthetic-differential-geometry time in continuous histories). One (§3.7) recaps their Kochen–Specker results: KS ⇔ the dual presheaf D(Â) = Hom(W_A, {0,1}) on the operator category O has no global sections (dim H > 2), and every state ψ gives a FUNC-obeying sieve-valued valuation ν^ψ(A ∈ Δ) = {f_O : Â → B̂ | Ê[B ∈ f(Δ)]ψ = ψ}. | Read |
| NOTE-600 | Contextuality-by-Default theory | A system is a set of stochastically unrelated bunches (one per context) linked by connections (one per content). It is noncontextual if some coupling of the bunches makes every connection a maximal coupling, which separates context-dependent marginals (“direct influences”) from contextuality. The test is linear-programming feasibility (Theorem 4.1). Signed quasi-couplings always exist (Theorem 6.1), and the minimal total variation minus 1 measures the degree of contextuality. | Read |
| NOTE-612 | The Topology of Causality | Builds the sheaf-theoretic framework for causality over spaces of input histories: causal functions are free assignments of outputs to tip events, causality is continuity in the lowerset topology, and the presheaf of causal functions is a sheaf exactly when the space has no “solipsistic contextuality” (always when tight). Empirical models are compatible families on any open cover; standard empirical models on causal switch spaces, including total orders, are always local. | Read |
| NOTE-623 | Probabilistic Foundations of Contextuality | In Kolmogorovian probability, joint distributedness is transitive, so treating a measurement as the same random variable in overlapping contexts already forces an overall joint distribution. A Kochen–Specker or Bell contradiction therefore refutes that identification, not the joint distribution. Contextuality is restated as the impossibility of a coupling of context-indexed variables whose same-content copies satisfy a property C. For inconsistently connected binary systems, C is multimaximality, characterized by adjacent pairs (Theorem II.3). | Read |
| NOTE-624 v2 | The Geometry of Causality | Empirical models on any cover of a space of input histories are exactly the points of a causaltope, a product of simplices sliced by linear causality equations, which makes supported and causally separable fractions linear programs. Defines causal separability relative to an ambient space and shows, with entangled and contextually controlled quantum switches, that the causally separable fraction is bounded below by the separable local fraction and can equal it. | Skimmed |
| NOTE-629 | Sheaf-theoretic structure of definite causality | Extends the Abramsky–Brandenburger sheaf framework from non-locality (discrete order) to any finite causal order of events. Sections are causal functions over families of inputs on lower sets. Empirical models are causal conditional distributions forming a polytope. Locality is a global section, equivalently a mixture of deterministic causal functions. The authors withdrew the paper in 2024 because its “locale of inputs” is not fit for purpose. This reading finds that Proposition 5’s meet can leave the poset and that distributivity fails. | Read |
| NOTE-640 | Contextuality in canonical systems | Contextuality is to be judged on a canonical representation in which every variable is replaced by binary splits and connections are coupled multimaximally. For two content-sharing k-valued variables with all splits kept, the canonical system is noncontextual if and only if one nominally dominates the other: its probabilities fall below the other’s for at most one value (Theorem 4.6). Only the 1- and 2-splits matter (Theorems 4.1, 4.3). For continuous densities, all splits make any difference in distribution contextual. | Read |
| NOTE-643 | Contextuality-by-Default 2.0 | Replaces CbD 1.0’s maximal coupling of each connection by a multimaximal one (every subset maximally coupled). For binary variables this coupling exists, is unique and has an explicit staircase form (Theorem 1), so a noncontextual system’s subsystems are noncontextual (Theorem 3) and partial and complete (non)contextuality coincide. Cyclic, consistently connected and two-copy systems are judged as before. For non-binary variables multimaximal couplings can fail to exist, can be non-unique, and are not stable under coarse-graining (Examples 1–3). | Read |
| NOTE-644 | Semantic Unification | Puts basic DRT into sheaf form: a DRS is a section of a presheaf of consistent literals, an anaphoric resolution is a cover by variable maps, and the discourse’s meaning is the gluing, unique if it exists (Proposition 1). All the interpretive work is in choosing the cover; the only obstruction to gluing shown is inconsistency, so the paper models context dependence and ambiguity, not contextuality in the Abramsky–Brandenburger sense. Its probabilistic section ranks covers by summed corpus counts, not by gluing distributions. | Read |
| NOTE-645 v2 | On the Quantum-like Contextuality of Ambiguous Phrases | Models meaning selection in two-word ambiguous phrases as a Bell-type measurement scenario. Hand-set supports give one possibilistically contextual (Hardy-type) model; every corpus-estimated model is signalling, so only Contextuality-by-Default applies, under which two noun–verb pairs read in both grammatical orders are contextual (1/30 and 7/30). The paper’s own bootstrap leaves both plausibly noncontextual (probabilities above .56 and .08), on very small counts. | Read |
| NOTE-646 | Combining contextuality and causality | Extends sheaf-theoretic contextuality to causal scenarios by an enabling relation on measurements and a game reading: Nature’s deterministic strategies, which may depend on causal history, replace the event sheaf, and the Abramsky–Brandenburger definitions then go through. Recovers flat contextuality and causal Bell scenarios, and expresses adaptive MBQC by Experimenter strategies. The strategy presheaf is not a sheaf: compatible deterministic local strategies can have no gluing or several. | Read |
| NOTE-647 | A comonadic view of simulation and quantum resources | Makes simulation between empirical models adaptive: measurement protocols form a comonoidal comonad MP, and a simulation of e by d is a deterministic map MP(d ⊗ c) → e with c non-contextual. Proves that such simulations are exactly the conversions by terms in the free operations of the resource theory of contextuality, which now include conditional measurement, with an equational theory and normal forms; the non-contextual fraction is monotone and contextual models cannot be cloned. | Read |
| NOTE-648 | Quantum-Like Contextuality in Large Language Models | Builds a three-sentence anaphora schema with the support of the PR prism, instantiates it 51,966,480 times from Simple English Wikipedia, and takes one referent probability per sentence from BERT: 0.148% of the models pass a signalling-corrected sheaf test and 71.1% the CbD test. Because the schema fixes the support, both verdicts depend only on how uncertain BERT is in the three sentences; the tie to embedding distance is a softmax identity with weak correlations. | Read |
| NOTE-650 | Closing Bell | Answers which maps between the empirical models of two scenarios are induced by classical, non-adaptive procedures: exactly those given by a non-contextual model of a hom scenario [S, T] whose outcomes are procedures, so deciding it is a linear program. A family of compatible local procedures glues into one global procedure exactly when that model is non-contextual; the rest are “contextual simulations”. The hom construction makes scenarios with predicates a closed category. | Read |
| NOTE-651 | Categories of Empirical Models | Gives empirical models on different measurement scenarios a category: a simulation answers each target measurement with a jointly measurable set of source measurements and a stochastic outcome map natural in the context. Non-contextuality becomes simulability from nothing, the non-contextual fraction becomes a functor (contextuality cannot grow along a simulation), strong contextuality is reflected, Graham reductions are simulations, and contextual models cannot be cloned. | Read |
| NOTE-654 | Analysing Ambiguous Nouns and Verbs with Quantum Contextuality Tools | Proves that in a binary cyclic system CbD’s signalling quantity Δ is twice the sum of each content’s minimal direct influence over Jones’s canonical causal models, which is the total-variation distance between its marginals. In 90 rank-2 noun–verb systems from British corpora, Δ is about 1.35 for every ambiguity class, and homonymous verbs carry about 70% of it against about 50% for polysemous verbs. That difference rests on 14 systems from six verbs and is marginal by a recomputed test (p ≈ 0.06 two-sided). No system is tested for contextuality. | Read |
| NOTE-737 v2 | Schmid, Selby & Spekkens — Unscrambling the omelette of causation and inference | In a process-theoretic framework that keeps causal and inferential structure apart, generalized noncontextuality becomes the demand that a realist representation preserve inferential equivalence. A Leibnizian classical realist representation implies a generalized-noncontextual one, so every noncontextuality no-go theorem is a no-go for Leibnizian representations; the converse is a conjecture. Bell-like theorems deny any classical realist representation, a weaker assumption, while noncontextuality theorems apply even to a prepare-measure scenario with no Bell-like constraint. | Skimmed |
| NOTE-748 | Spekkens — Contextuality for preparations, transformations, and unsharp measurements | Noncontextuality, redefined operationally so that operationally equivalent procedures get equivalent representations, fails for a qubit’s preparations, transformations and unsharp measurements, where no traditional Kochen–Specker proof exists. Preparation noncontextuality over the full set of quantum states implies outcome determinism for sharp measurements, so the old Kochen–Specker proofs refute universal noncontextuality. Measurement noncontextuality alone is consistent with quantum theory. | Read |
| NOTE-825 | Catani et al. — What is nonclassical about uncertainty relations? | For any state whose four-state reflection orbit is realizable (equal predictabilities with flipped signs, and ½s1+½s3 = ½s2+½s4), preparation noncontextuality forces |⟨X⟩| + |⟨Z⟩| ≤ 1, tight, without perfectly distinguishable states. In a theory where every state has such an orbit, the bound constrains the uncertainty relation itself: the qubit’s circle violates it, up to √2, the stabilizer octahedron saturates it, and the simplicial theory escapes it because its jointly predictable states lack the orbit. | Read |
| NOTE-844 | Budroni, Cabello, Gühne, Kleinmann & Larsson — Kochen-Specker Contextuality | A review of Kochen–Specker contextuality. It defines noncontextual hidden-variable models minimally, as a global distribution whose marginals are the context distributions (Fine’s theorem), with the sheaf, polytope, graph and hypergraph formulations called substantially equivalent. It argues that contexts need an operational definition stronger than joint measurability, which alone makes every nondisturbing correlation classically realizable. It surveys how disturbance is modelled in experiments, Kujala et al.’s maximally noncontextual models among them. Spekkens’s generalized contextuality is covered only to mark the difference, and the review nowhere derives the relation between the two notions. | Read |
| NOTE-1059 | Lee-Youngzie et al. — Towards a mathematical structure of global phenomenal consciousness | A hypothesis article with no data. It maps the parts of an experience, ordered by subsumption into a finite topology, to similarity-judgement matrices of their qualia by a presheaf, and reads compatibility of narrow qualia on overlaps as the condition for phenomenal binding, and the presheaf’s being a sheaf as the broad quale’s being determined by its parts. It reads a sheaf failure as disunity in binocular rivalry and as context dependence in the Ebbinghaus illusion, and gives no rule for telling the two apart. Its worked topology example is malformed, and by its own definitions disagreement on an overlap is not a sheaf failure. | Read |