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.
Quantum foundations — what quantum theory says about the world — contextuality, epistemic restrictions, interference, reconstructions and toy theories, quantum thermodynamics.
76 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-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-017 v6 | In a Hilbert-space model only unitarily invariant structure is intrinsic; a basis or tensor factorisation, and so any parts or features, is extra data supplied from outside the space, and the record’s Hilbert-space works differ in where they get it | Carroll (2021), LIT-123: a quantum theory is fixed up to unitary equivalence by the Hamiltonian’s spectrum, and subsystems come from a factorisation that the dynamics must select. Van Rijsbergen (LIT-262) computes only traces and inner products, and treats each observable’s eigenbasis as a “point of view”. DisCoCat’s ε/η composition (LIT-273) is orthogonally covariant, while its Frobenius sequel (LIT-272) stipulates a basis and composes by elementwise product in it. THEORY-004 is the same point for learned representations. This is a synthesis across the four, not a result any one of them states. It does not say that basis-dependent models are wrong; it says what they have assumed. | 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-021 v2 | In the exact configurations of uniform superposition (regular polygons, the tetrahedron, antipodal pairs, and tegum products of these that span the hidden space, with equal norms within each factor) the features form a rank-one POVM compressed from the n-feature basis: their dimensionality-weighted projectors sum to the identity | Elhage et al. (2022), LIT-323, found that features in uniform superposition settle into polytopes and tegum products, with feature dimensionalities clustering at 3/4, 2/3, 1/2, 2/5 and 3/8. The tight-frame and POVM reading is the reader’s inference in NOTE-278, checked numerically there. It was refined when filing: a tegum product is not globally tight, but the Dᵢ-weighted POVM still sums to the identity. None of this is in the paper. It does not make superposition contextual or quantum, and it says nothing yet about trained real models. | 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-041 | Birkhoff and von Neumann proposed the modular law, not orthomodularity, and proved it fails for closed subspaces in infinite dimension; Husimi used the orthomodular identity only as an unnamed proof step | Birkhoff & von Neumann (1936), LIT-306 — the lattice of closed subspaces is orthocomplemented and not distributive. They propose modularity (L5), motivated by a dimension function, and give an explicit infinite-dimensional pentagon that breaks it. The word “orthomodular” does not occur. Husimi (1937), LIT-357, derives modularity as the parallelogram law under a finite-chain assumption and uses the orthomodular identity as a step without naming it. Citing either paper for “the orthomodular lattice of quantum logic” misattributes it. | Active |
| THEORY-042 | Under a superselection rule a coherent superposition across sectors is operationally a mixture, because no observable connects the sectors; Wick, Wightman and Wigner proved such a rule for integer versus half-integer spin and only postulated it for charge | Wick, Wightman & Wigner (1952), LIT-339 — they define a superselection rule and show that a superposition across sectors “is not a pure state, but a statistical mixture”. They prove the rule from time reversal for integer versus half-integer angular momentum, and postulate it for charge with “no conclusive evidence”. What follows for Birkhoff–von Neumann’s lattice (LIT-306), a product of sector lattices with central sector projections, is the record’s inference. The centre-of-the-algebra formulation belongs to Haag, who is not read. | Active |
| THEORY-160 v2 | In the algebraic Hamiltonian setting, symmetry and conservation correspond because the bracket is antisymmetric, which for a bilinear bracket is each observable conserving itself; the theorem’s content lies in identifying observables with generators | Baez (2020), LIT-819, read in NOTE-630, Theorems 3, 4, 8 and 10, with Alfsen and Shultz’s theorem quoted as Theorem 12 and not checked here (QUESTION-142). With unique solutions to the flow equations, “a generates symmetries of b iff b generates symmetries of a” is {a, b} = 0 ⇔ {b, a} = 0. It assumes reversible one-parameter groups and an observable–generator map; it says nothing about dissipative or stochastic dynamics, nor about the Lagrangian form of Noether’s theorem. | 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-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-255 v3 | In Aerts’s subspace model of Hampton’s membership data, and in any lattice whose membership weight is order-preserving, whatever its negation, taking concept conjunction and disjunction as meet and join cannot produce overextension or underextension, so a model of the guppy-type deviations must take conjunction as some operation other than the meet or drop the monotone weight, while the Kolmogorov-type deviations can be had from the meet of a non-Boolean subspace lattice | Aerts (2009), LIT-934, Theorem 9 and §§2.2–3.3, read in full in NOTE-808. The impossibility is a proof, and it needs only that membership is monotone in the subspace. The fits that place the k-type deviations in a tilted subspace lattice and the ∆-type ones in an emergent sector are models with free parameters, not tests. Negation appears only as the orthocomplement used to derive the conjunction model from the disjunction model; no negated concept is measured. | Active |
| 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-416 | Quantum thermodynamics has at least four inequivalent notions of work, the ensemble average, the two-point-measurement random variable, the ε-deterministic single-shot work content and the resource-theory work, which answer different operational questions; only the two single-shot optima coincide, by identification of formulas and for energy-diagonal states | Vinjanampathy & Anders (2015/16), LIT-010, read in full in NOTE-011. The review’s one synthesis (§5.2, §7) sets four definitions side by side: ⟨W⟩ = ∫tr[ρḢ]dt (Eq. 2), W = E_m^(τ) − E_n^(0) (Eq. 24), A^ε ≈ −kT ln(Z_Λ*/Z) (Eq. 49) and w^max_ε = F^min_ε(ρ_S) − F(τ_S) (Eq. 50). Only the last two agree, and that agreement is an observation that two published formulas match, for states diagonal in energy. It is an informed judgement of a 2016 snapshot, not a theorem that the notions cannot be unified. | Proposed |
| THEORY-455 | Every finite stochastic transition matrix on a configuration space equals the entrywise squared modulus of a complex matrix, unitary after dilation, so the Hilbert-space formalism can be written over any indivisible stochastic process as a non-unique representation; within that representation interference is the term by which the process fails to divide at an intermediate time, relative to the chosen configurations, and an ideal correlating environment restores divisibility | Barandes (2023), LIT-086, read in full in NOTE-080. Γ_ij = |Θ_ij|² = tr(Θ†P_iΘP_j) is an identity (Θ_ij = √Γ_ij works), and a unitary Θ on the original space exists only for doubly stochastic Γ. Interference is the cross-term of Eq. 43 against a would-be Markov factorization, and a perfectly correlating environment that then evolves separately makes the process divisible (Eqs. 45–56). The “emergent” Schrödinger equation is the definition of H, unitarity is a choice the claimed gauge freedom does not preserve, and the decomposition is relative to a configuration basis the paper never fixes. | Active |
| THEORY-459 | Exact duality between two models is incompatible with ontological emergence of one from the other, reductive or not, because a duality is an isomorphism and ontological emergence needs a non-injective linkage whose interpretation does not commute; the two combine only when emergence runs beside the duality, as along the radial direction in AdS/CFT, through an approximate duality, or as merely epistemic emergence | De Haro & Butterfield (2025), LIT-199, §14.3, read in NOTE-178. A formal argument from equinumerosity and surjectivity, strictly proven for finite sets, with an argument on physical grounds for the infinite case (fn. 57). Emergence here is novel reference in the domain of application, a semantic condition, not an information measure. AdS/CFT is the exception only to incompatibility with non-epistemic emergence, not to “not indicative”: on a theoretically equivalent reading, its “emergent gravity” “cannot be understood as ontological emergence”. | Proposed |
| 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-479 | Shannon’s chain rule is the 1-cocycle equation of a cohomology of finite probability spaces whose action is averaged conditioning, and on connected, sufficiently rich structures of partitions every measurable 1-cocycle is a constant multiple of Shannon entropy, with no symmetry or continuity axiom assumed; in the unitary-invariant quantum version the first cohomology vanishes and von Neumann entropy is the 0-cochain whose coboundary is minus Shannon entropy | Baudot & Bennequin (2015), LIT-053, read in NOTE-088. Theorems 1 and 3 are proved for finite spaces, through the Tverberg–Kendall–Lee result on measurable solutions of the fundamental equation of information. The hypotheses are stated three different ways in the paper; Theorem 1’s is operative. The higher mutual informations appear as coboundaries, and Theorems B, D and F and the synergy reading are sketched or deferred to companion papers, so they are not part of this account. | Active |
| THEORY-482 | For a closed quantum system that starts thermal and is measured projectively in energy before and after a unitary drive, the two-point-measurement work obeys the Jarzynski equality and the Tasaki–Crooks relation in exactly the classical form, because those energy measurements erase the coherences in which a quantum difference could appear | Vinjanampathy & Anders (2015/16), LIT-010, read in full in NOTE-011, which reproduces the derivation (Eqs. 24–30). With W_{m,n} = E_m^(τ) − E_n^(0), a thermal start and closed unitary evolution, ⟨e^{−βW}⟩ = e^{−βΔF} follows from Σ_n p_{m|n} = 1 (Eq. 29), identical in form to the classical relation. The identity is exact under its conditions. Its classicality is bought by the definition of work: two projective energy measurements destroy coherences, which is why the definition is contested. It says nothing about work defined without them. | Active |
| THEORY-485 | Wave-function realism falsifies causal closure restricted to spacetime but is compatible with closure relative to fundamental physics, so quantum ontology opens no causal gap for non-physical causes; what it forces on the physicalist is a criterion of the physical and a bridge from dynamical to causal completeness | Poltorak (2026), LIT-164, an unrefereed preprint read in full in NOTE-112. “Every physical effect has a sufficient physical cause” has two tacit parameters, a domain and a completeness relation. With the domain set to spacetime the principle fails under wave-function realism; with it set to the ontology of a complete fundamental theory it survives. The move to a breach needs a premise that wave-function realists deny. The conclusions are modest and close to analytic once the terms are defined. The target is conceded to be a picture, not a published argument, and the dynamical-to-causal bridge is asserted, not argued. | Proposed |
| THEORY-513 | Observational entropy taken relative to a maximum-entropy prior τ, S(τ) − D_M(ρ‖τ), lies between S(ρ) and S(τ) for states meeting the prior’s constraint, is finite and continuous whenever S(τ) is, and reduces to about two dozen textbook entropies by choice of measurement and prior; its second laws are bounds on the time-averaged state’s divergence from the prior, proved small only under sufficient conditions (nondegenerate energy gaps for equilibration, the eigenstate thermalization hypothesis for fit to the prior) | Schindler, Strasberg, Galke, Winter & Jabbour (2025), LIT-082, read in full in NOTE-043, with Proofs 1, 2, 7, 10 and 11 checked line by line. The bounds, the special cases and the decomposition are proved. The central target, a small divergence of the time-averaged state from the prior, is proved for no concrete system; in the paper’s own examples “in none of those cases was the smallness proved here analytically” (p. 12). Unpublished as of the reading. | 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-535 | Quantum systems read as bundles of property-instances with no principle of individuality can have their kinds and their number stated in quasi-set theory, so that N indistinguishable particles get a definite quasi-cardinal without labels; the construction covers kinds and counting only, not states, actualization or dynamics | Holik, Jorge, Krause & Lombardi (2021), LIT-107, read in full from the preprint in NOTE-127. The Lombardi–da Costa ontology of properties makes a quantum system a bundle of instances of universal type-properties, with no principle of individuality. Krause’s quasi-set theory Q, reinterpreted over property-instances, represents an atomic bundle as a qset taking one instance from each qset of indiscernibles, guaranteed by Q’s Axiom of Choice, and N particles as a subqset of quasi-cardinal N. The new formal content is about two pages (§6), the printed proofs contain errors, and states, actualization and dynamics are not formalized. The claims about Kochen–Specker and non-separability are recharacterizations by definition, not results. | Proposed |
| THEORY-545 | Aerts and Gabora’s founding quantum model of concepts is a classical probability model written in a Hilbert space: every context it uses is a projector diagonal in one basis, so the contexts commute and generate a Boolean algebra, its entangled ‘pet fish’ state gives the same statistics as a classically correlated mixture for every context in the model, and its guppy weights are copied from single-concept ratings rather than predicted for the conjunction | Aerts & Gabora (2005), Parts II and I, LIT-312 and LIT-340, read in NOTE-299 and NOTE-294. The structural facts are checks of the published model, not of the authors’ prose: contexts are sums of basis projectors, counts are chosen to match rounded frequencies, and the authors call the result a “quantization” of a set-theoretical model. Part I’s mark of non-classicality (eq. 19) is met by Boolean projection lattices too, and its lattice structure is supposed, not derived. The model as printed is also infeasible in two cells. It does not say that no quantum model of concepts does better. | 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-584 | The quantum fidelity tr√(ρ1^{1/2}ρ0ρ1^{1/2}) is exactly the classical Bhattacharyya overlap of the two states’ outcome distributions minimized over all measurements, and the minimum is attained by a projective measurement whose eigenvalues are square roots of likelihood ratios | Fuchs (1995), LIT-018, read in full in NOTE-021. min over POVMs of Σ_b √(tr ρ0E_b)√(tr ρ1E_b) equals tr√(ρ1^{1/2}ρ0ρ1^{1/2}) (Eq. 3.28), attained in the eigenbasis of M = ρ1^{-1/2}√(ρ1^{1/2}ρ0ρ1^{1/2})ρ1^{-1/2} (Eq. 3.67), whose eigenvalues are √(tr ρ0E_b / tr ρ1E_b) (Eq. 3.92). Proved for invertible ρ1 with a separate support construction, in finite dimension. The fidelity is the unsquared one; Jozsa’s is its square. The thesis says nothing about trace distance, and the analogous problems for Rényi overlaps and the quantum Chernoff bound are left open. | Active |
| THEORY-585 v2 | In the Döring–Isham scheme for realising collections of systems in topoi, disjoint sums of quantum systems compose exactly; along a tensor product of finite-dimensional systems, the pull-back of a constituent’s quantity agrees with the composite’s own quantity at a context exactly when every projection in it with proper support on the first factor has the form P⊗1, so it fails for every non-scalar quantity and no operator on the composite realises the pull-back | Döring & Isham, paper IV (2007/8), LIT-310 (NOTE-285), restated in LIT-378 §§11–13 (NOTE-326). Classical physics satisfies the translation condition (3.18) exactly. For quantum disjoint sums the pull-back of δ̆(A₁⊕A₂) is δ̆(A₁) (Lemma 4.2, 4.24; checked). For H₁⊗H₂ the pull-back gives δ(Â₁)_{V_W}⊗1̂ at each context W, which equals δ(Â₁⊗1̂)_W on contexts V₁⊗ℂ1̂. That it differs elsewhere, and that no operator realises it, are asserted. The rules are “partly experimental”, and the trivial-system rule contradicts the series’ own definition of contexts. | Active |
| THEORY-586 | The ψ-ontology theorems exclude only overlap of the distributions that distinct quantum states induce over ontic states; overlap is sufficient but not necessary for reading ψ as knowledge, so a model in which the state is ψ-ontic in Harrigan and Spekkens’ sense can still have ψ represent partial knowledge | Hance, Rarity & Ladyman (2021), LIT-090, read in full in NOTE-072. The formal ψ-ontic/ψ-epistemic split is contradictory by stipulation, while the informal “ontic” and “epistemic” are not exclusive. So PBR and the related theorems bound the geometry of µ_ψ, not the interpretation of ψ. The paper proves nothing; its positive criterion (Eq. 6) is predictive incompleteness, and its Appendix A makes claims the record’s readings contradict. The defensible paraphrase of PBR is “not ψ-epistemic in the overlap sense, given preparation independence”. | Proposed |
| THEORY-592 | Every unital Banach *-algebra satisfying Gelfand and Naimark’s norm conditions is isometrically *-isomorphic to a norm-closed algebra of operators on a Hilbert space, built from positive functionals by what is now the GNS construction, and a commutative one is the algebra of all continuous functions on its compact maximal-ideal space | Gelfand & Naimark (1943), LIT-313, read in full in NOTE-303. Theorem 1 embeds every normed -ring in B(H) for a Hilbert space not assumed separable; Lemma 1 is the commutative case, resting on Gelfand’s 1941 paper and Šilov’s boundary. The paper never says “C-algebra” or “GNS”. It assumes two axioms it suspected redundant, and notes that a single norm identity may replace two others. It gives the object-level isomorphism R ≅ C(𝔐), not a categorical duality, and nothing on uniqueness or irreducibility of the representation. | Active |
| THEORY-594 | Unitarily inequivalent representations in quantum field theory need not refute ontic structural realism: what does physical work in spontaneous symmetry breaking and in the DHR derivation of quantum statistics is structure across representations, so a structural realist who takes structure to be modal and to span them can accept that work, though the modal conception is undeveloped and the removal of Howard’s premise rests on Baker’s sufficient condition for intertranslatability | French (2010 draft; SHPMP 2012), LIT-170, read in NOTE-162 from the unpaginated preprint. Every technical step is imported (Wallace, Earman, Ruetsche, Halvorson & Müger, Baker); the paper’s contribution is interpretive and informal. The DHR result that statistics and charge kinds follow from the algebra is strong physics; that it favours OSR is French’s reading. The modal “trans-world” structure is proposed, not developed, and the combined third option “obviously requires further elaboration”. | Proposed |
| THEORY-605 | In any ontological model that reproduces the quantum predictions and treats independently prepared systems as having product distributions over a joint state that is just the list of their states, distinct pure quantum states have distributions over the ontic state whose supports overlap in measure zero, so the pure state is fixed by the ontic state; approximate agreement within ε bounds the overlap by 2ε^{1/n} | Pusey, Barrett & Rudolph (2011), LIT-062, read in full in NOTE-030. For any two non-orthogonal pure states, n copies prepared independently and an entangled measurement in which each outcome is impossible for one product preparation force zero overlap; with ε error, D(µ0, µ1) ≥ 1 − 2ε^{1/n} (Eq. 7). Determinism and locality are not assumed. Preparation independence, in its strong product-space form, carries the weight, and dropping it permits ψ-epistemic models. The theorem excludes overlap, not every reading of ψ as knowledge, and it does not reach theories outside the ontological-models framework. | 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-621 | Indexing each quantum fact to the system it is a fact for, and computing probabilities only between facts relative to the same system, removes the contradiction between the collapse and unitary probability rules in Wigner’s-friend cases; the price is that values are not held at all times or by all systems alike, there is no global view, and no quantum state of the universe | Rovelli (2021), LIT-177, read in full in NOTE-174. For a fact a and exclusive facts bᵢ, the collapse rule Σᵢ|W(c,bᵢ)|²|W(bᵢ,a)|² and the unitary rule |Σᵢ W(c,bᵢ)W(bᵢ,a)|² differ by interference; RQM applies the first only when the bᵢ and c are relative to the same system. Decoherence makes some relative facts stable. The core rule is postulated, not derived, and inter-observer consistency gets one sentence. The chapter is expository, and several of its headline claims outrun its support. | Proposed |
| THEORY-630 | A protective measurement yields the expectation value ⟨A⟩ on a single system in the ideal limit, and with enough observables ψ up to a global phase; this shows ψ to be ontic only if the protection procedure carries no information about ψ, a premise that Zeno and adiabatic protection, which select ψ from a discrete eigenbasis the experimenter chose, do not meet | Gao (2016), LIT-121, read in full in NOTE-140. Under Zeno protection the pointer shifts by exactly ⟨A⟩ with no entanglement (eqs. 1.9–1.13), and projectors on regions plus a current operator give ρ and j (eqs. 1.14–1.16). Gao argues three routes from this to ψ-ontology, claimed to need no preparation independence. All three rest on the premise that the protection does not “know” ψ, which Gao’s own fn. 10 partly concedes is false. The random-discontinuous-motion ontology and the collapse model built on it are further, weaker steps. | Proposed |
| THEORY-631 | Standard unitary quantum theory and the general quantum theory of open systems are intertranslatable on their common domain, so neither dependence nor justification ranks them; the open theory comes out more fundamental only through premises about interpretation, that orthodox and Everettian readings exhaust the complete readings of the state vector, and that density operators precede state vectors in how states are assigned | Cuffaro & Hartmann (2021), LIT-037, read in full in NOTE-077. Stinespring dilation one way and dropping Lindblad terms the other make the two frameworks a tie on ontic dependence (OntFund-1) and on justification (EpFund-1). The verdict for the open theory comes from OntFund-2, which holds only if orthodox and Everettian readings are all that count, and from EpFund-2, which rests on imperfect preparation. Explanatory fundamentality is effectively abandoned. The paper proves nothing formal, and its “tout court” conclusion outruns §4. | Proposed |
| THEORY-635 | If the quantum state of a Bohmian system is identified with the velocity dispositions it induces on the particles, inequivalent states can share one dispositional history: every energy eigenstate of a free particle in a box induces zero velocity everywhere, so the reading erases differences of energy and of typicality unless the map from states to velocity fields is injective for generic solutions, which is conjectured, not proved | Belot (2011), LIT-100, read in full in NOTE-110. Under the guidance law ψ(t) gives a vector field X_t on configuration space, read as a holistic disposition. For a particle in [0,1], each φn(x) = sin(πnx) gives zero velocity everywhere, so infinitely many energy eigenstates share one dispositional history, and the distinction between φ1 and φ2 in energy and typicality is lost. The rescue rests on Goldstein’s unproved genericity conjecture (fn. 41), and the problem arises only for closed systems (fn. 42). It is a counterexample to one reading, not a verdict on ψ’s category. | Active |
| THEORY-656 | A single holistic power of the universe’s configuration, carried by bare matter points, cannot ground a subsystem’s effective wave function without changing the ontology, because the masses in a decoupled subsystem’s Hamiltonian must belong to that subsystem’s particles; dispositions intrinsic to particles or events need no such change | Dorato (2015), LIT-176, read in full in NOTE-105. Against Esfeld et al.’s holistic dispositionalism: when a subsystem effectively decouples, its Hamiltonian’s masses must be intrinsic dispositions of its particles, so the holistic view must alter its ontology between the universal and the effective wave function (pp. 14–15). The argument is moderate and posed partly as questions. The paper’s wider thesis, that events are a common primitive ontology for GRW, Bohm and ψ-antirealist views, shows compatibility only, and Dorato concedes the difference from Esfeld could be verbal. | Proposed |
| THEORY-664 | In a finite-dimensional probabilistic theory with unrestricted effects and local tomography, if every system can steer each of its own states from a composite with a copy of itself, every irreducible state space is homogeneous and weakly self-dual; steering does not yet give strong self-duality, so it stops short of the Jordan-algebraic and quantum state spaces | Barnum, Gaebler & Wilce (2009), LIT-081, read in full in NOTE-082. A bipartite state steers its marginal iff its map on effects is a strong quotient of order intervals (Thm 5.4). With matching dimensions a steering state is an order-isomorphism, and a cone is homogeneous iff every interior state purifies to an isomorphism state (Thm 4.1). Hence universal self-steering gives homogeneity and weak self-duality (Prop. 5.8). The weaker Prop. 5.7 is thinly argued. The C*-algebraic conclusion of §6 needs strong self-duality, which the paper assumes rather than derives. | Active |
| THEORY-669 | Reading the universal quantum state as nomological escapes the costs of reading it as a field only by paying in the theory of laws: on the strong reading, modelled on the classical Hamiltonian, a time-dependent ψ makes laws time-indexed unless the universal state is time-independent, as Wheeler–DeWitt would make it; on the weak and functionalist readings ψ need be neither unique nor time-independent, but only within an extended Humeanism whose criterion would equally make classical fields nomological | Chen (2018), LIT-204 (NOTE-175), maps the realist readings and splits the nomological one into strong and weak. Belot (2011), LIT-100 (NOTE-110), ranks the costs of ψ-as-law: time-indexed laws are the serious obstacle, grades of necessity tolerable. Allori (2021), LIT-200 (NOTE-154), makes ψ an ingredient of the law, which may be time-dependent and non-unique, and so concedes Belot’s point that ψ behaves like an initial condition. Each move is an informal argument. Chen reports, without endorsing, the objection that the weak reading is too cheap, and Allori’s reply embraces the case it treats as a reductio. | Proposed |
| THEORY-687 | For empirically equivalent dual theories read naively, adding the common core as a candidate world does not break the underdetermination, and neither do super-empirical virtues or an overarching theory: each route to a single actual world needs a further metaphysical principle, such as the identity of indiscernibles | Le Bihan & Read (2018), LIT-113, read in NOTE-152 from the accepted manuscript. A nontechnical survey whose central argument is informal. It assumes a duality relates empirically equivalent models (weaker than De Haro & Butterfield’s isomorphism of a bare theory), that each model is read naively and internally, and that structuralism is set aside. Its reading said it supports no existing THEORY directly; this files the conditional verdict the survey argues for, and nothing more. | Proposed |
| THEORY-690 | In the physical dualities examined, theoretically inequivalent duals turn out empirically inequivalent, so dualities yield no genuine in-principle underdetermination; where duals would contradict each other a cautious realist is warranted in committing only to their common core, and because the exact cases’ common cores are rich rather than empty, dualities give no support to structural realism | De Haro & Butterfield (2025), LIT-199, read in NOTE-178. A case-by-case argument over the book’s examples, with a logico-semantic fallback (each dual entails the common core) for a hypothetical genuine case. The rich-core verdict is argued from exact cases (bosonization, electric–magnetic duality, T-duality) and does not reach AdS/CFT or M-theory, where structural-realist readings were proposed and the common core is “partial … ongoing work in physics!”. The commitment holds only where an interpreted common core exists, which the authors say is not true in general. | Proposed |
| THEORY-695 | Two quantum states can be broadcast if and only if they commute, and cloned if and only if they are identical or orthogonal; the theorem is proved for invertible density operators and marks a line within quantum theory, not a witness of nonclassicality | Fuchs (1995), LIT-018, §4.3, read in full in NOTE-021, from the Barnum–Caves–Fuchs–Jozsa–Schumacher manuscript. Fidelity cannot decrease under partial trace or under the broadcasting map, so broadcasting forces equality conditions that make ρ0 commute with the optimal-fidelity operator. Proved for invertible ρ0, ρ1 only. Spekkens’ epistricted classical theories (LIT-007) reproduce no-broadcasting, so the theorem states where broadcastability ends inside quantum theory and does not by itself certify nonclassicality. | 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-721 | On a complex Hilbert space no orthonormal basis or tensor factorisation of given dimensions is distinguished by the space alone, and orthonormal bases correspond exactly to commutative special †-Frobenius algebras; over the reals that correspondence fails | Three results THEORY-017 rested on, held apart from its synthesis. (a) The unitary group acts transitively on the orthonormal bases of a finite-dimensional Hilbert space, and on its tensor factorisations of given dimensions, so neither is fixed by the space; a non-degenerate self-adjoint operator fixes a basis up to phases, and its invariant content is its spectrum. (b) Over ℂ, commutative special †-Frobenius algebras correspond exactly to orthonormal bases: Coecke, Pavlovic & Vicary, LIT-274, Thm 5.1 and §6, in finite dimension; Abramsky & Heunen, LIT-275, Thm 22, for the non-unital ones satisfying the H*-axiom, in any dimension. (c) Over ℝ it fails: ℂ as a real algebra, with multiplication scaled by 1/√2, is a commutative special †-Frobenius algebra with no nonzero copyable vector. | Active |
| THEORY-807 | The guppy-type overextension in Hampton’s membership data arises because a combined concept is in part a new, emergent concept and not only a logical combination of its parts, so human concept combination runs in two superposed layers, one classical and logical and one quantum and conceptual | Aerts’s reading, which THEORY-255’s title carried before the promotion audit narrowed it (batch 018) to the impossibility Theorem 9 proves. Aerts (2009), LIT-934, read in NOTE-808, fits the ∆-type deviations with one emergent subspace per pair and reads thought as two superposed layers. The narrowing was right that the theorem does not force an emergent concept, only dropping the meet or the monotone weight; this entry is the emergence reading as Aerts’s thesis. Filed under ADR-047 v4 so the wide form stays a thesis evidence can confirm or reject. | Proposed |
| THEORY-1053 | Under unitary evolution, two states of a quantum system can each leave a record in another system while themselves staying undisturbed only if they are orthogonal or the record does not distinguish them; so the outcomes that can be recorded repeatably form an orthogonal set, a result that uses only unitarity and repeatability and not the Born rule | Zurek (2009), LIT-1640, eq. (5), read in NOTE-1229. From |u⟩|e₀⟩ → |u⟩|e_u⟩ and |v⟩|e₀⟩ → |v⟩|e_v⟩, preservation of the scalar product gives ⟨u|v⟩ = ⟨u|v⟩⟨e_u|e_v⟩, so either the record is no record or ⟨u|v⟩ = 0. Zurek reads this as the origin of the outcome set of the collapse postulate. It does not give single outcomes, probabilities or which orthogonal set is chosen; that is the interaction’s. | Active |
| THEORY-1055 | In models of decoherence, the information a small fraction of the environment holds about a system rises steeply to a plateau at the system’s entropy H_S, so many disjoint fragments each carry nearly all of it, and this redundancy is high only for the pointer observable; Zurek identifies it with objective existence, many observers learning the pointer state independently and without disturbing the system, though the paper argues and does not prove that a plateau in mutual information gives each observer the same record | Zurek (2009), LIT-1640, section II and Figs. 2–3, read in NOTE-1229. Redundancy R_δ = 1/f_δ, the number of disjoint fragments each holding (1 − δ)H_S of the information about S, is large for states made by decoherence and absent for random states, and peaks sharply at the pointer observable. Those are model results the review cites. The step from redundancy to objectivity (“Large redundancy implies objectivity”) is an identification. The later caveat, that mutual information alone does not guarantee independently accessible records, is not in the paper. Proposed for that step. | Proposed |
| THEORY-1058 | Given constructor theory’s principles of locality and of classical information, a single further prohibition, that two information observables with mutually disjoint attributes have a union that is not an information observable, is enough for a medium to have information attributes that cannot be distinguished, unclonable and jointly unsharp observables, measurements that are deterministic yet unpredictable, irreducible disturbance by measurement, and locally inaccessible information; quantum information is an instance | Deutsch & Marletto (2015), LIT-1663, §§7–8, read in NOTE-1219. Active as a conditional. The derivations are informal but complete arguments from principles II–IX, and each feature is shown in the paper’s own terms with no probabilities. The principles themselves are conjectures. It does not say that superinformation singles out quantum theory, or that the quantum features are derived from anything not already assumed. | Active |
| THEORY-1066 | In constructor theory, a set of attributes is an information variable when every permutation of it and its cloning are possible tasks, and distinguishability is defined afterwards, as the possibility of mapping a variable onto an information variable; so information is fixed by counterfactual properties of a substrate without presupposing distinguishability, and instantiating it is stated as an intrinsic property of the substrate in the sense of referring to no other specific substrate | Deutsch & Marletto (2015), LIT-1663, §§3–5, read in NOTE-1219. Active as a fact about the construction: the definitions are given in that order, and the base they give the recursion of (1.1) is checkable on the page. It does not say that these notions are the intuitive ones, which the authors disclaim, nor that the principles built on them hold. Its “intrinsic” excludes reference to a specific other substrate, not to generic ones, which the cloning task and (5.1) both use. | Active |
| THEORY-1068 | In the founding statement of relational quantum mechanics the states and values of systems are relative to other systems, but the systems are not: the world is assumed decomposed, possibly in several ways, into systems each characterized by the questions that can be asked of it and a finite information capacity, so the relata precede the relations, as an assumption and without an ontology of events | Rovelli (1996), LIT-1635, read in arXiv v2 in NOTE-1227, §§II.C, III.A–B, III.D and IV.A. Active as a textual fact about the paper. It bears out, for 1996, what THEORY-1071 takes from Faye and Jaksland, who quote later texts for it. It does not say that RQM must keep systems prior, nor that the systems are uniquely given: the decomposition is assumed, not argued, and allowed to vary. | Active |
| THEORY-1069 | In a von Neumann measurement the measuring variable’s information about the measured variable grows continuously under the unitary coupling, in Di Biagio and Rovelli’s model as I_{A:B}(t) = sin²(ωt)H_A, so the discontinuity of a quantum measurement lies only in a threshold on when information counts as a fact; with an idealized pure ready state a fact conditional on a pointer value appears at once, which they attribute to the idealization | Di Biagio and Rovelli (2025), LIT-1676, read from arXiv v2 in NOTE-1214, §VII and App. B. Active as mathematics: (B7) follows from (B6), which I rederived; (B8) as printed has a sign error, and the correct form is I_A^max − cos²(ωt)H_A. The continuity is of the expected quantities. A conditional relative fact appears at once in the ideal model, and the full-rank case that would remove that is described, not computed. The authors say the point is not specifically quantum. | Active |
| THEORY-1071 | Quantum mechanics does not entail agential realism: Bohmian mechanics reproduces its predictions with an ontology of individual particles on determinate trajectories, and relational quantum mechanics, the interpretation Barad names as closest, makes values relational while keeping the systems prior to their interactions | Faye & Jaksland (2021), LIT-1672, read in NOTE-1220, §5. Active: the non-entailment follows from the existence of an empirically equivalent interpretation with a different metaphysics, and the authors do not promote that interpretation. It does not say agential realism is inconsistent with quantum mechanics; that is THEORY-1091, a separate and weaker argument. | Active |
| THEORY-1074 v2 | In Di Biagio and Rovelli’s relational account two classical subsystems’ perspectives merge, agreeing on a variable’s value and on each other’s, when they couple to that variable or to each other, and a coupling to a complementary variable can remove a relative fact from a perspective that did not interact; that this answers the combination problem and keeps perspectives consistent is shown only in worked examples computed relative to a single outside system | Di Biagio and Rovelli (2025), LIT-1676, read from arXiv v2 in NOTE-1214, §VI and Apps. D–E. The merge, and the disturbance of a third party’s relative fact, are computed in a three-system example and in Wigner’s friend. The general claims, a solution to RQM’s combination problem and consistency of perspectives, are asserted, not shown; whether they hold is THEORY-1213, Proposed. Every computation is relative to one outside system, where agreement is automatic. This is the same gap THEORY-621 and THEORY-1080 name. | Active |
| THEORY-1075 | In relational quantum mechanics as Di Biagio and Rovelli define it, a fact relative to one system is stable for another, so that the other may sum over it classically, only approximately and only relative to that other system: decoherence of the first system by an environment the second cannot reach gives the classical rule to order of the environment states’ overlap, a differently coupled system may still see interference, and a fact can be stable for a system for which it is not yet a fact | Di Biagio and Rovelli (2021), LIT-1666, read in NOTE-1226, §1 (pp. 2–6). Active: the definitions are the paper’s, and the result follows in a few lines from a partial trace (eqs. 5–8) under two stated conditions, ε small and the third system not interacting with the environment. It does not say that stable facts are absolute, that decoherence settles which outcome occurred, or what fixes the division into systems. | Active |
| THEORY-1076 | For Bohr a phenomenon is the observation obtained under a specified experimental arrangement, epistemic and derivative, with atomic object and instrument presupposed real; his relational holism is epistemic, and the subject–object, knower–known and word–world dualisms are presupposed by his account, so Bohr’s authority does not support agential realism | Faye & Jaksland (2021), LIT-1672, read in NOTE-1220, from Bohr’s writings and the secondary literature. Active as exegesis: Bohr’s own definitions of “phenomenon” (1938, 1949) and the convergence of realist and antirealist readings that Bohr never denied atomic objects. The dualisms half is interpretive and weaker. It does not say that Barad’s view is false, only that it is not Bohr’s. | Active |
| THEORY-1078 | Constructor theory puts constraint in two places: a principle is a law that constrains other laws and is tested through its rivals, and a constructor is a physical thing that keeps its ability to cause a transformation; a task is possible when the laws set no limit, short of perfection, on how well it could be performed and that ability retained, so possibility needs no actual constructor, and constructor-theoretic statements mention none | Deutsch & Marletto (2015), LIT-1663, §§1–2 and footnote 1, read in NOTE-1219. Active as a reading of the paper’s definitions, which are explicit. It bears on A11’s remark that constructor theory “could sharpen” what the record means by “a constraint being real”, and it splits that notion. A possibility is a fact about the laws, which no particular thing realizes; a constructor is realized, approximate and deteriorating. It does not say that the framework’s basic principle I is true, nor that a law of possibility is, or is not, a constraint realized by something (CLAIM-477). | Active |
| THEORY-1080 v2 | In relational quantum mechanics as Rovelli first stated it, the relation between two observers’ descriptions is itself a quantum fact relative to a third system, so no observer’s view can be deduced from another’s and there is no description in toto, only a net of partial descriptions; the views are held consistent only in that the third system predicts correlated outcomes, which is shown for a single measurement and asserted in general | Rovelli (1996), LIT-1635, read in arXiv v2 in NOTE-1227, §§II.D, III.D, IV.A–B. The first half (no deducible relation between views, no in-toto description) is Rovelli’s stated position, well supported by his text. The second half reports that consistency is shown for one case (von Neumann’s correlation, p. 9) and left to the reader in general (p. 15); whether it holds in general is THEORY-1222, Proposed. Rovelli’s own relativity analogy breaks where relativity supplies an invariant, which bears on QUESTION-021 by analogy only. | Active |
| THEORY-1081 v2 | Di Biagio and Rovelli locate the Frauchiger–Renner contradiction and the violation of the Local Friendliness inequalities in one step, a superobserver using facts relative to a friend he holds in full quantum control as if they were his own, which is the classical sum rule applied where those facts are not stable for him; they base quantum ontology on facts relative to systems rather than on stable facts, arguing that stability is itself relational and only approximate and counting the Local Friendliness violation as evidence, with an absolute macroreality emerging only approximately and only relative to systems for which decoherence is strong | Di Biagio and Rovelli (2021), LIT-1666, read in NOTE-1226, §2 (pp. 7–11). The translation of Frauchiger and Renner’s assumption (C) and of Bong et al.’s absoluteness of observed events into the use of eq. (3) across contexts is the paper’s and is clear. That nothing else goes wrong is cited to others, inter-observer agreement is one sentence, and an agent reasoning about himself is left undone. What the paper argues is held; whether relative facts cohere in general is THEORY-1230’s question. | Active |
| THEORY-1091 | Agential realism has no answer to the measurement problem as it stands: holding that measurement never disentangles apparatus and object, it cannot borrow relational quantum mechanics’ treatment of the wave function as bookkeeping without giving up the ontological holism, and its appeal to an improper mixture does not explain why one value is found | Faye & Jaksland (2021), LIT-1672, read in NOTE-1220, §5. Proposed: the authors present it as a challenge (“There might be other more subtle ways”), and conclude only that consistency with quantum mechanics is unshown (“a leap of faith”), not that agential realism is incoherent. The exchange of 2026-10-27 reported it as “an unresolved measurement problem”, which is the strength the text supports. | Proposed |
| THEORY-1093 | In Di Biagio and Rovelli’s reformulation of relational quantum mechanics a relative fact is a conditional probability concentrated on one value: A is a fact relative to B when the relative information I_{A|B} = I_A + I_{A:B} is maximal; since only commuting variables have a joint distribution, perspectives belong to commutative subalgebras of observables, not to quantum systems, so a qubit has none, and the joint distribution is itself relative to a further system, so the relativity iterates | Di Biagio and Rovelli (2025), LIT-1676, read from arXiv v2 in NOTE-1214, §§II–V and IX. Active as a statement of the paper’s definitions and of what follows from them: eq. (7) is an identity, and the restriction to commuting variables follows from the existence of joint distributions. It does not say that this resolves the problems the authors list, that observers play no role in fixing what counts as a fact, or that the choice of subalgebra is given by the physics. | Active |
| 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 |
| THEORY-1213 | In relational quantum mechanics as Di Biagio and Rovelli reformulate it, classical subsystems whose variables couple properly, so as to get correlated, come to agree, so that the merging of perspectives answers the combination problem and the facts held relative to different outside systems never conflict about the same variables | The general claim of Di Biagio and Rovelli (2025), LIT-1676, p. 5: “If the variables couple correctly so as to get correlated, their perspectives will agree”. Kept here when the twenty-second status review promoted THEORY-1074 as a report of the worked examples (ADR-065; ADR-047, kind 1). Asserted, not proved. THEORY-621 and THEORY-1080 leave the same gap open. | Proposed |
| THEORY-1222 | In relational quantum mechanics as stated in Rovelli (1996), rules (i) and (ii), that there is no state except within a further observer’s information and no information without interaction, exclude any contradiction between observers’ views: what a third system predicts of two observers’ information always agrees with what it finds on interacting with them | Rovelli’s general consistency claim (1996), LIT-1635, §III.D, p. 15, kept here when the twenty-second status review promoted THEORY-1080 as a report (ADR-065; ADR-047, kind 1). Shown for one measurement (p. 9) and introduced in general with “The reader may convince himself”. | Proposed |
| THEORY-1230 | In relational quantum mechanics, with facts fixed by interaction and the classical sum rule used only within one context or where facts are stable, facts relative to different systems never yield contradictory predictions in extended Wigner’s-friend scenarios, and a superobserver’s later facts agree with his friend’s | The consistency Di Biagio and Rovelli claim for relational quantum mechanics, filed beside THEORY-1081 by the twenty-fourth status review (ADR-065 §3; ADR-047 kind 1). THEORY-1081, Active, holds what they argue; whether relative facts cohere in general is this entry’s question, with THEORY-1081’s old condition. | Proposed |