Definiteness as Index reads a quantum outcome as an occupancy and rests on one choice of what a fact is. This paper shows that no local unitary physics can replace that choice. The object that would cross from structure to fact is a central two-valued grading that separates the branches of a record, and local unitary physics leaves that type empty. Physics that makes facts must give up unitary record formation, locality, or an algebra preserved by its own dynamics, and the facts it makes are absolute. Cosmological horizons separate record branches for every observer, but exactly only in the semiclassical limit. Results are offered at candidate status without specialist review.
Definiteness as Index reads a quantum outcome as an occupancy and rests on one choice of what a fact is. This paper shows that no local unitary physics can replace that choice. The object that would cross from structure to fact is a central two-valued grading that separates the branches of a record, and local unitary physics leaves that type empty. Physics that makes facts must give up unitary record formation, locality, or an algebra preserved by its own dynamics, and the facts it makes are absolute. Cosmological horizons separate record branches for every observer, but exactly only in the semiclassical limit. Results are offered at candidate status without specialist review.
A switch by itself has no fact attached to it. Call one position "occupied" and the other "vacant", but nothing in the switch tells you which convention you chose. A state becomes a fact only through comparison. This paper asks what follows if quantum outcomes are understood the same way. The answer is definiteness as index. An outcome is an occupancy: a yes-or-no distinction from a reference, located at a region of spacetime and relative to the measurement made there. It records that an outcome obtained, not which. Records can be read, but every reading makes a new fact for the reader rather than carrying an old one across. The Ground. Spacetime is typed into two primitives: extension, carrying total orientation, and sequence, carrying causal order and time orientation. Neither contains the other's orientation. The Index. Outcomes are occupancies over this ground. Quantum statistics are unchanged. In the Frauchiger-Renner argument, every link in the chain joins laboratories separated by extension, and the step that fails joins a record to a later, incompatible measurement separated by sequence. The Weld. What joins the two orientations? On a flat base only responses to spatial handedness can, and in the Standard Model their sole occupants are the axial couplings to the W and Z bosons. The weak interaction, not spacetime, links space and time orientation. The paper makes one postulate: outcomes are occupancies of contexts. It cannot be derived from the ground, the local algebras and the coherence conditions, which force only that the paradox fail somewhere. The postulate supplies what a fact is, and with it where the paradox stops. That postulate is enough. Any reading that locates facts and combines them by a fixed rule must keep incompatible measurements apart, and every such reading is represented exactly by occupancy. Rivals are this canonical form plus an addition. The result holds on curved spacetimes, for general measurements, and in every contextual theory examined, not only quantum theory. Version notes, Rev 3 line:Rev 3 (14 October 2026) extends the representation theorem to curved spacetimes and general measurements, and its necessity result to general probabilistic theories, where it holds in every contextual theory examined (Section 5, Appendix A.9). Submitted for technical scrutiny, not belief.
Wheeler proposed that acts of registration constitute classical reality through the formation of records. Taking the proposal literally requires a structure that turns what a finite observer can distinguish into persistent classical facts, and a condition that makes many local facts one spacetime. Such a structure is proposed on the observer's causal diamond. Quantum field theory and general relativity are unchanged. A record is a settled classical fact, formed when which-outcome information leaves the diamond. A central postulate is the record rule, which fills unrecorded content from the vacuum, conditioned on the existing records. Constitutive descent, the compatibility of nesting in time with gluing across space, is then proposed to join local records into one shared world. A framework is presented together with its consequences. First, gravity responds only to what has been recorded. Two masses that have been recorded, but whose positions remain in superposition, still attract, yet classically mediated gravity cannot entangle them, a prediction testable by tabletop experiments. Second, records are irreversible and only accumulate, and their accumulation carries an arrow, proposed here as the arrow of time. Third, the structure yields candidate values for quantities usually taken as inputs, including three generations, four spacetime dimensions (d = 4), the rate λ = 3/(16π²) at which recording resolution fails per logarithmic scale, the transfer g = 1/d and the Higgs bare quartic λ₀ = 1/8. Companion papers apply the same recording geometry to cosmological observables and to Standard Model mass ratios. No-go results show that local recording cannot fix absolute amplitudes or favour one allowed branch over another. Absolute scales must therefore be set by measured values, and amplitudes and branch selection are proposed to close through Wheeler's self-excited circuit, in which records fix the geometry that defines the observer. Shared reality is thus built from the records settled on each observer's causal diamond, joined by constitutive descent.
The formal reference record for the representation developed in the indexical-fiber preprint. Definiteness as Index gives the minimal reading of quantum outcomes; this document states the representation in which that reading is computed: a flat ℤ/2 local system over spacetime with a binary index, the structure-fact fence, the section-level content and the relational register. The rules of the typing are kept in the Typing Schema, Rev 4.6. Version notes, Revision 5.5 line:Revision 5.5 (15 October 2026) publishes the articulation as a standalone reference record under Definiteness as Index, Rev 3. A status paragraph in §0 places it as the record of the representation, with Definiteness as Index stating the reading. The body is unchanged from Revision 5.4. Submitted for technical scrutiny, not belief.
I present a kinematic representation of quantum definiteness: an account of what a definite outcome is, rather than of the process by which one comes about. The central claim is that whether an outcome has obtained is indexical content about a physical description, not a degree of freedom within it, a fact of the same kind as which point is here or which moment is now. To make this precise, I attach to a four-dimensional causal spacetime M₄ a fiber bundle with structure group ℤ/2 and two-element fiber Ω = {ω₀, ω₁}. The fiber is deliberately bare, carrying no measure, metric, order, or dynamics. Definiteness is simply the value this index takes, relative to a local observable algebra, at a region of spacetime. The representation introduces no new empirical content. It reproduces standard quantum statistics, predicts nothing that would distinguish it from standard quantum theory, and offers instead one coherent packaging of structure the theory already carries, under a discipline that keeps the object from acquiring anything it has not declared. Within that discipline I prove what the index forecloses. No deterministic law diagonal in the pointer basis can act on the index and reproduce Born statistics; it gives winner-take-all selection instead (Theorem 1). Every swap-invariant fact about the bare fiber reduces to a single holonomy class in H¹(M₄; ℤ/2), so the index cannot carry dynamical structure covertly (Theorem 2). The Born measure is not derived but inherited: Gleason's theorem fixes it on the projection lattice in dimension three and above, and the discrete index is provably too coarse to carry it. The positive work is to separate three obstructions to a global description of definiteness that are routinely conflated. A global choice of the manifest value exists exactly when a holonomy class A vanishes, in close analogy with the orientability of a double cover and its first Stiefel–Whitney class (Proposition 2). Distinct from A is C, the failure of a common section across incompatible measurement contexts meeting at one region; distinct again is B, Kochen–Specker contextuality on the projection lattice. I show that A and C are different objects (Proposition 4), and that C and B differ as well (Proposition 4′), leaving open only how C and B relate where both can occur. Throughout, I am explicit about which mathematics is inherited, which is elementary once isolated, and which is my own framing, and about what a dynamics inhabiting this kinematics would and would not be permitted to add. This version (v3) adds the result distinguishing the common-section obstruction from contextuality, on a single-qubit witness, and narrows the one open question accordingly. It settles the typology of the framework, marking which commitments are constitutive of the indexical reading and which are austerity choices relaxable at a stated cost, and records that the austerity's inviolability is secured by the theorems rather than merely stipulated. It adds a rigor clause to the first foreclosure result and a reference to the spontaneous-collapse bounds now under laboratory test. Submitted for technical scrutiny, not belief.
This paper develops a theory-neutral structural result concerning relational descriptions in physics. Many modern frameworks assign physical meaning through interactions rather than observer-independent intrinsic properties. This raises a general composition problem: if facts are generated locally within interaction contexts, what determines their coherent comparison across later chains or networks of interactions? Within a minimal framework of interacting systems, locally assigned relational facts, and maps between fact contexts, the paper establishes an interface necessity theorem: local fact assignments together with bare accessibility structure are not, in general, sufficient to determine unique cross-context composition outcomes whenever later comparison, inheritance, or aggregation of records is permitted. Some additional structure governing admissibility, translation, filtering, compatibility, or equivalence between relational fact spaces is generically required. This additional layer is termed interface structure and is used operationally rather than ontologically. No new force, hidden variable, or replacement dynamics is proposed. Instead, the result identifies a structural requirement linking local relationality to broader coherence. The paper discusses implications for relational quantum mechanics, decoherence-based narratives of record formation, Wigner-type multi-observer scenarios, and broader network descriptions of physical information. This work is related to the broader Horizons-as-Dynamical-Interface Framework (HDIF) program.
This paper is the thirtieth in a sequence developing an interpretive framework that redescribes physical reality as a causally consistent history of information updates rather than as a collection of independently existing objects. It is the second panel of the eighth grouping — a foundational-physics trilogy — and its quantum-structural centre. Paper 29 defined a quantum record's world-side physical-publicity capacity "at any declared admissible grain gamma," deferring the question of which grains are admissible; this paper pays that debt. Its subject is classicality: which observables support stable pointer structures and redundantly recorded outcome information, shareable as "the classical facts." The claim is that classicality is real but not authoritatively global. There is no Global Classicalizer: no physically privileged subsystem or process that primitively fixes the one system/environment tensor cut, the one set of pointer variables, the one authentic decoherent-history family, and the one true coarse-graining. Einselection selects pointer states, but only relative to a declared cut and interaction; the cut is not fixed by the bare global state, because tensor-product structure is observable-induced and admits inequivalent virtual subsystems. Decoherent and consistent histories select no unique family either. What disciplines this is not a global classicalizer but the series' admissibility machinery, here made operational. A classicality verdict is relative to a declared, anti-gerrymandered, challenge-open cut gamma and history-family kappa, is objectively assessable relative to that specification, and is profile-valued (ClassProf). The flagship R-A separates an unconditional kinematic part — a bare state fixes neither subsystem purity and entanglement nor which observables count as local; relative to a declared tensor-product structure it fixes a sharpness profile over the local-observable algebras, which a worked two-qubit Bell-state example computes (the same state is maximally entangled under one factorization and a product under a rotated one), although the Born sharpness of one fixed physical observable is not changed by a mere refactorization — from a conditional dynamical part: if one fixed dynamics admits more than one admissible factorization with distinct robust pointer structures, the classicality profiles need not be unique, an antecedent whose multiple-factorization and pointer-robustness components recent fixed-Hamiltonian searches support (Adil et al. 2026), without yet establishing its redundancy or history-family components. There is no primitive, state-only canonical cut, though a particular dynamics may contingently leave a unique admissible one. R-B lifts the set-selection problem: consistency does not single out a family, contrary inferences are possible, and whether quasiclassicality leaves a unique realm is unsettled; conditional on more than one admissible quasiclassical family, time-extended assertibility is family-relative, with a disposition trichotomy (determinate / admissibly open / spuriously unique). A coherence policy, not a theorem, governs cross-grain comparison: admissible grains agree on the full statistics of genuinely shared observables, while their publicity capacity profiles agree only given a common access and fragmentation specification; elsewhere they are declared incomparable, and the failure to glue globally is itself the signature of no global classicalizer, whose formalization is handed to Paper 31. This discharges Paper 29's grain-deferral and keeps classicality (world-side) type-distinct from warranted public standing (the warrant layer): classicality is grain-relative but objective — there is no primitive state-only canonical cut, and there is no anarchy either. ALAC Paper 30. Second panel of the eighth grouping — a foundational-physics trilogy (29 Public Quantum Records -> 30 Classicality Without a Global Classicalizer -> 31 Spacetime Localization Without a Global Frame). Part of the Consistency-Constrained Information History (Akashic Ledger Architecture Cosmology) series. Presents no new quantum mechanics; results are interpretive (L2) on imported physics (L1).