Proposals for observations in closed quantum gravity must specify how unresolved microscopic alternatives become measurement outcomes. We compare a recent independent-sum prescription with the same authors' earlier diagonal sum. A three-dimensional calibration changes a normalized probability from 2/3 to 1/2 under an unresolved basis sign change, while the projector probability remains 3/5. We propagate the associated Gram repair through the state functional and identify its selected-ray postselection. We then extend the earlier finite Gaussian microscopic model to separable anisotropic covariance and arbitrary predetermined finite recorded experiments. Its derived weight covariances give a total variation bound without assuming independent outcomes. Bayes conditioning on successful preparation yields an explicit microsector law and a uniform conditional-history bound that vanishes as the environmental effective rank grows. A pair of successive noncommuting measurements shows that two instruments with the same first outcome probabilities retain a nonzero history discrepancy in this limit. The results apply to the specified random-state ensemble and clarify what normalization and environmental concentration can establish. They do not derive a gravitational action, gauge-covariant apparatus, or the full reconstruction required by the motivating Grand Challenge. This preprint was written by exactory.ai (https://www.exactory.ai), an AI research system. The human author, Shiroshita, Ryosuke, authorized its preparation and publication and is responsible for it.
Proposals for observations in closed quantum gravity must specify how unresolved microscopic alternatives become measurement outcomes. We compare a recent independent-sum prescription with the same authors' earlier diagonal sum. A three-dimensional calibration changes a normalized probability from 2/3 to 1/2 under an unresolved basis sign change, while the projector probability remains 3/5. We propagate the associated Gram repair through the state functional and identify its selected-ray postselection. We then extend the earlier finite Gaussian microscopic model to separable anisotropic covariance and arbitrary predetermined finite recorded experiments. Its derived weight covariances give a total variation bound without assuming independent outcomes. Bayes conditioning on successful preparation yields an explicit microsector law and a uniform conditional-history bound that vanishes as the environmental effective rank grows. A pair of successive noncommuting measurements shows that two instruments with the same first outcome probabilities retain a nonzero history discrepancy in this limit. The results apply to the specified random-state ensemble and clarify what normalization and environmental concentration can establish. They do not derive a gravitational action, gauge-covariant apparatus, or the full reconstruction required by the motivating Grand Challenge. This preprint was written by exactory.ai (https://www.exactory.ai), an AI research system. The human author, Shiroshita, Ryosuke, authorized its preparation and publication and is responsible for it.
Most proposed table-top tests of gravity in the quantum regime use equal-amplitude spatial superpositions and seek either gravitationally induced entanglement or collapse-motivated loss of interference. This paper develops a complementary theory-classification framework in which branch weights are scanned as operational control parameters. A massive source is prepared in a two-branch state∣ψp⟩=p∣L⟩+1−p∣R⟩,or, more generally, in an m-branch state∣ψ⟩=∑a=1mpaeiθa∣a⟩.The elementary two-branch second cumulant p(1−p)(Δq)2 is treated as a baseline branch-resolution law, not as a quantum-gravity signature. The main object is an enlarged witness geometry combining mean response, branch-induced covariance and higher cumulants, operational recoverability, and excess-noise or irreversibility coordinates. The m-branch extension yields simplex and covariance-rank constraints; the n-particle extension distinguishes independent ensembles from collectively entangled branch states by n versus n2 scaling. Recoverability is formulated as a resource-theoretic witness convention: adaptive recovery may use probe instruments and classical feed-forward but may not introduce an independent branch-basis coherence resource; a separate joint-recovery functional captures coherent erasure using accessible source-probe correlations. Worked models illustrate deterministic expectation-value gravity, coherent branch-mediated interaction, effective irreversible branch-basis dephasing, and noisy classical measurement-feedback dynamics. A finite-record, calibrated measurement-feedback bound shows that, within that simulator class, reproducing nontrivial branch-conditioned response requires record distinguishability; the associated record overlaps bound adaptive recovery of source coherence, with response-calibrated corollaries when the feed-forward range is bounded. The resulting framework is not a new microscopic theory of gravity. It is a model-discrimination scheme for locating gravitational response models in a witness space generated by branch-weight, branch-number, and ensemble-size scans.
SCQG Paper 12 of 28 This paper sets out experiments for testing Semantic Commitment Quantum Gravity. It connects the theory’s physical equations to detector records, matched control interventions and decision rules fixed before data collection. The main laboratory proposal uses light coupled to a mechanical oscillator. It compares three conditions. Arm D adds measured noise independently of the record. Arm C measures the system and uses the result for feedback control. Arm S keeps that physical control matched and changes a stored instruction that selects a later action. The contrast C − D tests active record stabilization. The contrast S − C tests whether instruction content changes later choices on new task cases excluded from training and tuning. The paper gives equations for the cavity and oscillator, continuous measurement, feedback, noise, covariance reconstruction, work and heat. The calculations include the physical bath response, detector bandwidth, control latency and approximation error. Calibration and statistical procedures connect predicted changes in physical variability to quantities estimated from repeated runs. A source–receiver protocol distinguishes when a record becomes physically available from when the receiver can reliably identify its source. A separate clock protocol tests whether retained physical records can distinguish different cycles of a repeating clock. Gravity protocols combine causal order, discrete curvature, screen response, energy flux and tensor reconstruction to test the Einstein equation at specified scales. Each protocol specifies the controls, calibration, uncertainty, held-out evaluation, stopping rules and retained data needed to reproduce the analysis. These conditions determine when a result supports the tested prediction, reveals a physical discrepancy or remains inconclusive. This is Paper 12 of the Semantic Commitment / Quantum Gravity series.
Operational theorem package: R′ (resolution), T′ (common-mode invariance), C′ (sub-bin curvature irrelevance), D′ (near-null registrar trivialization), H′ (horizon implementability) This record contains the final manuscript and supporting materials for a strictly operational analysis of quantum measurement in spacetime. Following the introduction of Quantum Measurement Timeline Framework (QMTF), in which a measurement is defined as a POVM statement on a declared spacetime target frameD* = R* × T* at finite resolution (Δx, Δt). An event is the realization of a single POVM effect E_U on one spacetime bin U; all dynamical relations among alternatives—including gravitational influence—belong to pre-event evolution. Within this orthodox setting, we prove a five-part operational theorem package: R′ (resolution). Finite operational resolution is derived, not assumed, from the metrological chain quantum Fisher information → Bures/Fidelity → total variation distance, yielding explicit Δx_min and Δt_min at any discrimination threshold ε_disc. T′ (common-mode invariance). Uniform time dilation or global phases are probability-irrelevant for any POVM; only differential phases can affect outcome statistics. C′ (sub-bin curvature irrelevance). Curvature variations confined below the declared resolution cannot change single-bin event probabilities beyond ε_disc. After Hadamard-controlled spatial and temporal smearing, such effects are common-mode or strictly sub-threshold. D′ (near-null registrar trivialization). With finite information rate, the boundTVD ≤ √(F / 8) · τ implies that no nontrivial discrimination is possible as the registrar’s proper-time budget τ → 0. H′ (horizon implementability). An exterior laboratory cannot implement POVM effects localized strictly in the interior algebra of a black-hole spacetime; interior bins have zero operational support for exterior observers. Together, these results close “gravity at the event” in the single-run semiclassical domain: gravity can only shape pre-event phases and support via proper time and cannot appear as an event-internal degree of freedom at any finite operational resolution. Each theorem is stated with explicit inequalities and clean falsifiers (sub-resolution curvature tests, near-null discrimination limits, and exterior-only interior implementability), ensuring refutability. The framework uses no assumptions beyond standard quantum mechanics (POVMs and instruments) and general relativity (proper time and locality) and is consistent with interferometric observations such as COW neutron interferometry and Kasevich–Chu atom interferometers, where gravity appears exclusively through differential pre-event phases. Keywords: POVM measurement; operational quantum measurement; quantum Fisher information; distinguishability bounds; Unruh–DeWitt detector; Hadamard states; proper time; semiclassical quantum mechanics and general relativity; algebraic quantum field theory; interferometry, QMTF. Author: R. Necsanu ORCID: 0009‑0009‑1281‑9180 Reference record (QMTF): Necsanu (2026), Zenodo 10.5281/zenodo.18262158
We determine the minimum complex-Haar variance of the average purity over exactly n distinct balanced bipartitions of an n-party pure state, identifying complementary subsystems. For each n in {6,8,10,12,14,16}, the same explicit families are globally optimal for every integer equal local dimension d >= 2. The established fixed-pair Haar moment expresses the variance as a positive affine function of an even correlation cost. A parity floor settles n congruent to 2 modulo 4. For n congruent to 0 modulo 4, an established quadratic supersaturated-design bound combines with a strict scalar minorant, proved uniformly in d, to give the nonlinear optimum. The equality conditions characterize the entire minimizing set independently of dimension. We give exact score-gap identities, a direct sixteen-site grid construction, and an obstruction to attaining its bound by adjoining a column to a complete balanced orthogonal core. We also derive the exact mean variance of uniformly sampled families without replacement from the complement quotient. At fixed n>6, the relative gain has order d^(-2) with explicit coefficients; at n=6 every family is optimal. Explicit coordinates and a standalone exact-arithmetic checker accompany the proof. The results concern fluctuations across random states and provide finite benchmarks for selecting subsystems. Correspondence: Ryosuke.Shiroshita@exactory.ai This preprint was written by exactory.ai (https://www.exactory.ai), an AI research system. The human author, Shiroshita, Ryosuke, reviewed the full content and is responsible for it.
Recent work by Nomura and Ugajin has sharpened a foundational puzzle in closed quantum gravity: if the nonperturbative physical Hilbert space of a closed universe is effectively one-dimensional within a superselection sector, how can nontrivial predictions, measurement outcomes, semiclassical histories, and classical probabilities emerge for internal observers? Their answer is partial observability: internal observers access restricted degrees of freedom, and predictions are recovered by conditioning on observational data in an enlarged description. This paper does not modify that physical construction and does not report experimental, observational, or numerical results. It gives a descriptor-relative and question-limited audit of its predictive content. Partial observability is interpreted not as an ad hoc interpretive escape, but as a mathematically natural restriction principle for internal prediction in a constrained quantum system. A physical prediction in a closed universe is closure-valid only when an observer-accessible descriptor, an admissible conditioning operation, and a preserved answer-determining structure jointly determine the answer. The main contribution is a Quantitative Closure Audit. For an internal clock-prediction question, the paper derives a closure condition using a reduced density matrix, clock-difference variance, observer-relative environmental entropy or direct residual bounds, an error hierarchy, and a tolerance threshold. It also introduces upgrade-warning indicators, algebraic alternatives to tensor-factor splits, robust non-Gaussian fallback bounds, a Class II audit of ΛCDM’s strongest closed-universe reading, a Hubble-tension residual marker, executability burdens, estimation rules for S_E and σ_desc, an assumption map, glossary, pseudocode protocol, and finite-dimensional toy illustration. The result is a theorem-side audit tool: partial observability gives prediction, while question-limited closure gives its boundary.
Detector outcome probabilities can be independent of a later measurement setting even when earlier timestamps, detector seeds, or environmental records depend on that setting. We characterize complete-record preservation for a positive wrapped-Cauchy retrocausal spin source. An antipodal identity yields necessary and sufficient conditions for passive and environmental readouts, and source compensation permits a common normalized analyzer for source spins and prepared continuations. Gaussian controller and reset calculations distinguish inverse raw history weights from normalized thermal operations. A quantum instrument provides an operational benchmark, whereas a setting-dependent separable source produces setting-dependent statistics at an earlier joint probe. For two equal-width contexts, a calibrated weak probe requires a minimum source change of sech(2g)/8 in trace distance for exact protection at every nonzero strength. The signal--source-change tradeoff is sharp for this pair of contexts. A contextual positive-history construction recovers the isolated hidden law and preserves records for a specified class of finite adaptive quantum apparatuses, subject to quantum calibration and restricted field access. Direct readout of an added likelihood field distinguishes two future axes with unit probability. The analytical results are supported by continuous-angle and quantum-trajectory simulations, deterministic quadrature, and exhaustive enumeration of a finite policy class. The analysis concerns the specified statistical models; their microscopic physical realization remains an open question.