Varying the probabilities of the branches in a massive spatial superposition provides a controlled way to test gravitational response models. We develop this comparison for fixed source configurations and calibrated probe measurements. The between-branch covariance obeys a pairwise-distance law on the probability simplex and has rank at most one less than the number of occupied branches. Higher cumulants and ensemble-size scans constrain the same response model, although their statistics can also be produced by classical branch mixtures. Coherence recovery adds information when its permitted operations and accessible records are specified independently. For a branch-preserving measurement that produces an irreversible classical record and drives a common feed-forward response, we derive an upper bound on recovered source coherence in terms of record overlaps. A calibrated response diameter converts this into a response--recovery inequality. A second bound relates recovery to the conditional response variances and remains applicable to unbounded feedback with finite second moments. An explicit binary model saturates both inequalities. Coherent momentum transfer provides a contrasting example in which the probe statistics remain branch resolved while an eraser measurement restores source coherence. These comparisons require separate measurements of conditional probe noise, trajectories, and calibration parameters. The bounds apply to the stated classical-record channel; their application to a gravitational theory requires a derivation of that channel from the theory. Branch-weight scans therefore support quantitative tests of specified models without providing a theory-independent criterion for quantized gravity.
Varying the probabilities of the branches in a massive spatial superposition provides a controlled way to test gravitational response models. We develop this comparison for fixed source configurations and calibrated probe measurements. The between-branch covariance obeys a pairwise-distance law on the probability simplex and has rank at most one less than the number of occupied branches. Higher cumulants and ensemble-size scans constrain the same response model, although their statistics can also be produced by classical branch mixtures. Coherence recovery adds information when its permitted operations and accessible records are specified independently. For a branch-preserving measurement that produces an irreversible classical record and drives a common feed-forward response, we derive an upper bound on recovered source coherence in terms of record overlaps. A calibrated response diameter converts this into a response--recovery inequality. A second bound relates recovery to the conditional response variances and remains applicable to unbounded feedback with finite second moments. An explicit binary model saturates both inequalities. Coherent momentum transfer provides a contrasting example in which the probe statistics remain branch resolved while an eraser measurement restores source coherence. These comparisons require separate measurements of conditional probe noise, trajectories, and calibration parameters. The bounds apply to the stated classical-record channel; their application to a gravitational theory requires a derivation of that channel from the theory. Branch-weight scans therefore support quantitative tests of specified models without providing a theory-independent criterion for quantized gravity.
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.
Abstract Decoherent-histories methods identify time-extended alternatives whose diagonal weights may support probabilistic interpretation, while environmental-record approaches ask which alternatives a specified observer can recover. We formulate their intersection as a finite branch-record packing problem generated from one cross-branch construction. A codebook is admissible only if its declared coarse-graining obeys a bounded probability-sum-rule error and its accessible states can be decoded under a specified observer policy with finite error. Uniform reweighting defines a geometric packing number; a communication interpretation additionally requires a preparation instrument. Retrospective resolution is stricter: the base history family is exhaustive, selected histories must cover sufficient physical diagonal weight and be individually recoverable, and the same declared quantum-to-classical measurement channel used for decoding must preserve approximate consistency after histories are refined by its registered outcomes. This measurement-refined condition quantitatively controls the difference between the actual outcome distribution and the normalized diagonal classical-quantum prediction. For uniform branch-record packing and its communication realizations, general converses follow from accessible dimension, fixed outcome count, Holevo-Fano information, and hypothesis testing. Exact models quantify record compression, access, memory, measurement policy, temporal dependence, and shared latent errors. In a jointly realized four-bit benchmark, scalar consistency and recovery admit six histories, whereas direct measurement-refined consistency under the declared local Helstrom instrument admits four at the same tolerances. Finite-sample procedures distinguish held-out recovery achievability, structure-conditional consistency certification, structural converses, independently constructed parameter intervals, and abstention.
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.
Gravity changes clock rates, and the free point-particle action converts proper-duration differences into relative phase. Coherence lost to an unresolved duration difference can be recovered only through a correlated physical record and a conditional correction. I derive an exact ceiling on that recovery. For a uniform phase window of width 0<Θ≤2π and a record retaining M classical values, V≤sinc(Θ/(2M)), attained by equal phase bins. The physical question is what fixes M. I take it to be set by the record interface. With n readable binary lines of which at most S⋆ can be asserted together, the reachable codebook has at most ∑j=0S⋆(jn) words, so V≤sinc(2∑j=0S⋆(jn)Θ), and the coherence deficit falls as n−2S⋆ rather than 4−n. Two cases fix S⋆ by physics rather than by design. A single-quantum position probe of the apparatus coordinate is weight-one by particle number, giving V≤sinc(π/n) at one full cycle and 0.9745 for eight detectors. A peak-assertion budget of S⋆ lines sets the exponent rather than the prefactor. For held or guided branches with matched velocity histories in a weak uniform field, Θ=mgTΔz/ℏ, and a calibrated layer-time count in a static spacetime has rate r=νN, so gravity, the count, quantum phase, record interface, and recovered coherence occur in one operational chain. I state a complete record channel and a protocol that leaves the interfering particle undisturbed.
I register the prediction that no experiment will witness gravitationally induced entanglement between two masses, each in two branches, while their entangling phase stays below 2 rad, at any constant rate at which each mass's environment records its position. Under gravity whose source in each description is a function of the system's reduced state, conditioned on every record that exists, two masses that nothing records stay in a product state at every entangling phase. Recorded masses stay unentangled while the phase is below 4 rad with each mass's share counted once, or below 2 rad with each mass taking its full potential. Every published parameter set computed here lies below both, between 0.0150 rad and 0.594 rad. A witness of gravitationally induced entanglement reported at 5 standard deviations in any such experiment excludes the prediction on its own, whatever the recording rate. Quantized gravity entangles the masses only while each is recorded more slowly than a threshold set by the experiment's parameters, 0.0623 /s at Bose et al.'s, so a null result counts against it only where an experiment establishes its recording rate below that threshold. The source in the description occupying branch A is n_r^A = n_A + f(η) (n_B − n_A)/2, where n_A and n_B are the branches' densities and η is the overlap of the mass's two branch records, e^(−Γ t) at recording rate Γ. The product state is derived; the weight f(η) = η is derived from the stated condition that the source depend affinely on the coherence; the phase bound is computed in a two-branch open-system model and rests on the stated two-body form. Nothing is fitted. The statistic is the reported witness with the recording rate the experiment establishes, read against both predictions at its own parameters; the chance of a false exclusion from statistical fluctuation alone is 2.9 × 10⁻⁷ for each experiment.
SuperTimePosition (STP) and Gravitational Phase-Lock (GPL) are developed as a conditional model program for Bell-type correlations. The proposal retains local response functions and asks whether a hidden phase can become statistically dependent on detector settings through a physical phase-lock process. This changes the measurement-independence premise used in standard Bell arguments; it does not refute Bell's theorem and is not validated merely because Bell inequalities are experimentally violated. This revision adds an exact, bounded finite-lock benchmark. A phase on the circle follows a setting-conditioned diffusion whose stationary density is an equal mixture of two shifted hyperbolic-cosine components. With explicit local binary response laws, the construction yields exactly unbiased marginals, a closed joint probability law, and a cosine correlation with a Bessel-function visibility. It also admits a deterministic local completion. The mathematical closure comes at a measurable cost: Hall's measurement-dependence fraction falls below one half at the onset of CHSH violation and approaches zero as the singlet visibility is approached. A causal-timing proposition further shows that a strictly retarded detector-to-source mechanism cannot produce a setting-conditioned emission state when the settings are selected outside the emission event's past light cone without an additional common-past, retrocausal, nonlocal, or late-update premise. The result is therefore two-sided. Version 8 closes the stationary-density, full binary-joint, and binary-marginal obligations for one explicit family, but it does not derive the lock strength from gravity, establish a physical value of the phase-diffusion rate, explain all experimental records, or prove the wider Super Information Theory framework. STP/GPL remains a falsifier-first research program whose next decisive requirement is an independently calibrated map from apparatus and gravitational variables to the model parameters.