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 \( 0<\Theta\leq2\pi \) and a record retaining M classical values, \( \mathcal V\leq sinc(\Theta/(2M)) \), 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 \( S_\star \) can be asserted together, the reachable codebook has at most \( \sum_{j=0}^{S_\star}\binom nj \) words, so \( \mathcal V\leq sinc\!\left(\frac{\Theta}{2\sum_{j=0}^{S_\star}\binom nj}\right), \) and the coherence deficit falls as \( n^{-2S_\star} \) rather than \( 4^{−n} \). Two cases fix \( S_\star \) by physics rather than by design. A single-quantum position probe of the apparatus coordinate is weight-one by particle number, giving \( \mathcal V\leq sinc(\pi/n) \) at one full cycle and 0.9745 for eight detectors. A peak-assertion budget of \( S_\star \) lines sets the exponent rather than the prefactor. For held or guided branches with matched velocity histories in a weak uniform field, \( \Theta=mgT\Delta z/\hbar \), and a calibrated layer-time count in a static spacetime has rate \( r=\nu N \), 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.
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<\Theta\leq2\pi ) and a record retaining M classical values, ( \mathcal V\leq sinc(\Theta/(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_\star ) can be asserted together, the reachable codebook has at most ( \sum_{j=0}^{S_\star}\binom nj ) words, so ( \mathcal V\leq sinc!\left(\frac{\Theta}{2\sum_{j=0}^{S_\star}\binom nj}\right), ) and the coherence deficit falls as ( n^{-2S_\star} ) rather than ( 4^{−n} ). Two cases fix ( S_\star ) by physics rather than by design. A single-quantum position probe of the apparatus coordinate is weight-one by particle number, giving ( \mathcal V\leq sinc(\pi/n) ) at one full cycle and 0.9745 for eight detectors. A peak-assertion budget of ( S_\star ) lines sets the exponent rather than the prefactor. For held or guided branches with matched velocity histories in a weak uniform field, ( \Theta=mgT\Delta z/\hbar ), and a calibrated layer-time count in a static spacetime has rate ( r=\nu N ), 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.
We prove an exact interface adaptation of three separately represented binary measurements to a prescribed conical spacetime. A finite consumed clock context produces a classical time code and Ramsey outcome while retaining the complete conditional matter state, including arbitrary untouched references. The adaptation preserves the positive record contrasts and exact interpolation-off controls of the three represented models. Spectral-mask convergence at fixed particle-number cutoff is strengthened to convergence of the complete recorded channels in diamond norm; initial-edge removal in the unbounded model instead gives pointwise trace-norm convergence, without an unsupported uniform channel-norm claim. A separate target-adapted SWAP construction transports finite payloads exactly along prescribed local null segments, with an explicit register ledger. Two corrections are essential. Local flatness of a cone does not identify its global field representation or Newton inverse with the corresponding Minkowski objects. We therefore state the flat-completion prescription explicitly and prove its local pullback identities, rather than claiming an intrinsic quantum field theory on the entire cone. Likewise, assigning a time to a global controlled unitary does not establish a compact causal implementation. The causal theorem applies to the certified finite transport and control network, not to an unconstructed local realization of the global field apparatus. The contribution is thus an exact, reference-stable Grade-S interface construction with a precisely delimited geometric interpretation. Its potential usefulness is methodological: represented signals, conditional residuals, regulator errors, geometric calibration, and physical implementation can be compared without identifying their distinct mathematical objects. No priority claim is made for the underlying measurement identities. Records do not determine the metric, lapse, or deficit angle. No spacetime-emergence theorem, Einstein dynamics, gravity-generated-entanglement test, inherited gravitational quantum coefficient, or finite-qubit compilation is asserted.
This record is part of the Mass, Proper Time, and Gravity series. Full series community: https://zenodo.org/communities/mass-proper-time-gravity/ This part proves no new theorem about the measure; it establishes one identification and draws the reading it forces. The Barbu phase of Parts LXIX-LXXI is a single object read in three registers: the internal clock Phi_B = e^{-i omega_B tau_C} (omega_B = mc^2/hbar, with the physical c), the phase of the history amplitude A(C) = W(C) e^{-i phi_B(C)}, and the mass kernel on worldlines. The old role is kept and lifted: the clock of mass becomes the phase of the causal history. The identification is checked numerically -- the history amplitude's phase responds to omega_B with exactly the clock's proper time (d(arg A)/d omega_B = sum_x depth(x), while normalized ratios are nearly clock-free); the dephasing rate between histories is linear in omega_B (Gaussian visibility law, rms 0.002); and branch separation grows with omega_B inside a readable window that closes exactly at omega_B = 2pi, where the integer clock aliases and the overlap revives. The reading it forces: not geometries in superposition, but phased causal histories in superposition, with geometry as the crystallized branch -- C is the combinatorial history, (C, phi_B) the interfering quantum branch, mu selects the readable branches, g_{mu nu} the resulting classical crystal. Mass is the rate at which causal order becomes phase, and numerically the rate at which branches of the blur become distinguishable. The extension breaks nothing: the new objects inherit the relabeling covariance and the quantum-measure structure of the old. The dynamical half is separate and already derived: the crystallized branch obeys the Einstein equation obtained through the readable Dirac operator (coefficient 8 pi G_ind / c_obs^4). The value of m is a declared input throughout; what is new is named as what it is -- an identification, seven gates of measurement, and a reading. Each result has a reproducible Python script (included).
A quantum record can have locally accessible populations while its distinguishing phase remains correlated with a distant source. We study this access boundary in a specified finite recording apparatus with a returning, vacuum/one-excitation source. Source-position weights give finite-time cutoff bounds without removing any physical hopping or return coupling. For an initially far-tagged record and its incoherent mixture, every reader in a declared position-preserving local-control class obeys a phase-visibility envelope and a necessary access-time inequality. A separate finite local probe shows why that state-discrimination limit is not an unrestricted limit on distinguishing two dynamical laws: fresh local coherence can reveal a stipulated added dephaser without recovering the old record phase. We construct a bounded, degree-three reader accessing only source positions 1–32. With the initial tag fixed at position 65, exact finite-source arrival certificates and an analytical tail comparison yield recovery uniformly over every finite total source length at least 65. Accessible control faults are charged against the arrived signed-phase norm, while source-moving drift is charged against the full norm. At the fixed deadline 25.02/J, the matched phase-dependent difference between coherent and archive-gated dynamics exceeds 0.005, including the stated simultaneous control faults and four additional absolute response allowances of 0.008 each. Complementary results cover a vacuum-ready source and a stronger endpoint-prepared finite example. The conclusions are conditional on the supplied model, preparations, common realized controls and calibration bounds. They are not a switchable-fundamental-law experiment, a nuisance-independent classifier, an optimal-speed theorem or an end-to-end formal verification. The supporting Lean companion contains 59 declarations in eight modules with accepted returned Mac compilation, type and axiom evidence; physical analytical interfaces remain explicit hypotheses or outside that subset. The deposit files include the main manuscript, technical supplement and full research/reproduction package.
From a finite event record to Bell correlations and their loss under recording A pair is prepared together, read at two separated instruments, and allowed to leave a material record. This paper builds the correlation law from a real source geometry in Artian's Quantum Traction Theory. Its source-to-access equation is pK(r,s∣a,b)=C(KΩ)C[(Πr(a)⊗Πs(b)⊗I)KΩ] Here C is an additive, basis-invariant event capacity, Omega is the normalized orientation-neutral two-channel source, K is a specified record contact, and the projectors select the two instrument outputs. A real quarter-turn and a qualified shared-reference composition generate the readout algebra. Capacity symmetry fixes its quadratic weight. A separately stated capacity-to-frequency condition connects that weight to laboratory counts. The correlation follows before the Bell comparison For a phase-compensated record contact with overlap g between its two normalized record profiles, the construction gives EK(a,b)=−azbz−g(axbx+ayby),0≤g≤1. The intact-source limit is E = -a dot b. The same calculation yields the fixed-setting and optimized Bell responses: S45=2(1+g),Sopt=21+g2. Fresh independent record contacts multiply their overlaps. The paper derives the repeated-contact law, a capacity-based overlap calibration, uncertainty bounds, and a protocol that separates calibration from the Bell observations being judged. A source-first account with an explicit dependency map A1 supplies event-time labels and the clock-angle correspondence; A4 supplies the real dial; A5-X supplies completed-event support, with its inherited A6/A7 conditions. The two-channel preparation, balanced composition, capacity symmetry, frequency bridge, and record coupling are printed separately. Each theorem states exactly which conditions it uses. The Access uncertainty commutator is treated as a distinct inherited algebraic premise, rather than inferred from Bell correlations. When a receiver follows the source Version 2.0 constructs a matched receiver rather than assigning its transformation by name. Preserving every probability of the stated bilinear contact forces its transport to be the conjugate of the source transport, up to an overall phase: ∣rTVTUs∣2=∣rTs∣2for all r,s⟹V=eiαU. A finite set of basis and sum probes certifies this relation. A robust extension converts imperfect probe probabilities into an operator-error bound. Finite clock and shift operations then produce the comparison loop L=M+ω(I−M),ω=e2πi/d. The matched sector cancels the comparison phase while the unmatched sector retains it. This is a joint comparison law; each local readout can remain incompatible. The paper identifies the binary loop's ambiguity, provides additional probes that distinguish it, and transfers the Bell correlations into a complete detector record when the original carrier is consumed. One contact, two observable roles A specified marker contact supplies both the Bell record overlap and a resolved weak-measurement instrument: γK0K1=sinθ,=diag(cos(θ/2),sin(θ/2)),=diag(sin(θ/2),cos(θ/2)). An independent replay executes this instrument on all 40,032 tree records in the public Feng and colleagues archive, reproducing every stored decoder success/failure score. The main five-setting batch contains 32,000 records; the complete archive has six settings. The reproduced job-cluster residual probabilities are p = 0.0188753 and p = 0.0442603, respectively. These diagnose modest tension with the ideal instrument under the stated retrospective covariance. The matched QTT and quantum representations make the same archival predictions, so this replay is not a significance test between them. The package preserves the complete source-first Bell construction and adds finite receiver certificates, physical transport-error bounds, a common-contact derivation, five vector figures, a twelve-item achievements ledger, and offline reproducibility materials. The next operational question is precise: which independently qualified physical contact fixes both the record overlap and the receiver comparison response? Dependencies: QTT Main Book; finite address-capacity counting; real source histories and composition; A1-CHSH spinor character; Observation as Access.
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.
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.