Joint force and coherence constraints are implemented for one specified Gaussian Diósi–Penrose generator in a fixed finite-time protocol. The analysis retains kinetic energy, correlated two-body noise, three-dimensional wave packets, and local decoding followed by tracing out motion. A trusted normalized initial-force bound of 0.995 restricts the common smearing scale from above. Uniformly over the remaining positive scales, the local statistic has Newton mean greater than 0.9965 and DP absolute mean less than 0.4581. An entanglement witness from the same measurement record also has a positive prediction gap greater than 0.03761, but entanglement is not necessary for this model exclusion. The small-smearing argument bounds full coherence blocks by an early completely positive instrument and includes subsequent interacting evolution in the bound. The general force–decoherence principle is known; the contribution is the controlled finite-readout implementation. This is a conditional nonrelativistic theoretical result with trusted ideal preparation, force calibration, and readout, not an empirical exclusion or a general certification of quantum gravity. The companion archive includes the full LaTeX source, standalone Python checks, exact rational certificates, and reproducibility instructions. The work has undergone internal checks, not independent peer review. Generative-AI assistance is disclosed in the paper. Licensing: the manuscript PDF, LaTeX source, documentation and numerical records are licensed under CC BY 4.0. The Python software and its embedded tests are licensed under MIT. These licenses apply to separate file categories, as specified in the companion archive; they are not alternative licenses for every file.
Joint force and coherence constraints are implemented for one specified Gaussian Diósi–Penrose generator in a fixed finite-time protocol. The analysis retains kinetic energy, correlated two-body noise, three-dimensional wave packets, and local decoding followed by tracing out motion. A trusted normalized initial-force bound of 0.995 restricts the common smearing scale from above. Uniformly over the remaining positive scales, the local statistic has Newton mean greater than 0.9965 and DP absolute mean less than 0.4581. An entanglement witness from the same measurement record also has a positive prediction gap greater than 0.03761, but entanglement is not necessary for this model exclusion. The small-smearing argument bounds full coherence blocks by an early completely positive instrument and includes subsequent interacting evolution in the bound. The general force–decoherence principle is known; the contribution is the controlled finite-readout implementation. This is a conditional nonrelativistic theoretical result with trusted ideal preparation, force calibration, and readout, not an empirical exclusion or a general certification of quantum gravity. The companion archive includes the full LaTeX source, standalone Python checks, exact rational certificates, and reproducibility instructions. The work has undergone internal checks, not independent peer review. Generative-AI assistance is disclosed in the paper. Licensing: the manuscript PDF, LaTeX source, documentation and numerical records are licensed under CC BY 4.0. The Python software and its embedded tests are licensed under MIT. These licenses apply to separate file categories, as specified in the companion archive; they are not alternative licenses for every file.
A durable quantum record, the location of its coherence, and a uniquely actual outcome are different physical questions. We study their separation in a supplied finite-dimensional quantum theory. An explicit, time-independent apparatus couples a system–detector encoding to a controller, a distinct archive, and a finite returning source. A conditional energy penalty suppresses release of the original record without deleting its return coupling. An invariant reduction and a one-sided spectral-gap estimate yield a certified interval with archive occupation above 0.98438, controller-latched occupation above 0.99161, and filled-but-unlatched weight below 2.402 × 10^-7 in one stated design. The same record statistics admit different source-label overlaps and hence different coherence on a specified retained boundary. A conserved product of complementary exchanges accesses that coherence when the finite source is included. Given a calibrated multiregister reader, its finite-duration response separates the coherent apparatus from an independently added archive-gated reduction law, with the added process left active during readout. A conservative example retains a response gap above 0.01717 after separately stipulated one-percent error allowances. The contribution is the finite construction and its quantitative retention, access, and readout interfaces. Quantum carriers, Hamiltonian couplings, trace readout, source preparation, and the reader are supplied; local reader synthesis, empirical calibration, absolute rate selection, and unique-event actualization are not established. Paper code: CFQR-P1 (Complementarity-First Quantum Records — Paper 1). The associated bundle contains the technical supplement, editable LaTeX, numerical checking programs and rational certificates, and selected Lean sources with returned build and axiom-audit evidence. The 39 supporting declarations are partially formalized; eleven recorded type excerpts contain printing elisions. This is not end-to-end formalization, external human peer review, an experimental detection of fundamental collapse, or a derivation of unique-event actualization. Author-owned manuscripts, documentation and mathematical data are CC BY 4.0; author-owned software is MIT, subject to the bundle’s licence map and third-party notices.
A source-inclusive coherence observable is useful only when its measurement resources are admitted. This preprint constructs a bounded local reader for the conserved exchange observable of a specified finite quantum-record apparatus. A degree-three graph uses one independently prepared probe, twenty relays with arbitrary joint states, and finite-duration two-register extraction and full-SWAP interactions. The original apparatus Hamiltonian and an independently added archive-gated process remain active throughout their respective implementations. A prefix-dependent control-frame comparison, symmetry-resolved effect estimate, and explicit gain, phase and finite-slew waveform bounds yield a sufficient response separation greater than 0.005139889 for the stated fixed, fully accessible sixteen-position source and remaining response-error budgets. This is a conditional mathematical result, not measured hardware calibration, a partial-source-access theorem, or a unique diagnosis or derivation of fundamental collapse. The package contains the main manuscript, technical supplement, editable LaTeX, direct numerical reproduction sources, and accepted returned Mac evidence for 56 paper-specific supporting Lean declarations. That subset verifies selected algebra, scalar inequalities and the actual-constant numerical expression; it does not formalize the full physical/continuous-time theorem end-to-end. Separate-session AI review, numerical reproduction and returned kernel evidence are distinguished. Author-owned manuscripts, documentation and mathematical data are CC BY 4.0; newly authored numerical and Lean software is MIT. Predecessor and third-party notices remain unchanged; the reproduction package contains the licence map. No external funding; no competing interests declared. Public preprint v1.0; edition date 18 October 2026; DOI 10.5281/zenodo.23442579.
Removing a common displacement from a gravitational channel test need not preserve its ability to exclude classical communication between quantum laboratories. We give a quantitative construction for four oscillators in a passive Newtonian rotating-wave model, using independent unknown coherent inputs, local heterodyne measurements, and classical subtraction of the common mode. An analytic bound on a bounded score holds for every normal local-operations-and-classical-communication (LOCC) channel, without an output-energy or Gaussian restriction. The ideal quantum mean is 0.125, whereas the LOCC mean is below 0.124068. With residual gain errors of 0.1%, phase errors of 0.01 radians, and an independently bounded common displacement, the respective bounds remain above 0.124581 and below 0.124438. We exhibit a common-noise regime in which the original vacuum-outcome criterion loses its guarantee while the relative score retains one. A conservative fixed-sample test controls false exclusion with memory in the null. The result assumes quantum local matter and trusted measurement structure; it neither excludes all classical phase-space models nor establishes experimental feasibility. This record contains the preprint, editable LaTeX source, and an offline reproducibility archive with exact-arithmetic certificates and 26 computational tests. One project-history test requiring undistributed literature copies is explicitly excluded from the public runner. Substantial use of generative AI is disclosed in the manuscript. This preprint has not undergone journal peer review. Licensing: the manuscript, LaTeX source, documentation and numerical records are licensed under CC BY 4.0; Python software and tests are licensed under MIT. These licences apply to separate file categories, as specified in the archive.
We study classical-communication simulation of the joint source and probe statistics of a qubit-controlled momentum kick. Competitors retain quantum local matter, arbitrary causal classical memory and two-way communication, but no shared entanglement or quantum communication. For fixed Gaussian probe preparation and specified source preparations and readouts, an explicit local instrument approximates the complete continuous momentum statistics arbitrarily well while preserving branch-control distributions exactly. An independently bounded full output position second moment gives a strictly positive total-variation lower bound against the entire competitor class; the explicit simulator attains the same asymptotic order. At fixed nonzero kick separation, the minimum RMS spatial resource for error d scales as Theta(d^(-1/2)); at fixed relative size greater than one, the minimum error scales as Theta(eta^2) in the weak-kick parameter eta. Fixed finite bins admit exact simulation at sufficiently large finite resource. These are statements about specified readout statistics, not full-channel approximation, a Newtonian realization of the simulator, or demonstrated experimental feasibility. The manuscript discusses conditional routes to independent resource certification. This record contains the preprint, editable LaTeX source and an offline reproducibility archive. The archive reproduces Table 1 and runs 22 computational tests; three project-history tests requiring undistributed materials are explicitly excluded. The preprint has not undergone external peer review. Licensing: the manuscript, documentation and numerical records are licensed under CC BY 4.0; the Python software and tests are licensed under MIT. The archive specifies these separate scopes.
This repository contains the computational reproducibility and verification package accompanying the frozen Version v1.0 manuscript: “Phase Curvature and Assumption-Budgeted Certification in Gravity-Mediated Entanglement.” The associated manuscript develops an operational certification framework for gravity-mediated entanglement experiments. Its central aim is to quantify when an observed entanglement signal excludes a specified neighborhood of local classical-mediator models under explicit assumptions and separately controlled nuisance channels. The package supports the manuscript’s analytical and numerical results concerning: gauge-invariant nonseparable phase curvature for diagonal two-path interactions; exact concurrence and separability-distance formulas for pure two-qubit outputs; assumption-budgeted exclusion bounds around the classical-mediator free class; primal and dual PPT/semidefinite-program certification; finite-shot confidence bounds for experimentally accessible Pauli correlators; certified residual bounds for physically compensated coherent nuisance interactions; stochastic geometry and Casimir–Polder uncertainty budgets; matter-bypass and common-auxiliary-channel bookkeeping; circular-shield mode analysis, including the azimuthal matched-null obstruction; thermal shield-channel factorization; finite-footprint high-mode suppression; an analytic positive high-mode tail bound for the shield benchmark; and a conservative outward-rounded audit of the finite numerical mode block. The frozen manuscript does not claim that a particular experimental apparatus has already closed every systematic-error channel. Quantities such as preparation error, matter-channel leakage, shield-model discrepancy, control error, and readout error remain apparatus-dependent inputs to the certification framework. Package contents The archive includes: the frozen Version v1.0 manuscript source; deterministic verification scripts for the theorem-core identities; finite-shot and Casimir–Polder statistical/geometry checks; shield-mode and analytic-tail verification; conservative floating-point interval/audit checks; submission-interface regression checks; machine-readable verification reports; and a SHA256 manifest for file-integrity verification. All verification scripts distributed with the Version v1.0 package return PASS under the documented software environment. The numerical audit is intended as a transparent reproducibility layer for the stated model calculations. It should not be interpreted as a formal interval-special-function proof or as certification of a realized experimental apparatus.
We study idealized levitated protocols that create spatial superpositions of massive test particles. For each protocol, we compare the dimensionless contrast-loss exponent of mass-proportional continuous spontaneous localization (CSL) with the Diósi--Penrose (DP) self-energy exponent EGτ/ℏ. We first prove that the point-particle CSL separation kernel has an exact random-unitary realization: Gaussian momentum kicks arriving at Poisson-distributed times produce the same unconditional decay of spatial coherence, although a pure state conditioned on the complete kick record remains pure. The separation kernel alone therefore specifies an operational decoherence law, not the occurrence of objective collapse. We then show that the ratio of the CSL and DP exponents is independent of particle mass and interrogation time. In the point-particle model it depends only on branch separation and an effective distance; for the standard GRW reference parameters, its resolved-superposition crossover is x∗≈1.91nm. For rigid spherical bodies with an arbitrary normalized radial mass profile, total mass, overall density scale, and interrogation time again cancel, leaving a dimensionless geometry factor. The results distinguish three requirements for a decisive experiment: detectable absolute effects, a controlled comparison of CSL and DP scales, and observables capable of discriminating physically different dynamics that share the same ensemble decoherence kernel.