Surprisal-Timed Collapse (STC) was proposed as a deterministic modification of the Diósi–Penrose (DP) gravitational reduction model: a superposition reduces when the accumulated relative gravitational phase reaches unity, with no stochastic field, and the Born rule is said to follow from stationary phase of an informational path integral. We audit the filed proposal claim by claim, with each claim typed as physical, derivational, self-descriptive or mathematical, and each verdict drawn from a closed vocabulary fixed before the audit began. Six consistency obligations are tested: a defined reduction energy, operational no-signalling, an outcome rule, a time and frame standard, consistency with data, and consistency with radiation bounds. As filed, STC discharges none of the first four and not the sixth; the fifth is discharged only for a binding model of the free inputs. The reduction energy depends on a smearing length, a profile and a normalisation the text does not fix (published normalisations span a factor 8π); the two rate formulas the proposal quotes are mutually inconsistent by a factor of two; one natural reading of its locality referent permits signalling, conditional on a locally observable record of the reduction; it supplies no outcome selector, and the only recovered written version of its Born-rule argument is circular; and its exemption from spontaneous-radiation bounds is an assumption rather than a calculation. Under the audited assumptions, no qualifying experiment excludes the whole admissible domain, so the proposal is not falsified by data; the one exclusion found inside that domain is conditional on a rigid-nucleus density prescription, the normalisation and the coherent interval, and disappears if the zero-point spread of the nuclei enters the density. This is not a finding that the proposal agrees with experiment. For its proposed interferometric test, the forecasts made with the filed per-trace estimator are not reproduced, and that test is not viable as filed; other analyses of the same apparatus were not adjudicated. Three central ideas of the proposal have prior art. The filed theory is therefore underdetermined. We identify requirements that a decidable version of this framework would need to satisfy. We do not claim a falsification of the Born rule, a no-go theorem for deterministic collapse, or any experimental support for STC. The author of this audit is also the author of the original STC proposal. This is a self-audit conducted with adversarial AI assistance, not an independent external peer review. Preprint version 1, 29 October 2026 (version label). The audited text is the recovered filed version of Surprisal-Timed Collapse, identified by the reserved DOI 10.5281/zenodo.23772944. This paper was prepared with substantial assistance from AI systems, as described in its Sec. III; the author is responsible for its content. File SHA-256 ad5b63c88503b3ee61264c30bd47bd96ca20415e64e4611e36aa2ba32a380367; source SHA-256 0cf82a6de5d976d4988a6f973727e4fb68d19ade622f28f3cb36ee37a32e80f0. Known presentation defects: loose interword spacing in reference [8], and a single closing line at the top of the left column of page 2. The hashes identify the archived bytes; they do not independently verify the history the audit records.
Surprisal-Timed Collapse (STC) was proposed as a deterministic modification of the Diósi–Penrose (DP) gravitational reduction model: a superposition reduces when the accumulated relative gravitational phase reaches unity, with no stochastic field, and the Born rule is said to follow from stationary phase of an informational path integral. We audit the filed proposal claim by claim, with each claim typed as physical, derivational, self-descriptive or mathematical, and each verdict drawn from a closed vocabulary fixed before the audit began. Six consistency obligations are tested: a defined reduction energy, operational no-signalling, an outcome rule, a time and frame standard, consistency with data, and consistency with radiation bounds. As filed, STC discharges none of the first four and not the sixth; the fifth is discharged only for a binding model of the free inputs. The reduction energy depends on a smearing length, a profile and a normalisation the text does not fix (published normalisations span a factor 8π); the two rate formulas the proposal quotes are mutually inconsistent by a factor of two; one natural reading of its locality referent permits signalling, conditional on a locally observable record of the reduction; it supplies no outcome selector, and the only recovered written version of its Born-rule argument is circular; and its exemption from spontaneous-radiation bounds is an assumption rather than a calculation. Under the audited assumptions, no qualifying experiment excludes the whole admissible domain, so the proposal is not falsified by data; the one exclusion found inside that domain is conditional on a rigid-nucleus density prescription, the normalisation and the coherent interval, and disappears if the zero-point spread of the nuclei enters the density. This is not a finding that the proposal agrees with experiment. For its proposed interferometric test, the forecasts made with the filed per-trace estimator are not reproduced, and that test is not viable as filed; other analyses of the same apparatus were not adjudicated. Three central ideas of the proposal have prior art. The filed theory is therefore underdetermined. We identify requirements that a decidable version of this framework would need to satisfy. We do not claim a falsification of the Born rule, a no-go theorem for deterministic collapse, or any experimental support for STC. The author of this audit is also the author of the original STC proposal. This is a self-audit conducted with adversarial AI assistance, not an independent external peer review. Preprint version 1, 29 October 2026 (version label). The audited text is the recovered filed version of Surprisal-Timed Collapse, identified by the reserved DOI 10.5281/zenodo.23772944. This paper was prepared with substantial assistance from AI systems, as described in its Sec. III; the author is responsible for its content. File SHA-256 ad5b63c88503b3ee61264c30bd47bd96ca20415e64e4611e36aa2ba32a380367; source SHA-256 0cf82a6de5d976d4988a6f973727e4fb68d19ade622f28f3cb36ee37a32e80f0. Known presentation defects: loose interword spacing in reference [8], and a single closing line at the top of the left column of page 2. The hashes identify the archived bytes; they do not independently verify the history the audit records.
Version 2.8 — submission manuscript. Preprint prepared for submission to Foundations of Physics. Supersedes v2.6, v2.5, v2.3, v2.2 and v1. A gravitational collapse model in which spacetime geometry is postulated to be irreducibly classical and superpositions of massive systems decay under a stochastic dynamics driven by a physical temporal medium: one stationary noise field combining the Diósi–Penrose spatial kernel with a coloured temporal kernel of finite universal bandwidth ω_u — the single new parameter of the primary model. The decoherence envelope is derived exactly (Gaussian onset, DP exponential tail), and two universality propositions are proved: the DP tail is fixed by the kernel's zero-frequency weight alone, and a Gaussian onset is generic for any finite-bandwidth medium — making the crossover, not any particular kernel, the experimental signature. A selectivity theorem shows each configuration draws its collapse dominantly from noise modes near its own gravitational frequency ΔE_g/ℏ. The parameter-free tuning of earlier versions is retained as named Conjecture C1, with a proof that no single stationary spectrum realises it for all configurations at once. The coloured kernel suppresses collapse-induced spontaneous radiation, reconciling the model with underground null results; heating bounds survive at full strength. Predictions include a closed-form optimal measurement window (separation 0.330 at t = 0.837 τ_dec under C1) and a mass-and-time ceiling on Bell violations, with five falsification conditions. The BMV/GIE treatment is current with the 2024–2026 literature. Changes in v2.8 (Appendix B, B11–B13): universal-bandwidth primary model with derived (ω_u, R_0) window; C1 demoted to conjecture with proved obstruction; no-signalling corrected and branch-conditioned; non-Markovian trajectory literature engaged, Born-rule theorem declared open; one prediction and the "present moment" identification withdrawn with reasons; GIE dispute disentangled; references verified. This paper builds on v1 of the companion collapse-model work (10.5281/zenodo.19960071). The lowest-energy principle assumed here was withdrawn in v2.2 of that paper and does not appear in the current version (v2.8); the framework presented here has not been revised accordingly. Retained as a record of the earlier line of enquiry All revisions, withdrawn claims, and corrected errors are documented in Appendix B; open problems in Section 8. AI tools (Claude, Anthropic) assisted with formalisation and editing; the conceptual framework originated with the author, who takes full responsibility. Full declaration in the manuscript.
Time Cosmology (TC) reads the dark sectors as tenses and identifies the present with an irreversible selection performed by the fundamental forces. At the background and recent-universe level TC is observationally degenerate with quintessence. This paper exhibits the program's first non-cosmological discriminant. Carried to the laboratory, the irreversible recording of an outcome into the gravitational ledger is governed by the Penrose energy-time criterion tau ~ hbar/E_G, a parameter-free collapse time for spatial superpositions; TC supplies the ontological reason Penrose left open (collapse = writing to the past) and attaches a Landauer cost. Because TC selection is a quantum non-demolition (QND) measurement by the existing forces, not a stochastic noise field, it carries no continuous momentum diffusion and hence no spontaneous radiation; it therefore survives the 2021 Gran Sasso experiment that excluded the parameter-free Diosi-Penrose model. The prediction is falsifiable: a spatial superposition of ~1e-17 to 1e-15 kg held beyond tau must collapse; the gap to capability is ~6 orders of magnitude for second-scale experiments, shrinking to ~1-2 orders for long-hold MAQRO-class proposals. Scope is stated explicitly: the collapse time reproduces Penrose's (the novelty is the grounding and the non-radiative survival); the non-radiativity rests on strict non-stochasticity, with a residual-diffusion bound left as the central open calculation; the test is not within current reach. All numerical claims are reproduced by the archived code included in this record. Companion records: Indispensable Present (10.5281/zenodo.20707004), N3 (10.5281/zenodo.20564003), N5 calorimeter (10.5281/zenodo.20617808).
Objective-collapse models are usually tested one model at a time: a spatial noise kernel is proposed, its parameters are constrained, and surviving variants are then modified by changing the kernel, the temporal spectrum, or the dissipation mechanism. We formulate a complementary spectral framework, collapse kernel tomography, in which stationary Gaussian mass-density collapse processes are represented by a non-negative spectral measure S(k, omega) and each experiment supplies a linear response functional. Null experiments define upper half-spaces; classicality requirements define lower half-spaces; and Farkas-type dual certificates can rule out entire spectral classes rather than individual parameter points. We show that lower requirements must first pass an admissibility test relative to the reference collapse law they are meant to constrain: a pointer criterion that is not satisfied by the maximal reference law cannot consistently be used as a ceiling on a bounded deformative subfamily. Applying this logic to a screened gravitational test kernel bounded above by UV-smeared Diosi-Penrose collapse removes the single-layer graphene-disk criterion as an admissible ceiling and yields a criterion-dependent silica-sphere frontier m_star = 1.683e-14 kg for l = 100 nm, Delta x = 2R, and Gamma_req = 100 per second. For the same kernel we derive a rigid-center-of-mass heating ceiling, reducing to 2 pi G hbar rho for a homogeneous bulk body; for silica this is 9.73e-41 W. A benchmark screened kernel with kappa = 2.1886e6 per meter and l = 100 nm predicts an order-one suppression relative to UV-smeared DP in the 1e-14 to 1e-13 kg probe range. Finally, we propose form-factor matched filtering using layered test masses, with the design rule p of at least 4l for usable and 8l for strong density-modulation contrast. The result is a convex, falsifiable geometry for collapse searches rather than a single-model parameter scan. This record contains the manuscript PDF and the full reproducibility package: the numerical engine, unit tests (all anchor tests pass), figure-generation scripts that produce Figure 1 exactly, numerical anchors, and documentation. Language-model tools were used in preparation and verification; every quantitative claim is independently reproduced by the released code, and the author takes sole responsibility for the content.
This record preserves the current working state of From Geometric Closure to Physical Test: An Operational and Falsification Audit of the ENSO Framework. The package contains the 41-page audit paper, the nine ENSO papers included in the audited corpus, their TeX source files and associated validation suites, the complete audit-side script collection, and the reports, ledgers, and supporting outputs generated during the project. The materials are organised so that the internal audit suite can be run from a single folder, while the individual predecessor validators remain available with the papers to which they belong. The purpose of the audit is to distinguish, claim by claim, what is mathematically proved, what is conditionally established within ENSO, what reconstructs standard quantum mechanics, what is numerically supported, what remains an identification, and what is still open to empirical test. The audit reports that the load-bearing mathematical architecture survives separate re-derivation and computational testing within the project. It verifies the reciprocal closure invariant, the canonical reciprocal-phase amplitude map under its stated assumptions, conjugation and quadratic closure, the quadratic-weight result, the binary closure projection theorem, the log-affine edge-closure proposition, the mathematical golden-ratio attractor, and the geometric derivation of the Resolution Gap. The framework also reconstructs twenty standard quantum-mechanical cases and obtains the Born-rule route through a non-circular stochastic argument within an imported Hilbert-space and measurement setting. These results are classified as reconstruction rather than as independent empirical confirmation. The audit also states plainly that the standard quantum-mechanical baseline remains ontologically incomplete, particularly at measurement, and that ENSO’s atemporal intrinsic-closure ontology is therefore being assessed against a framework that does not itself provide a settled account of the transition from propagation to recorded outcome. The present package is an author-side, AI-assisted internal audit and should not be treated as external peer review or independent replication. It is deposited as a working research project rather than as the final completed audit. The current version preserves the research record, publication sequence, scripts, corrections, provenance notes, and claim classifications while further work proceeds on the operational discriminator, the measurement-rate identification, and the empirical conditions under which ENSO may be distinguished from standard continuous-measurement quantum mechanics. The package retains both positive and negative results. The audit-side suite contains no unresolved failures, while a deliberately retained predecessor negative result is preserved rather than removed. The operational frontier remains open: the mathematical and reconstructive architecture is established within its stated premises, but a fully developed and experimentally validated discriminator is the next stage of the research programme. For further information about the ENSO Framework, please contact Eric Needham: ensotheory1@gmail.com
This technical report develops and tests TWMSE Candidate Equation 4A, a phenomenological, threshold-activated model of observer-induced quantum collapse formulated to preserve Born weights and operational no-signalling while producing experimentally distinguishable dynamics. Candidate Equation 4A introduces a branch-sensitive Lindblad term whose activation depends on whether an operationally defined observer record exceeds a specified threshold. The report evaluates the equation’s mathematical consistency, including trace preservation, positivity, Born-weight preservation and operational no-signalling. It also examines individual stochastic trajectories, ensemble behaviour, synthetic count-level parameter recovery, statistical power and the consequences of model misspecification. A retrospective analysis is performed using published fitted GHZ decoherence-rate summaries from two superconducting-qubit studies. This is not an analysis of original laboratory shot-level data. The combined profile analysis finds no robust positive signal for Candidate Equation 4A. Instead, it establishes provisional, threshold-dependent upper limits on the additional collapse rate. Across the report’s primary threshold range of R* = 1–9, the largest pointwise one-sided 95% upper limit is approximately 7.3 × 10³ s⁻¹, while the tightest limit is approximately 3.0 × 10³ s⁻¹ at R* = 8. These are pointwise limits and do not constitute a simultaneous confidence band. The retrospective results therefore constrain but do not favour Candidate Equation 4A. Standard quantum mechanics remains sufficient to describe the analysed GHZ summaries and does so with fewer parameters. Candidate Equation 4A survives this preliminary confrontation only in the limited scientific sense that portions of its parameter space remain unexcluded. This non-exclusion is not evidence that the candidate is correct. The report consequently specifies a dedicated amplify–hold–erase experiment using matched record-forming and coherent-control circuits. The proposed test varies observer-record size, conditional record strength and dwell time while collecting count-level measurement outcomes and contemporaneous calibrations of conventional noise. The protocol is designed to distinguish a threshold-activated observer-record contribution from smooth, conventional decoherence and other experimental effects. A preregistration template, empirical-data schema and data dictionary are supplied so that the proposed experiment can be performed and analysed as an independently reproducible and falsifiable test. The accompanying ZIP archive is the complete, self-contained reproducibility package for the results reported here. It contains the code, simulation data, published GHZ rate summaries used as inputs, derived numerical outputs, documentation, software requirements and integrity checks required to reproduce the reported computational analyses and verify the packaged results. The archive contains: • the complete report in PDF, DOCX and Markdown formats;• deterministic Python reproduction scripts;• results from 500 density-matrix consistency trials;• 250,000 simulated stochastic trajectories;• 14,336 synthetic count-level circuit rows;• synthetic parameter-recovery and statistical-power results;• model-misspecification tests;• the published fitted GHZ rate summaries used in the retrospective analysis;• individual and joint GHZ profile-likelihood results;• prediction grids and report figures;• an empty 37-column template for future empirical raw data;• a data dictionary and preregistration template;• software-environment requirements and citation metadata; and• a SHA-256 manifest for package-integrity verification. The simulated trajectories and synthetic circuit counts are computational data rather than laboratory observations. The included GHZ inputs are published fitted rate summaries and are not original experimental shot counts. No new laboratory data are included, and no empirical discovery claim is made. Successful reproduction verifies that the supplied code generates the reported mathematical checks, simulations and retrospective statistical results. It does not establish that nature follows Candidate Equation 4A, demonstrate observer-induced collapse, or show that TWMSE is empirically preferred over standard quantum mechanics. The physical ideas, TWMSE framework, research direction and scientific interpretation are those of the author. Computational assistance was used for mathematical checking, simulation, statistical analysis, document preparation and reproducibility auditing. The author directed the research and accepts responsibility for the methodology, scientific claims, interpretations and conclusions. Candidate Equation 4A should therefore be understood as an explicit, internally testable and falsifiable phenomenological candidate that has passed the reported mathematical and computational consistency checks, remains compatible with the limited published summaries examined, and now requires the proposed dedicated raw-data experiment for a meaningful empirical test.
Preprint of a manuscript prepared for submission to Physical Review A. All numerical claims are reproduced by the archived code included in this record (Behenck_RecordGrain_code_v1.zip; a README maps each script to the corresponding paper section). Abstract: We ask whether the free parameters of objective-collapse models can be fixed by a closure rule rather than postulated. We propose one: the smearing length of a Diosi-type gravitational-collapse master equation is promoted to a local field sigma(x)=f[n_r] set by the density n_r of a classical, adapted record of realized outcomes (an operational definition, carrying no ontological commitment). A per-event bit accounting, whose rank-1/log N structure is derived in a solvable Gaussian toy (reproduced in an appendix), fixes sigma proportional to rho^(-1/2) up to an O(1) counting slop, yielding sigma of about 5.9 angstrom (Ge) and 8.0 angstrom (Xe). A dissipative completion with a single relaxation time - a labelled hypothesis, with tau_c = sigma/c the causal lower bound saturated - selects a Lorentzian noise spectrum with cutoff Omega_c = c/sigma, cutoff and profile descending together. We prove four consistency results: equivariance of the state-dependent dynamics under joint translation; a ledger-time invariance lemma showing the law reads the accumulated record, not a wall clock; no-signalling via outcome-based feedback (classical rate, quantum outcome), which is linear and CPTP; and well-posedness of the coupled fixed-point process as a non-exploding piecewise-deterministic Markov process, with a single threshold 3*alpha = 1 governing fixed-point bistability, birth-process explosion, and loop stability. Confronted with XENONnT, Majorana, IGM calorimetry, cryogenic heat-leak, and neutron-star bounds, the declared grain window in Xe, [4.4, 44] angstrom, survives even in the white-noise limit (death line 4.34 angstrom); the Lorentzian cutoff lowers the death line to 1.85 angstrom, with margins from ~50 to ~10^3, while the IGM heat loop closes by 51 orders of magnitude. The model yields three dated, falsifiable signatures: a composition-normalized Ge/Xe rate ratio (rho_Ge/rho_LXe)^(3/2) = 2.50 +/- 0.09 (density error), subject to an O(1) crystalline/liquid writability systematic, to be quantified - every rival predicts 1.00; a material-dependent excess heat proportional to rho^(3/2); and a bistable-window prediction for levitated nanospheres. The model is not a new dynamical class but a closure of the colored-noise family, and we list the open problems.