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.
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.
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.
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.
VERSION NOTE (v2, 2026-07-02): This version supersedes v1 (April 2026). The central empirical-viability claims of v1 — a thermodynamically viable collapse kernel and a favorable DESI DR1 cosmological signature — were falsified by the author's own subsequent analysis. Fixing the smearing length to its holographically mandated value forces confrontation with the full hierarchy of collapse bounds, where spontaneous-heating measurements exclude it by ~9 orders of magnitude. The work has been rewritten as a parameter-free no-go constraint. v1 is retained below for the version record but should not be cited as a viability result. ABSTRACT (v2): The Diósi–Penrose (DP) model of gravity-induced wavefunction collapse requires an ad hoc mass-smearing length, set phenomenologically at the nucleon scale, R0 ~ 1e-15 m. We show that this scale is fixed by holographic cosmological geometry: evaluating the Károlyházy metric variance over the cosmological apparent horizon, as mandated by the Bousso covariant entropy bound, yields R0 = (lP^2 RH)^(1/3) = 3.3 fm from measured constants alone — a parameter-free reproduction of the historical choice. The decoherence-time kinematics survive every current test: a quantum–classical partition at m_crit ≈ 120 m_e protects atomic chemistry (electron tau ~ 1e21 s) and matter-wave interferometry (C60: ~115 yr) while imposing definiteness on macroscopic bodies, with the ambiguous mesoscopic window falling in the macromolecular regime accessible to near-term interferometry. The standard dynamical realization does not survive. The Einstein Equivalence Principle suppresses single-nucleus dipole bremsstrahlung by a derived factor (k_X R0)^2 ≈ 3e-8, and any noise cutoff below 1e18 Hz evades the underground X-ray bound; but neither defense touches spontaneous heating, which with the standard prefactor predicts ~28 mW/kg — nine orders of magnitude above cryogenic heat-leak ceilings. The heating is charge-independent and probes THz phonons via the relative momentum diffusion of atoms separated by 1e5 correlation lengths, so it is immune to the equivalence principle and robust to any high-frequency cutoff. The framework derives exactly two temporal scales (the pixel light-crossing rate ~1e22 Hz and the horizon refresh rate ~1e-19 Hz); neither lands in the fifteen-decade escape window, and inserting one by hand reinjects the free parameter the construction eliminates. We conclude that if objective collapse is sourced by cosmological holographic geometry, it cannot be mediated by continuous stochastic momentum diffusion: a parameter-free no-go constraint forcing gravity-induced reduction toward non-dissipative or purely kinematic mechanisms.
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.
In the Diósi–Penrose (DP) model a superposition of two mass distributions decays at the rate E_G/ħ. Diósi's master equation uses the mass-density operator smeared over a length R0; Penrose's formulation uses the density of the stationary state, and the "parameter-free" choice R0 = u_rms (the zero-point amplitude) links the two. This preprint examines what each choice implies for spontaneous heating and for collapse rates, and states separately which results are standard and which are new. Main results:• Heating per unit mass is 2πGħ∫g², i.e. Għ/(4√π σxσyσz) for Gaussian smearing of per-axis widths σi. With R0 equal to the per-axis zero-point amplitude, Diósi's functional reproduces Penrose's E_G for displacements smaller than the lattice spacing.• For a crystal ball, E_G splits exactly into a continuum term and a per-atom granular term. The continuum term is already contained in the per-atom term (the gravitational analogue of the Lorentz local field), the granular term is lattice periodic, and it carries a Madelung reduction of 0.90 (Cu) and 0.29 (⁴He).• Copper is predicted to heat at 12.1–12.8 pW/kg. This is in mild tension with the 10 pW/kg figure adopted after background subtraction from the Bayreuth heat leak.• The published Debye–Waller values of hcp ⁴He follow a convention in which the reported ⟨u²⟩ is half the one-dimensional mean-square displacement. One direct cross-check and four consistency checks support this reading. With it, the solid-helium prediction becomes 6–8 fW/kg instead of 21 fW/kg.• For any liquid (⁴He or ³He) the one-body density is uniform, so Penrose's granular E_G vanishes. The solid/liquid ⁴He collapse-rate ratio is ≈6 for d ≪ u, 2.8 at 0.2 nm and 1.15 at 1 nm, which quantifies a conjecture of Diósi (2013).• Heating under Penrose's prescription depends on the dynamical completion. For every completion that splits ⟨ρ⟩ into non-negative pieces, the liquid heats at most 2πGħn = 1.15 fW/kg; maximal localization then gives a liquid/solid ratio of 0.155. Density-matrix and configuration-based completions give anything from ~10⁻²⁶ to order one.• Experiment: – Ionizing radiation deposits nearly the same power per kilogram in every material and therefore mimics the fixed-R0 signal. – Underground at LNGS, unshielded environmental gammas still deposit 0.6–8 pW/kg, so ≥20 cm of lead is needed. – The nearest-term test of the zero-point prescription is to compare the heat leaks of heavy, stiff metals with copper; tungsten is predicted at ≈77 pW/kg, six times copper. – Underground helium calorimetry at 1–0.1 pW/kg would test colored fixed-R0 models up to R0 ≈ 10–21 pm, provided the cell-wall heat release can be subtracted to 5–0.5%.
This repository contains a short theoretical preprint proposing a phenomenological, local coarse-grained criterion for gravity-related loss of coherence in massive spatial superpositions. In the weak-field Newtonian regime we define a gravitational distinguishability densityρG(r)=∣∇Φ1(r)−∇Φ2(r)∣2/(8πG)ρG(r)=∣∇Φ1(r)−∇Φ2(r)∣2/(8πG)and argue that any collapse criterion based on local coarse-graining over a fixed length scale ℓℓ predicts a robust scaling signature: for large separations d≫Rd≫R (object radius), the coherence time saturates, τ(d)→constτ(d)→const, whereas the Penrose–Diósi global self-energy criterion predicts τPD(d)∝dτPD(d)∝d.The manuscript emphasizes falsifiability via a scaling test of τ(d)τ(d) at fixed mass and size, and includes a reproducible script/figure illustrating the contrasting asymptotic behaviors.