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.
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.
Final preprint (v3) of a manuscript prepared for submission. All numerical claims are reproduced by the archived code included in this record (Behenck_RecordGrain_code_v3.zip; a README maps each script to the corresponding paper section). Abstract: Objective-collapse models postulate their strength and length parameters; we ask whether a closure rule can fix them instead. We study a Diosi-type gravitational master equation whose smearing length is promoted to a local field sigma(x) determined by the density of a classical, filtration-adapted record of realized outcomes - an operational definition carrying no ontological commitment. A per-event information accounting, whose rank-1 and log N structure is computed exactly in a solvable Gaussian toy model reproduced in an appendix, combines with a posited writing-balance condition (a labelled hypothesis, [H-close]) to give sigma proportional to rho^(-1/2): sigma of about 5.9 angstrom in germanium and 8.0 angstrom in liquid xenon, within a declared factor-of-ten parameter window. A labelled single-relaxation-time hypothesis, saturating the causal bound tau_c = sigma/c, selects a Lorentzian noise spectrum with cutoff Omega_c = c/sigma. We prove translational and rotational equivariance of the state-dependent dynamics, no-signalling of the ensemble evolution under classical, record-read event rates, a ledger-time invariance lemma, and well-posedness of the coupled dynamics 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. Against the published XENONnT limit (R_0 > 4.9 angstrom at 90% C.L.) the fiducial grains survive in both the white-noise and Lorentzian branches; the low end of the declared window requires the cutoff. Neutron-star heating bounds are met only under a labelled writability hypothesis, stated as load-bearing. The closure yields a signature no universal-parameter model shares: a composition-normalized Ge/Xe spontaneous-radiation rate ratio (rho_Ge/rho_LXe)^(3/2) = 2.50 +/- 0.09, subject to a declared O(1) crystal-versus-liquid systematic; every rival predicts 1.00. Two further dated signatures - a material-dependent excess heat proportional to rho^(3/2) and a bistable-window prediction for levitated nanospheres - are stated with explicit death criteria.
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.
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.
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%.
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.
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.