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trajectory literature engaged, Born-rule theorem declared open; one prediction and the "present moment" identification withdrawn with reasons; GIE dispute disentangled; references verified.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 The lowest-energy principle assumed here was withdrawn in v2.2 of that paper and does not appear in the current version (v2.8); the framework presented here has not been revised accordingly. Retained as a record of the earlier line of enquiry All revisions, withdrawn claims, and corrected errors are documented in Appendix B; open problems in Section 8.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.
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.
We develop a gravitational collapse model in which spacetime geometry is postulated to beirreducibly classical and quantum superpositions of massive systems decay under a stochasticdynamics driven by a physical temporal medium. The model combines the Diósi–Penrosespatial kernel with a coloured temporal kernel of finite correlation time _c; the hypothesis _c τ τ= / E_g renders it parameter-free. The decoherence envelope is derived exactly: Gaussian at ℏ Δearly times, crossing to exponential Diósi–Penrose decay — a signature distinguishing themodel from thermal decoherence and from all Markovian collapse models. The coloured kernelsuppresses collapse-induced spontaneous radiation by ( _c) ², reconciling gravitational ωτ ⁻collapse with the underground null results that exclude the parameter-free Markovian model.We give quantitative predictions for levitated nanospheres and matter-wave interferometry, sixfalsification conditions, and outline interpretive consequences: a classicality wavefrontdefining the present moment, a selective arrow of time, and dark energy as the unimodularaccumulation of collapse-injected energy.
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.
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.
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.
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).
We derive an objective-collapse prediction for massive spatial superpositions from a singlepremise — that physical distinguishability is finite and discrete — and show that it evades thespontaneous-radiation bounds that exclude the parameter-free Di´osi–Penrose model. The mechanism is conservative: a superposition of a massive body in two locations is a superposition oftwo gravitational configurations, and when the gravitational self-energy difference ∆E betweenthem reaches the capacity of one distinguishability cell, coherence commits, on the timescaleτ ∼ℏ/∆E. This reproduces the Di´osi–Penrose collapse time, here derived rather than posited,with a regularisation length fixed without tuning as the nucleon Compton wavelength, giving acollapse mass ceiling of order 1012–1014 amu. The prediction is consistent with every matterwave interference experiment performed — at the current record (∼ 105 amu) the predictedcoherence time exceeds the experimental one by ten orders of magnitude — and lies withinreach of next-generation nanoparticle interferometry. Crucially, we derive the collapse masterequation and show that the momentum-diffusion coefficient, which controls spontaneous electromagnetic radiation and by which white-noise collapse models are experimentally excluded,vanishes exactly. The reason is structural: because the distinguishability ledger is discrete,the collapse rate as a function of branch separation is identically zero below a threshold — ahard step, not a smooth rise — so its curvature at zero separation, which sets the momentumdiffusion, is exactly zero. Localised charges therefore radiate nothing, and the undergroundradiation bounds do not apply. The result rests on one stated assumption, strict discreteness ofthe distinguishability count, which is the premise itself; granting it, the evasion of the radiationbounds is a theorem rather than a tuning.