The Yamagishi Macroscopic Superposition Limit Theory ── 3rd ed.: The Density Correction Never Reached the Table of Radii, and E_G=Gm²/R Hides the Separation ── [Paper 55]
For the problem of the limit of macroscopic superposition, epitomised by "Schr\"odinger's cat," we present the picture of an auto-commit mechanism in the Universe OS and evaluate its critical particle number N_crit quantitatively using existing objective collapse models. The core of this paper is a correction. The first edition held that N_crit≈10¹¹ is fixed by overflow of the thread memory cost M(N) = M₀·2^N; but confronting this 2^N model with the holographic information capacity of the universe, ~10¹²² bits, yields N 405, so that the model itself disagrees with the asserted value by eight orders of magnitude (Theorem 2.1). Moreover the 2^N model carries the strong premise that "a classical substrate simulates quantum mechanics." This revision therefore relocates the grounds for N_crit to collapse models, presenting evaluation tables from the CSL model (Γ=λ N²) and Penrose gravitational collapse (τ=ħ/E_G) (Section 3). The result positions N_crit~10¹¹ as a marker of the quantum--classical transition region corresponding to microsecond-scale collapse under standard CSL parameters. That value, however, depends on the model and time criterion adopted and is not derivable from the OS picture alone. The current reach of molecular interference experiments is N~10³--10⁴, far from testing this regime (Section 4). Two further qualifications added in the second edition: (i) the CSL law Γ=λ N² holds only within the correlation length r_C≈10⁻⁷ m, and N=10¹¹ (R≈0.86\ μm) exceeds that condition by about ninefold --- that row is an extrapolation (note to Proposition 3.1). (ii) The Penrose table computes mass from a nucleon count but volume from an atom count, so its effective density is about 62 kg/m³ rather than solid density; recomputing at solid density shortens τ uniformly by about 3.2×, leaving the order-of-magnitude conclusions unchanged (note to Proposition 3.2). Both qualifications reinforce this paper's conclusion that N_crit is not uniquely determined. A note on the aim of this work. This is a structural reinterpretation of well-established physics, not a proposal for a new physical law. Every relation shown is a substitution into, or a geometric re-reading of, equations that are already known and that remain unchanged. The aim is a modest one: to make a few recurring geometric structures — in particular the solid angle 4π and the exponent n = 2 — easier to see within a single picture. Where a particular unit convention is adopted (for example G = 4π), this is a choice of notation, not a claim about nature. Nothing here is intended to contradict existing results. On the making of this work: The ideas and content of this work stem from the author's own considerations. Assistance from an AI (a large language model) was used for structuring, English translation, and checking the algebra. Any remaining errors or misinterpretations are solely the author's. Feedback and corrections are sincerely appreciated. ----- 「シュレーディンガーの猫」に代表されるマクロ重ね合わせの限界問題に対し、宇宙OSの自動コミット機構という描像を提示し、その臨界粒子数 N_crit を既存の客観的収縮模型により定量評価する。本稿の中核は訂正にある。初版はスレッドメモリコスト M(N) = M₀·2^N のオーバーフローにより N_crit≈10¹¹ が決まるとしたが、この 2^N 模型を宇宙のホログラフィック情報容量 ~10¹²² ビットに突き合わせると N 405 となり、模型自身が主張値と8桁食い違う(定理2.1)。さらに 2^N 模型は「量子力学を古典的基盤が模擬している」という強い前提を含む。そこで本改訂版は N_crit の根拠を崩壊模型へ移し、CSL模型(Γ=λ N²)およびPenroseの重力崩壊(τ=ħ/E_G)による評価表を提示する(第3節)。結果として N_crit~10¹¹ は、CSL標準パラメータの下でマイクロ秒スケールの収縮に対応する量子・古典転移域の目安として位置づけられる。ただしその値は採用する模型と時間規準に依存し、OS描像のみからは導出されない。 第2版で追加した2つの限定:(i) CSLの Γ=λ N² は相関長 r_C≈10⁻⁷ m の内部に限られる増幅則であり、N=10¹¹(R≈0.86\ μm)はこの条件を約9倍超過している——当該行は外挿値である(命題3.1の注記)。(ii) Penrose表は質量を核子数、体積を原子数として計算しているため実効密度が約 62 kg/m³ となり固体密度ではない;固体密度で計算し直すと τ は一律約 3.2 倍短くなるがオーダーの結論は不変である(命題3.2の注記)。いずれも「N_crit は一意に定まらない」という本稿の結論を補強する方向に働く。現行の分子干渉実験の到達点は N~10³--10⁴ であり、この領域を検証する能力はまだない(第4節)。 本稿の位置づけ。本稿は確立した物理法則に対する構造的解釈であり、新たな物理法則を提案するものではありません。示される関係はいずれも既知の式への代入、またはその幾何学的な読み替えであり、元の式は変わりません。目的はささやかで、繰り返し現れる幾何構造——とくに立体角 4π と指数 n = 2——を一つの描像の中で見やすくすることにあります。特定の単位系(例:G = 4π)を採る箇所は記法上の約束であって、自然についての主張ではありません。既存の結果と矛盾する意図はありません。 作成にあたって:本稿の着想と内容は、著者自身の考察に基づくものです。文章の構成整理や英訳、数式の確認には AI(大規模言語モデル)の助力を得ました。最終的な内容の解釈や誤りがあれば、それらはすべて著者の責に帰します。お気づきの点があれば、ご教示いただければ幸いです。
For the problem of the limit of macroscopic superposition, epitomised by "Schr"odinger's cat," we present the picture of an auto-commit mechanism in the Universe OS and evaluate its critical particle number N_crit quantitatively using existing objective collapse models. The core of this paper is a correction. The first edition held that N_crit≈10¹¹ is fixed by overflow of the thread memory cost M(N) = M₀·2^N; but confronting this 2^N model with the holographic information capacity of the universe, 10¹²² bits, yields N 405, so that the model itself disagrees with the asserted value by eight orders of magnitude (Theorem 2.1). Moreover the 2^N model carries the strong premise that "a classical substrate simulates quantum mechanics." This revision therefore relocates the grounds for N_crit to collapse models, presenting evaluation tables from the CSL model (Γ=λ N²) and Penrose gravitational collapse (τ=ħ/E_G) (Section 3). The result positions N_crit10¹¹ as a marker of the quantum--classical transition region corresponding to microsecond-scale collapse under standard CSL parameters. That value, however, depends on the model and time criterion adopted and is not derivable from the OS picture alone. The current reach of molecular interference experiments is N10³--10⁴, far from testing this regime (Section 4). Two further qualifications added in the second edition: (i) the CSL law Γ=λ N² holds only within the correlation length r_C≈10⁻⁷ m, and N=10¹¹ (R≈0.86\ μm) exceeds that condition by about ninefold --- that row is an extrapolation (note to Proposition 3.1). (ii) The Penrose table computes mass from a nucleon count but volume from an atom count, so its effective density is about 62 kg/m³ rather than solid density; recomputing at solid density shortens τ uniformly by about 3.2×, leaving the order-of-magnitude conclusions unchanged (note to Proposition 3.2). Both qualifications reinforce this paper's conclusion that N_crit is not uniquely determined. A note on the aim of this work. This is a structural reinterpretation of well-established physics, not a proposal for a new physical law. Every relation shown is a substitution into, or a geometric re-reading of, equations that are already known and that remain unchanged. The aim is a modest one: to make a few recurring geometric structures — in particular the solid angle 4π and the exponent n = 2 — easier to see within a single picture. Where a particular unit convention is adopted (for example G = 4π), this is a choice of notation, not a claim about nature. Nothing here is intended to contradict existing results. On the making of this work: The ideas and content of this work stem from the author's own considerations. Assistance from an AI (a large language model) was used for structuring, English translation, and checking the algebra. Any remaining errors or misinterpretations are solely the author's. Feedback and corrections are sincerely appreciated. ----- 「シュレーディンガーの猫」に代表されるマクロ重ね合わせの限界問題に対し、宇宙OSの自動コミット機構という描像を提示し、その臨界粒子数 N_crit を既存の客観的収縮模型により定量評価する。本稿の中核は訂正にある。初版はスレッドメモリコスト M(N) = M₀·2^N のオーバーフローにより N_crit≈10¹¹ が決まるとしたが、この 2^N 模型を宇宙のホログラフィック情報容量 10¹²² ビットに突き合わせると N 405 となり、模型自身が主張値と8桁食い違う(定理2.1)。さらに 2^N 模型は「量子力学を古典的基盤が模擬している」という強い前提を含む。そこで本改訂版は N_crit の根拠を崩壊模型へ移し、CSL模型(Γ=λ N²)およびPenroseの重力崩壊(τ=ħ/E_G)による評価表を提示する(第3節)。結果として N_crit10¹¹ は、CSL標準パラメータの下でマイクロ秒スケールの収縮に対応する量子・古典転移域の目安として位置づけられる。ただしその値は採用する模型と時間規準に依存し、OS描像のみからは導出されない。 第2版で追加した2つの限定:(i) CSLの Γ=λ N² は相関長 r_C≈10⁻⁷ m の内部に限られる増幅則であり、N=10¹¹(R≈0.86\ μm)はこの条件を約9倍超過している——当該行は外挿値である(命題3.1の注記)。(ii) Penrose表は質量を核子数、体積を原子数として計算しているため実効密度が約 62 kg/m³ となり固体密度ではない;固体密度で計算し直すと τ は一律約 3.2 倍短くなるがオーダーの結論は不変である(命題3.2の注記)。いずれも「N_crit は一意に定まらない」という本稿の結論を補強する方向に働く。現行の分子干渉実験の到達点は N10³--10⁴ であり、この領域を検証する能力はまだない(第4節)。 本稿の位置づけ。本稿は確立した物理法則に対する構造的解釈であり、新たな物理法則を提案するものではありません。示される関係はいずれも既知の式への代入、またはその幾何学的な読み替えであり、元の式は変わりません。目的はささやかで、繰り返し現れる幾何構造——とくに立体角 4π と指数 n = 2——を一つの描像の中で見やすくすることにあります。特定の単位系(例:G = 4π)を採る箇所は記法上の約束であって、自然についての主張ではありません。既存の結果と矛盾する意図はありません。 作成にあたって:本稿の着想と内容は、著者自身の考察に基づくものです。文章の構成整理や英訳、数式の確認には AI(大規模言語モデル)の助力を得ました。最終的な内容の解釈や誤りがあれば、それらはすべて著者の責に帰します。お気づきの点があれば、ご教示いただければ幸いです。
Version 4 (October 2026), interim correction: an independent review found that the main result is a reformulation rather than a recovery. Both inputs to the budget-saturation condition, the superposition cost and the budget B = ħ/τ, are posited, so its agreement with the Penrose–Diósi criterion holds by construction. The uniform-sphere coefficient in the testable prediction is off by a factor of 6/5, and the tabulated collapse times use a small-displacement formula outside its range. These results should not be cited until the revised version is posted. Details are in the Revision History of the PDF.We show that the Penrose–Diósi gravitational collapse criterion — which predicts that quantum superpositions decay on a timescale τ = ℏ/E_G, where E_G is the gravitational self-energy of the difference mass distribution — arises as the budget-saturation condition of the selective reconstruction framework (Russell 2026a). When the reconstruction budget B is identified with ℏ/τ_local via the Margolus–Levitin theorem, the Russell constraint C_super ≤ B becomes the Penrose–Diósi inequality E_G ≤ ℏ/τ. "Observation" is thereby reframed not as a primitive physical event but as the condition under which the gravitational self-energy of a superposition exhausts the geometric reconstruction budget of the boundary observer. The result is observer-dependent and recovers relational quantum mechanics as a consequence of resource constraints. A falsifiable, mass-scaling prediction (τ ∝ M⁻² d⁻² R³) is derived for levitated-nanosphere experiments. A structural isomorphism with Nanite's LOD scheduling algorithm is noted as a conceptual heuristic. Epistemic status: The budget identification is motivated by the Margolus–Levitin theorem but is not formally derived from AdS/CFT. This is a working paper inviting scrutiny, not an established result.v3 (2026-05-27): Format converted from HTML to LaTeX. §5 collapse-time table recomputed under the stated d=R, ρ=2200 kg/m³ convention (prior values were inconsistent with the formula by ~30 orders of magnitude). Reference 8 updated per consolidation of Virtualized Geometry into Spacetime as Optimal Allocation. Minor text corrections: sub-femtokelvin → sub-microkelvin, Verlinde (2010) → (2011), Stanford → ETH Zurich. Figures regenerated with layout fixes (no content changes). ORCID, email, and concept DOI added to front matter.
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%.
In the Bose–Marletto–Vedral (BMV) class of tabletop gravity experiments, two mesoscopic masses are each placed in a spatial superposition and their Newtonian interaction is used as a witness of gravitationally induced entanglement. Aspelmeyer [5] has sharpened the standard argument: observing entanglement at the 10-15 kg scale already rules out current Diósi–Penrose (DP) collapse models. Here we ask a complementary question: when the source mass itself is the object in superposition, what is the sign of the gravity-induced decoherence *rate* as a function of M/r (mass over characteristic superposition scale), and where in the mass range is that rate actually measurable? We compare three branches: (A) linearized quantum field theory, which gives reversible phase accumulation and Gamma = 0; (B) DP / continuous spontaneous localization (CSL) collapse, for which Gamma > 0 and grows steeply with M/r (positive trend); and (C) a phenomenological strawman of variable vacuum-foam / stochastic-spacetime suppression, Gammafoam = Gammafbg exp(-3 kappa GM/(rc2)), for which the trend is negative. Branch C is not derived from any specific quantum-gravity model; it is introduced only to give the sign question a non-trivial alternative. We solve the rates for a uniform sphere (density rho = 2000 kg/m3, superposition separation d = 10 r) and find: (i) a rate-resolved window M ~ 2×10-16 to 10-14 kg in which the DP rate exceeds a BMV-class environmental floor of 0.05 s-1 but is still measurable — this window lies below the regime where entanglement-survival alone, à la Aspelmeyer, already excludes DP; (ii) the phenomenological strawman foam-suppression branch is observationally degenerate with QFT-zero on Earth, because d ln Gammafoam / d ln M = -2 kappa GM/(rc2) ~ -10-37 to -10-35 across the entire lab range. Discriminating this toy from QFT-zero would require the near-Schwarzschild regime x = GM/(rc2) ~ O(1). Shot-noise-limited run counts are ~6 at M = 10-15 kg, ~104 at M = 10-16 kg, and environment-limited below M = 10-16 kg. All numerical values are illustrative/synthetic order-of-magnitude estimates.
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.
See changelog below. The full derivations are provided in the attached paper. Every result is reproducible from the stated inputs. This paper derives the complete Standard Model, quantum mechanics, spacetime, and gravity — 85 quantitative results at sub-percent precision spanning 15 orders of magnitude — from a single postulate, four structural principles, and one measurement. The Standard Model has seventeen free parameters. General relativity has no quantum theory. The measurement problem has been open for a century. The cosmological constant is wrong by 120 orders of magnitude. The question of why there is something rather than nothing has no physical answer in any existing framework. Each of these failures shares a common omission: none ask where time comes from. This paper takes that question seriously. A single physical principle — information cannot be destroyed — is self-sealing: its own violation is incoherent. Its formal expression is Postulate I: each foreclosed quantum branch produces exactly one chronon — a massless spin-1 gauge boson of U(1)_T, the unique gauge group forced by the complex ray structure of the Hilbert space and the single scalar collapse charge. We call it the chronon. Time is not the background in which physics happens; it is generated by physics, irreversibly, at every collapse. These requirements yield a single Lagrangian, ℒ_QT, that extends the Standard Model by one massless spin-1 field and one coupling constant. From this — combined with one measurement, Newton’s gravitational constant G — we derive: all of quantum mechanics via the Piron–Soler–Gleason chain (not assumed); the complete Standard Model with all dimensionless parameters determined; the complete resolution of the measurement problem, including the environmental decoherence cascade; and 85 quantitative physical results spanning fifteen orders of magnitude in energy. Three spatial dimensions follow from the channel-matching principle (D = N_c) and the Weinberg angle consistency condition (N_c = 3). The Big Bang was not initiated — it was mandatory. The numerical precision is sharp. The worst result where the theoretical prediction exceeds experimental precision is 0.5%. For the majority of results, the framework’s prediction is already more precise than the measurement. The proton-to-electron mass ratio m_p/m_e = 2N_cπ⁵(1 + α²/√(N_c²−1)) agrees to sub-ppb precision. The proton charge radius matches muonic hydrogen to five significant figures. The Higgs boson mass to 0.002% via the full cascade derivation (0.25% from the explicit formula). The W boson mass to 0.001%. The fine structure constant to 0.026% (1/α = 137 exactly at tree level). The cosmological constant — wrong by 120 orders of magnitude in standard QFT — is derived to 0.03%. The Hubble tension, a 5σ discrepancy unresolved in standard cosmology, follows from the same structure: H₀_local = H₀ × 13/12 = 73.0 km/s/Mpc (0.05%). All four PMNS neutrino mixing parameters, previously unexplained, are derived to sub-0.5%. Sub-percent agreement spans from neutrino mass splittings at ~9 meV to the CMB temperature at 2.725 K — fifteen orders of magnitude from a single dimensionful input. The framework makes ten falsifiable predictions currently under test: an electron electric dipole moment of exactly zero (ACME III is live); a spin-1 gravitational wave breathing mode at ~9% of the + polarisation amplitude (testable with LIGO O4/O5 data); no dark matter particle in any direct-detection experiment; no graviton — gravity is geometric drift in a proper-time gradient sourced by the energy-momentum tensor, not exchange of a spin-2 particle; there is nothing to detect. A confirmed non-zero electron EDM or a detected graviton falsifies the framework immediately. The logical order, from bottom to top: information cannot be destroyed → P-I (one chronon per foreclosed branch) → proposition lattice with axioms P0–P4 → Piron–Soler–Gleason chain → complex Hilbert space → ray phase redundancy → single scalar collapse charge → U(1)_T gauge field with Maxwell dynamics → channel-matching principle gives D = N_c → Weinberg angle selects N_c = 3 → D = 3 → adding G through the Planck cascade gives λ_conf = 0.40092 fm → the complete Standard Model follows. Spacetime, quantum mechanics, and the Standard Model are not independent inputs — they follow as consequences of P-I, the structural principles, and one observational consistency condition. ______________________________________________________________________________________________________ v86 Changelog (April 7–8 2026) — All numerical results unchanged from v85. No formulas modified. Foundational structure and derivation justifications rebuilt following adversarial review by two independent AI systems (Claude, GPT-4o). Foundational hardening: §2.2: Formal axiom framework P0–P4 added. Piron lattice conditions now follow as a theorem given five named structural axioms, not as informal physical arguments. P-I motivates four directly; P0 (admissibility closure) is a structural axiom on the proposition space. §2.5: ℝ exclusion replaced. Old iε propagator argument replaced with operational compositionality / local tomography argument requiring no field-theoretic machinery. §3.1: Gauge derivation rebuilt from complex ray structure forward. U(1)_T now derived from phase redundancy + single scalar collapse charge + rank-1 compact Lie group + label-free emission. Removes prior dependence on Noether's theorem invocation and energy minimization principle. §8.1.1: Channel-matching theorem added. D = N_c derived from information-balance between spatial export channels and internal confinement channels via mismatch functional. Replaces prior mutual-reinforcement argument. §1.5.1: Epistemic taxonomy added classifying all 85 results into three tiers: theorem-level (Piron, Soler, Gleason), physical-argument (gauge structure, mass formulas), and observational-consistency (N_c = 3 from Weinberg angle, cascade from G). §12: New section — Structural Analysis. Result classification (5 epistemic tiers, ~12 independent core results, compression ratio 85:19), axiom necessity (what breaks without each of P0–P4 and D1–D4), and ablation tests (N_c = 2, N_c = 4, drop P4, change coupling exponent, allow D ≠ N_c — every perturbation destroys the majority of results). Framework premise expanded from "one postulate" to "one postulate, four structural principles, and one measurement." Front matter aligned with body throughout. One derivation story, no internal contradictions. Derivation upgrades: Proton-to-electron mass ratio (§9.3): Replaced "2 spin states × N_c colours" with rigorous hyperspherical decomposition. S³ forced by massless emission in (3+1)D; S⁵ forced by K=0 ground state of 3-quark system in 6D relative coordinates. Neutral pion mass (§9.9.1): Factor 5 now derived as 2N_c − 1. Denominator 2π identified as one-loop coefficient of U(1)_T vector gauge coupling. Neutron-proton mass difference (§9.3.2): Replaced "circular loop + straight line" with flux tube arm derivation. π from SU(2) isospin rotation; +1 from chromoelectric flux tube arm to Y-junction. CP phase δ (§9.8.2): Replaced "axial-to-spherical flux ratio" with V−A vertex structure. The ratio 4/π is universal across all generation spaces because any unitary rotation lies on a great circle of S². W boson mass corrections (§9.5.1): Both NLO terms fully derived. Direct vertex α_s/(8π): C_F cancelled by non-relativistic reduction. Exchange α_s/(12π²): two vertices × Dirac-to-colour projection ratio. Charm mass (§9.13.4): Factor 4/π identified as axial-to-vector coupling ratio through V−A weak vertex. Systematic correction — QCD dressing factor: The coefficient 1/(2π) appearing in ~10 results was previously attributed to "hemisphere projection geometry." Replaced throughout: mass in the chronon framework is a U(1)_T vector gauge coupling, not a scalar Yukawa coupling. The factor 1/2 confirmed by two independent routes: (i) Dirac algebra (γ^α γ^μ γ_α = −2γ^μ vs scalar = 4); (ii) C_F cancellation by non-relativistic reduction. Label correction: CKM geometric factor (§9.8.1): "four-dimensional solid angle" corrected to "three-dimensional solid angle S² = 4π." Numbers unchanged. ______________________________________________________________________________________________________ v85 Changelog (April 6 2026) — Electroweak corrections, |V_cb| prediction, consistency audit Four physics improvements and a comprehensive numerical audit, all from first principles with zero free parameters. Top quark mass (0.41% → 0.06%): The electroweak self-energy correction factor changed from (N_c+1) to (N_c−1). The factor (N_c−1) = 2 counts the charged weak boson states (W⁺, W⁻) mediating the t→b→t self-energy loop — the SU(2)_L charge-raising/lowering generators. m_t = 172,803 MeV vs observed 172,700 MeV. CKM θ₂₃ / |V_cb| prediction (1.3% → 0.3%): The framework predicts |V_cb| = 42.1 × 10⁻³, essentially identical to the PDG inclusive determination (42.2 ± 0.5) × 10⁻³ and inconsistent with the exclusive determination (39.8 ± 0.6) × 10⁻³. The inclusive/exclusive |V_cb| tension is one of the open questions in flavour physics; the framework picks a side. Falsifiable prediction. Baryon asymmetry η (0.5% → <0.1%): The sphaleron efficiency κ correction changed from α_s/(2π²) to α/(2π). The sphaleron is an SU(2)_L electroweak process; its one-loop vertex correction uses the QED coupling α/(2π), not the QCD coupling. Neutrino mass splitting Δm²₂₃ (0.3% → 0.08%): QED vacuum polarization correction −α/(2π) added to G₃ alongside the existing QCD correction +α_s/π. Sign pattern (QCD adds, QED subtracts) matches the W boson mass derivation. Numerical audit (22 corrections): Full line-by-line verification of every formula, table entry, agreement claim, and cross-reference. Corrections include: D/H value (2.62→2.58 × 10⁻⁵, 1.3σ→1.8σ — stale from pre-κ η); He-4 agreement (0.5σ→0.7σ); z_
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.