This is a physics paper, not a mathematics paper: nothing here is proved about the Riemann zeta function, and nothing is claimed beyond what is derived or measured. Modular Entropic Gravity (MEG) derives a projection from its completed vacuum structure to the observable level, whose spectral representation is the previously established transfer identity T₃ = ζ(½+iD). Under that identity the non-trivial zeros acquire a physical reading: they are the deficit of the projection — the frequencies at which transmission fails. This paper turns that reading into a falsifiable physical prediction and tests it under a frozen, pre-registered protocol whose pipeline never evaluates the zeta function. The naive prediction — that an observer's distinguishability metric is the transfer-weighted |ζ|² metric — is shown to be wrong as physics: for Gaussian states restricted to the blocked observable algebra, the Fisher metric involves the inverse restricted covariance, and an ideal observer inverts any invertible channel. The corrected prediction is a noise-limited saturating metric, M_N ≈ |ζ|²/(|ζ|² + N_eff), with quantitative laws attached. In one sentence: the zeros are the only places where a finite-resolution observer cannot undo the projection. The prediction was tested under a frozen protocol (freeze → run → open comparison → interpret) whose pipeline never evaluates the zeta function: the arithmetic enters only through the axiomatic integer ladder. The covariance matrix and probe vector are computed by literal ladder sums, the vacuum weight through its Bessel closed form, and the pole term by direct quadrature. Reference values of ζ' and the zero ordinates enter only at the open-comparison stage, after detection is locked. The honest phrase is "zeta-not-evaluated," not zeta-unrelated: the arithmetic is in the construction, by axiom, and that is the point. Results: six zeros in the swept range [10, 40], six blind detections, zero false positives. The shuffled-ladder control destroys the entire Fisher signal (coherent multiplicative structure is necessary for any transmission). The zero-free damped-ladder control (symbol ζ(1.1+ir), identical zeta-not-evaluated machinery, matched instruments) heals as the noise floor is lowered while the true scars are invariant: 615× discrimination. The pre-registered packet-shift law Δr = −πσ²/4 is confirmed quantitatively at two packet widths, with raw blind centres locking to the zeros within 0.03 at the finest packet — meeting the frozen criterion with no calibration. The deficit is shown to be grading-blind: the boundedly invertible p = 2 deformation (1−2W₂) leaves the zero-channel deficit unchanged while killing the pole condensate, confirming the invariance tier of the spectral dictionary established in the companion paper (doi:10.5281/zenodo.21308830). Verdict: strong positive with one confirmed quantitative lock. No frozen fail condition triggered. A frozen finite-resolution Fisher test recovers the first six Riemann zero scars from the MEG Level-3 ladder observer, with no zeta evaluation in the pipeline, a confirmed packet-shift law, and strong zero-free controls. The verdict is deliberately not inflated: this is severity, not proof. Relation to the spectral tradition: the Hilbert-Pólya programme seeks a quantum system whose emission spectrum is the zeros. This result is of the opposite polarity — in the MEG reading the zeros are an absorption structure. What this paper adds to the absorption tradition is what it has always lacked: an observer. The statement "the zeros are missing spectral lines" becomes a statement about measurement — a finite-resolution observer of a specific, independently constructed physical vacuum demonstrably cannot distinguish states at exactly those frequencies. The accompanying deposit includes the complete frozen protocol document, the reference implementation code, verification scripts, and all data files needed for independent reproduction. Independent reimplementation from the protocol document alone is invited. Keywords: Riemann zeta function, zeros, projection deficit, Fisher information, distinguishability metric, noise-limited observer, frozen protocol, blind detection, absorption spectrum, vacuum entanglement kernel, transfer operator, integer ladder, grading blindness, spectral dictionary, modular entropic gravity
This is a physics paper, not a mathematics paper: nothing here is proved about the Riemann zeta function, and nothing is claimed beyond what is derived or measured. Modular Entropic Gravity (MEG) derives a projection from its completed vacuum structure to the observable level, whose spectral representation is the previously established transfer identity T₃ = ζ(½+iD). Under that identity the non-trivial zeros acquire a physical reading: they are the deficit of the projection — the frequencies at which transmission fails. This paper turns that reading into a falsifiable physical prediction and tests it under a frozen, pre-registered protocol whose pipeline never evaluates the zeta function. The naive prediction — that an observer's distinguishability metric is the transfer-weighted |ζ|² metric — is shown to be wrong as physics: for Gaussian states restricted to the blocked observable algebra, the Fisher metric involves the inverse restricted covariance, and an ideal observer inverts any invertible channel. The corrected prediction is a noise-limited saturating metric, M_N ≈ |ζ|²/(|ζ|² + N_eff), with quantitative laws attached. In one sentence: the zeros are the only places where a finite-resolution observer cannot undo the projection. The prediction was tested under a frozen protocol (freeze → run → open comparison → interpret) whose pipeline never evaluates the zeta function: the arithmetic enters only through the axiomatic integer ladder. The covariance matrix and probe vector are computed by literal ladder sums, the vacuum weight through its Bessel closed form, and the pole term by direct quadrature. Reference values of ζ' and the zero ordinates enter only at the open-comparison stage, after detection is locked. The honest phrase is "zeta-not-evaluated," not zeta-unrelated: the arithmetic is in the construction, by axiom, and that is the point. Results: six zeros in the swept range [10, 40], six blind detections, zero false positives. The shuffled-ladder control destroys the entire Fisher signal (coherent multiplicative structure is necessary for any transmission). The zero-free damped-ladder control (symbol ζ(1.1+ir), identical zeta-not-evaluated machinery, matched instruments) heals as the noise floor is lowered while the true scars are invariant: 615× discrimination. The pre-registered packet-shift law Δr = −πσ²/4 is confirmed quantitatively at two packet widths, with raw blind centres locking to the zeros within 0.03 at the finest packet — meeting the frozen criterion with no calibration. The deficit is shown to be grading-blind: the boundedly invertible p = 2 deformation (1−2W₂) leaves the zero-channel deficit unchanged while killing the pole condensate, confirming the invariance tier of the spectral dictionary established in the companion paper (doi:10.5281/zenodo.21308830). Verdict: strong positive with one confirmed quantitative lock. No frozen fail condition triggered. A frozen finite-resolution Fisher test recovers the first six Riemann zero scars from the MEG Level-3 ladder observer, with no zeta evaluation in the pipeline, a confirmed packet-shift law, and strong zero-free controls. The verdict is deliberately not inflated: this is severity, not proof. Relation to the spectral tradition: the Hilbert-Pólya programme seeks a quantum system whose emission spectrum is the zeros. This result is of the opposite polarity — in the MEG reading the zeros are an absorption structure. What this paper adds to the absorption tradition is what it has always lacked: an observer. The statement "the zeros are missing spectral lines" becomes a statement about measurement — a finite-resolution observer of a specific, independently constructed physical vacuum demonstrably cannot distinguish states at exactly those frequencies. The accompanying deposit includes the complete frozen protocol document, the reference implementation code, verification scripts, and all data files needed for independent reproduction. Independent reimplementation from the protocol document alone is invited. Keywords: Riemann zeta function, zeros, projection deficit, Fisher information, distinguishability metric, noise-limited observer, frozen protocol, blind detection, absorption spectrum, vacuum entanglement kernel, transfer operator, integer ladder, grading blindness, spectral dictionary, modular entropic gravity
The Geometric Vacuum (GeoVac) framework separates into two structurally distinct layers, and that separation is the organizing principle of its precision-observation arc. Layer 1 is a bare combinatorial graph: quantum-number labels (n,ℓ,m,…), integer eigenvalues, rational or algebraic matrix elements, no physical units, and—verified symbolically—no π. Layer 2 is a finite family of named projections from that graph onto continuous physical settings; every physical variable, every dimension, and every transcendental constant that appears in any GeoVac calculation enters through exactly one projection and is traceable to it. This synthesis assembles the four Group 6 papers into a single narrative built on that thesis. The spine is: the projection taxonomy and its three-axis tagging (Paper 34 [ref]); time as the prototype free-side projection—π enters the Klein–Gordon spectrum on S3×R at exactly one step, temporal compactification, while rest mass preserves the algebraic ring (Paper 35 [ref]); entropy as an embedding-class projection artifact, identically zero on the one-body graph and finite only after the metric embedding of the two-body repulsion (Paper 27 [ref]); and the entanglement structure that isolates that repulsion in the angular-momentum eigenbasis (Paper 26 [ref]). A multi-observable focal-length program closes the arc: Roothaan autopsies decompose precision atomic observables into projection-chain-tagged components, exposing literature convention mismatches and framework kernel gaps that single-observable analyses cannot see. Two disciplines run throughout. First, every transcendental named here is tagged to its projection—π via the Hopf and Fock volume measures, π2k via the spectral action, ζ(2k) via even-zeta Dirichlet series, odd ζ and Catalan G via the half-integer-Hurwitz spinor lift, 2π via temporal compactification. Second, the precision matches are sub-percent framework-native agreements that surface convention and kernel issues; they are not first-principles predictions of the constants, and the multi-focal-composition wall—the framework has no native theorem for composing multiple Fock-style projections—is named as an active boundary. The unifying reading is that ``discreteness is compactness'' made operational: the discrete skeleton is the compact/closed regime, and a transcendental is precisely the price of releasing compactness by integrating over a promoted continuous parameter. GeoVac synthesis document. Part of the GeoVac research corpus (synthesis / reading guide group). Code, tests, and the full paper series: https://github.com/jloutey-hash/geovac. Corpus archive DOI: 10.5281/zenodo.20482394. Corpus version at deposit: v4.75.0.
Overview This Zenodo record gathers the connected mathematical, computational and methodological corpus developed by Thierry Origas under the title Riemann Strong Origas. The corpus is organised as a three-level scientific programme: the local level — World A, represented by Galilean and Einsteinian local frames, experimentally accessible measurements, spectral outputs, operators and predictive results; the exchange and reconstruction level — the Cabine 1/2, represented by Point 0, the structural bridge Kstr, the finite arithmetic prototype KX, the global history parameter T and the differentiated local branches t+ and t−; the frozen non-local level — World B, represented by an independent EPR-type observational question asking whether the proposed Double RingCross Origas structure is physically real. The central reconstruction problem The central mathematical question is whether a common local observation, a spectrum, a determinant or a predictive output is sufficient to reconstruct the complete structure that produced it. The corpus studies situations in which two differentiated sectors A and B may project onto the same observable Point 0 while retaining different order, projector, phase, orientation, holonomy, gluing and history data. In such a case, a representation that depends only on the common projected output is not conservative. The Cabine 1/2 is therefore introduced as an over-arching reconstruction framework rather than as an additional local measurement device. In its consolidated mathematical formulation, it is represented by a third object connecting two local sectors through a common observation space. The corpus makes a strict distinction between: Kstr: the structural gluing datum required to preserve the fibre, order, phases, projectors, holonomy and history; KX: a finite, prime-generated arithmetic prototype proposed as a candidate realisation of this bridge; T: a global parameter of history, provenance and ordering; t+ and t−: two differentiated local branches associated respectively with predictive or spectral information and with differential, historical or geometric information. Mathematical and computational programme The successive manuscripts develop two-sector chiral operators, spectral-blindness and non-reconstruction theorems, four graded roots around Point 0, B-completeness criteria, oriented holonomy, topos-conservative reconstruction, prime-power-generated phases, sealed out-of-sample predictions, Null tests, Bridge-OFF controls and criteria for temporal and conservative completeness. A recurring result of the programme is that identical spectral outputs do not necessarily determine identical projectors, indices, orientations, histories or hidden geometries. The ordinary spectrum may describe a common visible channel while leaving a differentiated wing undetermined. The finite arithmetic bridge KX is constructed from declared prime and prime-power data and frozen parameters. Its numerical performance, phases, wing labels and sealed predictions are computational results. KX is not identified with the final infinite Riemann operator unless convergence toward the completed Riemann function, determinant identification, self-adjointness and complete conservative reconstruction are independently established. Relationship to the Wang–Kakeya publication This corpus is directly related to the previously published Zenodo record DOI 10.5281/zenodo.21535840, which applies a corresponding conservative A+B methodology to Kakeya geometry. The Wang–Kakeya record constitutes a specific application of the broader reconstruction question developed here: a projected spatial support or a correct theoretical result may remain insufficient to reconstruct incidence histories, non-commutative order, multiscale structure, oriented holonomy or all the information carried by the complete A+B object. The purpose of the A+B lift is not to invalidate or replace the original Kakeya result. It is to investigate whether a richer conservative representation can preserve additional operational information while leaving the established result intact. Relationship to Aspect, Connes and contemporary programmes The published works of Alain Aspect, Alain Connes, Hong Wang and the other researchers cited in the manuscripts are used as scientific references, comparison points and boundary cases. Their presence in this record does not imply collaboration, endorsement or agreement with the author’s interpretations. The corpus does not claim that their established experimental or mathematical results are invalid. It asks a different and stronger reconstruction question: in addition to producing a correct observable or spectral output, does a model preserve the order, projectors, phases, holonomy, gluing data and history required to reconstruct the complete differentiated structure? Non-commutativity is treated not merely as an algebraic complication but as a possible carrier of order and meaning. Commutativisation may be legitimate for a declared output while remaining non-conservative for the complete history from which that output was derived. The frozen non-local EPR question A separate series of prior Zenodo deposits contains frozen, dated and publicly traceable predictions associated with an EPR-type question posed to Nature: is the proposed Double RingCross Origas structure real? This question is not presented in the present record as already answered. The Double RingCross, its proposed role as an external clock or space-time structure, the non-local interpretation of World B and the physical interpretation of T remain hypotheses awaiting independent observational adjudication. Within the author’s methodology, Nature is treated as the final empirical adjudicator. This means that the outcome must be determined by observations made under declared coordinates, tolerances, instruments and protocols, without post-hoc modification of the frozen question or predictions. If the independent observations answer negatively, the corresponding non-local interpretation must be rejected or revised. If they answer positively under the frozen conditions, the result would provide an external empirical anchor for the relationship between the local sector, the Cabine 1/2 exchange level and the proposed non-local sector. In neither case may the mathematical requirements of the Riemann programme be replaced by a physical interpretation. Scientific status This record does not claim: a completed proof of the Riemann Hypothesis; the established non-existence of Planet Nine; the present observational validation of the Double RingCross; the experimental establishment of a universal absolute physical reference frame; the physical identification of Kstr, KX or T without an independent test. The corpus contains several distinct levels of result: exact mathematical statements under explicitly declared assumptions; finite and reproducible computational constructions; numerical audits and sealed predictions; methodological interpretations and proposed reconstruction criteria; local physical analogies and protocols; open non-local hypotheses awaiting independent observational adjudication. These levels must be evaluated separately. A result established at one level is not automatically promoted to a stronger mathematical, physical or ontological status. Corpus organisation Strong Origas XI is the consolidated mathematical entry point. Earlier manuscripts preserve the chronological development of the programme, including corrections, negative results, intermediate constructions, proof-status distinctions and computational stages. The principal international editions are provided in English. Two French-language source manuscripts are retained in their original language where exact authorial formulation is considered important. Their language does not alter their scientific status.
Wei et al. (Nat. Commun., 2026; preprint arXiv:2511.11199v1) report a quantum algorithm for ζ(½+it) and compare its cost against direct Riemann–Siegel summation. This note examines that comparison. The speedup claim is correct against the baselines the paper names, and correct for a single isolated evaluation. It is, however, applied to locating and verifying zeros, which is a bulk task, and the classical state of the art for bulk evaluation is amortized. Odlyzko–Schönhage (1988) amortizes to T^ε per point, for every ε > 0, over blocks of length T^(1/2) after one precomputation, where the quantum method offers no amortization mechanism at all and pays its per-point cost every time; Hiary's amortized method (Math. Comp., 2011) reaches the same T^(1/4) exponent classically fifteen years earlier. Neither is cited in the preprint's 47-item reference list — a finding scoped to arXiv:2511.11199v1 and to that version only, for reasons given below. The Hiary paper the preprint does cite is the later Annals method, not the amortized one. Odlyzko–Schönhage is present in the source bibliography database but uncited, one of 16 uncited entries of 65, a set that also contains Riemann (1859); no intent is inferred. One argument is developed and one is withdrawn. The withdrawn one is a precision penalty. A measurement made for this note over 6200 Gram points spanning six decades of height finds |Z| height-flat (fitted slope −0.00005941, R² = 0.000333), so the sampling resolution δ is a large constant factor, not an asymptotic penalty. What survives is practical rather than asymptotic and rests on a single datum, the most extreme value in the sources obtained here; no distribution for that tail is stated in any of them, so the datum is not an upper bound on the precision required. The argument that carries the weight is categorical rather than complexity-theoretic: amplitude estimation returns confidence intervals, whereas rigorous verification of the Riemann Hypothesis to a given height requires certified enclosures. Platt–Trudgian's accounting of their 3×10¹² computation supports this, attributing a 725× cost of rigour to interval arithmetic and sampling rate and explicitly not to precision. Separately, the paper's correspondence theorem is shown to hold at every zero in the strip, not only on the critical line; this is a statement about the construction, which is therefore coextensive with the Riemann Hypothesis rather than evidence bearing on it. Nothing here bears on the hypothesis itself, and nothing here disputes the physics. Every claim is traced to a hashed artifact and classified by the strength of its warrant. The bibliography findings are scoped to arXiv:2511.11199v1: the published record is an Accelerated Article Preview carrying no reference list, and the published version is known to differ from v1, so a recheck is registered against the edited version when it appears. Three blockers are left open and stated rather than closed — the unavailable published reference list, the absent tail distribution, and what actually sets the operative resolution for sign-change-based verification, given that precision was demonstrably not the binding classical constraint. An appendix registers one pre-specified, falsifiable prediction about quantum block-amortized cost.
This is the demonstration layer of the Phase III central proposition of the research programme on the rigidity of geometric incidence. The predecessor framework supplies the quantum-measurement collapse arrow as a purely geometric datum — the causal structure and temporal orientability of Minkowski space — while keeping the global evolution unitary, and records the irreversibility of a measurement event as a causal monotone tied to the four-volume of the causal diamond between event and observer. The same data admit two readings: a geometric reading, in which the functional form of the irreversibility is rigidly determined by the modular geometry of the diamond (fixed up to an overall normalization) and is invariant under a change of geometry without recalibration; and an effective reading, in which the law is merely carried by a thermodynamic registration channel whose coefficient is free and must be recalibrated for each geometry. The paper poses the decision between them as a single theorem of empirical non-equivalence, built symmetrically so that either verdict — rigidity (new physics) or equivalence (reduction to einselection with an imported thermodynamic arrow) — would be a valid, publishable outcome. Working in algebraic quantum field theory, where the local algebras are type III₁, it establishes (on a reference state with geometric modular action — the vacuum, via Bisognano–Wichmann) that the irreversibility functional is determined by the diamond's modular data up to one normalization constant (Tomita–Takesaki, Casini–Huerta–Myers, Araki relative entropy), with the entire residual freedom localized in the modular status of the record-carrying state. Whether that normalization is itself geometric (the value π/24) is graded as a conjecture and is not load-bearing; the decisive content is invariance under a change of geometry, and the value is adjustable. In the genuine type III₁ continuum, both halves of the discriminating apparatus return a third verdict: the registered antisymmetric orientation is geometric and irreducible to any CPTP channel (in type III₁ there is no reduced density matrix to dilate, so no Stinespring dilation can readmit it "as only an ancilla"), yet it coincides with the Borchers–Wiesbrock spectral condition (energy positivity) — already-known QFT serving as the arrow, rather than a new irreducible mechanism. Any genuinely new positive is localized to two named sites: the interacting / non-geometric-flow sector (β ≠ 2π/a, where the Connes–Rovelli thermal-time reading must be rebutted, not assumed) and the orientation of the modular inclusion. A preregistered finite-N Gaussian discriminator returns equivalence in the simulable (type I) class — reported honestly as inconclusive for the fundamental reading, since the decisive type III₁ regime is not reached at any finite N. Scope: special-relativistic (Minkowski); gravity and quantum gravity are deferred. All results are explicitly graded (theorem / proposition / conjecture / computation / inherited), and the type III₁ instruments and verdict data are included with the deposit. Changes in v2 (2026-07-08). This version adds Phase IV, step 3 — the two-axis closure of the region left open by the free-sector verdict. Route (b), non-geometric Gaussian flow (multi-interval): the multi-interval vacuum modular flow is genuinely non-geometric (bilocal strength ρbi ∈ [0.004, 0.064]) yet carries a single modular temperature on every channel (D ≡ 0 at βmod = 1 to 10-12, continuum-stable), with the independent-scales einselection foil detected at D = 0.148 — NULL. Route (a), perturbative non-Gaussianity (tree-level λφ3): the T-odd connected cumulant onsets at first connected order (|A3| ∝ λ) but its separating content is zero (D = 0, dD/dλ = 0), while the multi-scale and FDT-breaking foils fire at 0.138 and 0.177 — NULL / recalibrable; the third verdict extends to the perturbative interacting sector. Both axes were pre-registered before running (frozen 2026-06-26 and 2026-06-25 respectively); no v1 result is altered. New verified references: Peschel (2003), Casini–Huerta (2009), Peschel–Eisler (2009), Arias–Casini–Huerta–Pontello (2018).
TL;DR — The Core Finding Contrary to the initial expectation that arithmetic structures (e.g., the coprime-to-6 mask or the Möbius mask) generate distinct number-theoretic spectral signatures, this work provides numerical and formally certified evidence that the Non-Ergodic Extended (NEE) phase is entirely governed by the preservation of first-neighbor connectivity (d=1). Suppressing the d=1 hopping channel induces a topological collapse into strong spatial localization (D2≈0.288→0.045, a factor of 6.4), representing a single-particle spatial analogue of Hilbert Space Fragmentation (HSF). Furthermore, the deep arithmetic logic of the Möbius function acts as topological white noise, in compliance with the Möbius Randomness Principle (Sarnak conjecture): since 86.05% of the interaction variance is concentrated in short-range bonds (d≤5), deeper arithmetic channels are swamped by the finite-size GUE noise floor (σGUE∼1/N). Theoretical and Physical Framework Deterministic-stochastic hybrid Hamiltonian. Combines an exact Riemann–von Mangoldt diagonal potential (inverted deterministically via the Lambert WW function) with Power-Law Random Banded Matrix (PRBM) off-diagonal disorder. Sparse hopping constraints. Hopping is filtered by deterministic arithmetic sieves (coprime-to-6 mask Ξ6, square-free Möbius mask Ξμ, Liouville mask Ξλ) and controlled random Bernoulli ensembles. Single-particle Hilbert space fragmentation. Without d=1, adjacent spatial transitions (i→i+1) require higher-order virtual paths (i→i+5→i+1) that suffer severe energy detuning from the fluctuating diagonal potential. The one-dimensional metric graph shatters into decoupled spatial clusters. Coupling variance dominance. The power-law decay (d−1.5 in variance) concentrates 86.05% of the interaction weight in d∈{1,2,3,5}. Deeper arithmetic channels (d≥6) remain buried beneath the finite-size GUE noise floor. Parameter-free operating point. ν=0.75 (exact center of the critical window 0.5<ν<1); local resonance coupling analytically derived as ϵc=π2; Maslov phase 7/8. Mechanized Formal Verification in Lean 4 The algebraic, topological, and connectivity constraints governing the model are certified 100% sorry-free by the Lean 4 kernel (v4.34.1 with Mathlib4), across 13 Level N1 modules (23 theorems, 11 definitions, 34 total verified statements): WheelChannelStructure.lean — Confinement to active chiral sublattices (d≡1,5(mod6)). UnitCellMeasure.lean — Unit cell totient measure (∑d=16Ξ(d)=2 ⟹ φ(6)/6=1/3). ChiralPhaseAbsorption.lean — Invertibility of coprime residues modulo 6. KatoRellichRegime.lean — Self-adjointness domain window (1/2<ν<1). LocalResonanceCoupling.lean — Hybridization resonance condition (ϵc=π2). ChannelDensityContraction.lean — Strict density hierarchy (4/15<1/3<1/2<1). NonErgodicPhaseBound.lean — Non-triviality of the bipartite ceiling (1/4<1). PolyphaseFilterZ6.lean — Complete stopband annihilation for non-coprime channels. FirstNeighborPreservation.lean — Guaranteed base coordination degree (w1=2). DihedralQuantization.lean — Reflection involution and percolation threshold bounds. BipartiteInterferenceBound.lean — Certified upper bound D2≤1/4 under chiral equiprobability. ExpectedDegreeBound.lean — Mean degree lower bound (⟨deg⟩local≥2). FractalDimensionUpperBound.lean — Generalized Jensen inequality for the IPR and universal bound D2≤φ(m)/m. Empirical validation of Lean 4 axioms. Extensive GPU audits up to N=12 000 confirm that the chiral equiprobability axiom (c1=c5=1/2) holds strictly at the ensemble level (⟨W1−W5⟩=−0.000048≈0), with local mass fluctuations decaying monotonically as N→∞. Comprehensive Experimental Validation Matrix Observable Empirical Result Benchmark Physical significance Macroscopic alignment (R2) >0.999999 R2→1 Autonomous Weyl law tracking; zero empirical rescaling Bulk spacing ratio ⟨r⟩ 0.5891±0.0024 GUE 0.5996 / Poisson 0.3863 Intermediate non-ergodic extended statistics SFF ramp exponent γ 0.6086±0.0103 GUE γ=1 Sub-diffusive spectral ramp characteristic of NEE FSS thermodynamic limit D2∞ 0.113±0.003 Anderson D2=0 39σ rejection of Anderson localization Chalker scaling β=2D2 β=0.5549±0.0020 2D2=0.5562±0.0054 0.2σ agreement between transport and fractal support Multifractal curvature ΔD D0−D2=0.730 Ergodic ΔD=0 Strict convexity of Dq for q∈[−3,4]; width Δα=3.726 First-neighbor removal D2=0.0448±0.0009 Preserved: 0.2882 Sixfold collapse into strong localization (HSF) Short-range rescue (d=1) D2=0.2849±0.0007 Unforced: 0.0556 Forcing d=1 restores the NEE phase in random masks Topological pinning (ε=εc) D2no/D2with≈0.17 Healed ratio →1→1 Collapse cannot be overcome at the critical resonance Riemann zeros control (SFF) γzeros=0.94±0.12 GUE γ=1γ=1 Real zeros are ergodic; the NEE ramp is intrinsic to the mask Repository Structure and Reproducibility The codebase is fully vectorized, GPU-accelerated (PyTorch cuSOLVER in complex128), and audited via an automated SHA-256 manifest. The notebook regenerates every figure and table of the manuscript from a fixed random seed (SEED = 42). PRBM_Modular_Lean/ — Standalone Lean 4 (v4.34.1) project containing all 13 verified .lean files and lakefile.lean. Modules 00a–00c — System setup, forensic audit of the 100,000-zero Riemann dataset, and vectorized Hamiltonian engine (complex128). Modules 01–03 — Exact diagonalization at N=10 000; local level statistics P(s) and ⟨r⟩; spectral form factor ensemble averaging (M=100, N=15 000). Modules 04–06 — Channel-density scaling and finite-size scaling; FSS collapse of P(d2,N) across N∈{2000,4000,8000,12000}; AIC/BIC model selection. Modules 07–09 — Anderson transition sweep (ν∈[0.5,3.0]); systematic mask comparison suite; Möbius equivalence and density sweep. Modules 10–12 — Full multifractal spectrum Dq,f(α); microscopic GPU diagonalization at N=12 000; quantum dynamics (MSD, survival probability, Shannon and entanglement entropies). Modules 13–15 — Riemann zeros control SFF; coupling sweep over ε/εc∈[0.2,4.0]; chiral equiprobability audit ⟨Wr⟩ across residue classes. Module 16 — Automated high-resolution vector export (PDF/PNG 300 DPI) and cryptographic manifest generation (MANIFEST_SHA256.txt). Open-Access Dual Licensing Source code (Lean 4, Python, PyTorch): released under the MIT License. Free for academic, educational, and commercial replication. Manuscript, figures, manifests, and data: released under the Creative Commons Attribution 4.0 International License (CC BY 4.0). Declarations Author contributions. Conceptualization, methodology, software, formal analysis, formal verification, investigation, data curation, validation, writing (original draft and revision), visualization, project administration. Competing interests. The author declares no competing interests, financial or otherwise. Funding. No external funding was received for this research. Ethics. Ethical approval was not required, as this research is theoretical and numerical and involves no human participants or animal subjects. Generative AI disclosure. Google Gemini and DeepSeek were used exclusively as auxiliary tools for language editing, adversarial logical review ("red-teaming"), and code debugging. They were not used to produce any original scientific content: all model design, numerical experiments, theoretical derivations, and interpretations are the author's own work. Every AI-assisted output has been reviewed and validated by the author. Scientific Epilogue "In the beginner's mind there are many possibilities, but in the expert's there are few." — Shunyu Suzuki What began as an inquiry into whether number-theoretic structures dictate quantum chaos revealed a simpler, deeper, and more universal physical law: geometry and local connectivity precede arithmetic complexity. The code, formal proofs, and data deposited here are provided to ensure complete auditability, verifiable down to the individual logical inferences of the Lean 4 kernel. Archival snapshot: October 2026 · Certified Level N1 · Built with Lean 4, PyTorch, NumPy, SciPy, and Google Colab. Version: v4 ( submission EPJB-D-26-00793)
This record contains the first public frozen deposit of internal manuscript revision 3.1 of the “Immutable Semantic Ledger”, a mathematical work presenting a proposed proof of the Riemann Hypothesis. The manuscript develops a binary A/B observer model and a typed mathematical chain connecting observer-relative binary structure, an analytic zero-state, an exact scale eigenvalue, a four-branch A/B construction, and a final reciprocal-scale forcing argument. The frozen source organizes the mathematical development into definitions and theorem nodes S1–S18. The load-bearing analytic and forcing chain considered for independent review is S8–S18. The deposit is intentionally frozen so that independent reviewers can examine one exact and reproducible mathematical object rather than a changing manuscript. Frozen primary source: IMMUTABLE_SEMANTIC_LEDGER_V3_1_RU.md SHA-256: 26efca21096db288ad46c7cc7f282270db1de108dbd7a7dd423f1155fbb3b537 Accompanying files provide the freeze manifest, independent-review instructions, and a standardized response template for reporting PASS/FAIL decisions on the individual mathematical nodes. The purpose of this deposit is public timestamping, persistent identification, reproducible citation, and independent mathematical verification of the exact frozen source. This record presents a proposed proof for external scrutiny. Publication on Zenodo should not itself be interpreted as peer review, independent validation, or general acceptance of the claimed proof by the mathematical community. Classical results used in the manuscript, including standard properties of the Riemann zeta function, the Dirichlet eta function, Hasse-type representations, and the functional equation, are used as established mathematical inputs and are not claimed as original results of the author. The claimed original contribution is the specific mathematical construction and proof chain developed in the deposited manuscript.