This preprint proposes that residual deviations of the CHSH parameter from the Tsirelson bound be analyzed not only in terms of apparatus quality and mass number, but also in terms of the purity of the readout sector. Within a register picture developed in companion papers, the measured value alpha^{-1} ≈ 137.036 is read as a sectoral transmission/readout number rather than a free dimensionless coupling. A small, falsifiable phenomenological form ΔS_sector ≈ 2√2 · ε · (N_active / 137.036) is introduced, whose operationally sharp content is the sector ratio (F5) between two variants of the same setup. The paper is a hypothesis paper: it identifies a candidate observable and proposes isotope-controlled and architecture-controlled comparison experiments as its test bed. Not peer reviewed. Prepared with the assistance of artificial intelligence. Bilingual (EN + DE).
This preprint proposes that residual deviations of the CHSH parameter from the Tsirelson bound be analyzed not only in terms of apparatus quality and mass number, but also in terms of the purity of the readout sector. Within a register picture developed in companion papers, the measured value alpha^{-1} ≈ 137.036 is read as a sectoral transmission/readout number rather than a free dimensionless coupling. A small, falsifiable phenomenological form ΔS_sector ≈ 2√2 · ε · (N_active / 137.036) is introduced, whose operationally sharp content is the sector ratio (F5) between two variants of the same setup. The paper is a hypothesis paper: it identifies a candidate observable and proposes isotope-controlled and architecture-controlled comparison experiments as its test bed. Not peer reviewed. Prepared with the assistance of artificial intelligence. Bilingual (EN + DE).
Evidence Paper VII of the Existence Equation series. The Gross-Pitaevskii equation governs Bose-Einstein condensates, superfluids, and superconductors — one of the most successful equations in condensed matter physics. This paper demonstrates that it is not an independent theory but the non-relativistic, low-energy limit of the Existence Equation: (1/c²)∂²Ψ/∂t² = ∇²Ψ + λΨ − α|Ψ|²Ψ When the relativistic term (1/c²)Ψ̈ becomes negligible, the ED equation reduces to the time-dependent Gross-Pitaevskii equation. The Josephson effect — the hallmark of macroscopic quantum coherence — then emerges as a direct structural consequence of a barrier potential, with no phenomenological input and no GP assumption. Input: 4 items. Nothing else. # Input Description 1 ED equation (1/c²)Ψ̈ = ∇²Ψ + λΨ − α|Ψ|²Ψ 2 1D lattice 512 points, periodic boundary 3 Barrier potential Localized λ suppression (width=2.0, depth=85%) 4 Chemical potential Δμ Split-operator phase kick (standard technique) No GP equation. No Josephson relations. No condensate order parameter. No phenomenological coupling. Output: Three tests, all passed. Test Phenomenon Prediction Result Metric A. DC Josephson Supercurrent ∝ sin(Δφ) J = J_c sin(Δφ) Sin fit across 31 phase points R² > 0.99 B. AC Josephson Phase rate ∝ Δμ dΔφ/dt = Δμ (NR limit) Linear regression, 6 values Δμ (0.03–0.30) R² > 0.99 C. f_Φ̇ channel Temporal phase gradient force No GP counterpart (relativistic) Junction-localized force, ΔΦ̇/Δμ ≈ 1 Ratio ≫ 1 Why this matters: Tests A and B reproduce textbook Josephson physics from the ED equation alone. Test C goes beyond GP: the temporal phase gradient ∂_t(arg Ψ) generates an independent force channel that exists only because the ED equation is second-order in time — a relativistic term that the first-order GP equation cannot contain. This is a falsifiable prediction: any system where GP fails at high frequency should exhibit the f_Φ̇ channel. When does GP break down? The ε-regime map: The validity of GP is controlled by a single dimensionless parameter ε = k²/(4λ) = c²k²/(2μ²_ED), where μ_ED = c√(2λ) is the intrinsic Higgs gap of the ED equation. Where ε ≪ 1, GP is exact. Where ε ~ O(0.1–1), ED corrections become measurable — and where ε ~ O(1), GP is structurally inapplicable: the antiparticle channel and the amplitude inertial mode (Higgs sector) become dynamically active. Physical system μ_ED (estimate) ε (estimate) Regime SC Josephson, V ≪ Δ_gap Δ_gap (~meV) ~10⁻⁶ GP exact BEC Bragg, low k healing freq. ~kHz ~10⁻³ GP exact ULDM / fuzzy scalar dark matter m_φ ~ 10⁻²² eV ~10⁻⁴⁰ GP exact BEC Bragg, high k healing freq. 0.05–0.2 ED correction (5–20%) SC Josephson, V ~ Δ_gap Δ_gap 0.1–1 ED required Neutron-star superfluid core pairing gap O(0.1–1) ED required QCD chiral condensate f_π O(1) ED fundamental Bold entries mark regimes where GP-ED deviations are experimentally or observationally accessible. At ε ~ 0.1, systematic 5–20% deviations appear in dispersion observables. At ε ~ 1, the Ψ̈ term cannot be dropped — the antiparticle channel and Higgs sector become active, and GP is no longer a valid description. Four falsifiable predictions are identified: (1) high-momentum Bogoliubov dispersion shift in BEC Bragg spectroscopy, (2) asymmetric AC Josephson response at gap-scale voltages, (3) deep Shapiro delay correction, and (4) condensate fragmentation near ω ~ 2μ_ED. Capstone of the Evidence Program: The same equation that produces quantum scars (EP I), fractional quantum Hall states and anyon braiding (EP II), helical chirality (EP III), non-commutative algebra (EP IV), galaxy rotation curves from topological phase persistence (EP V), and the Tsirelson bound (EP VI) also contains macroscopic quantum coherence as its low-energy sector. Seven phenomena. One equation. No postulates beyond "existence = deviation; deviation smooths." Evidence Program — Complete Summary: EP ED mechanism What emerges Key result I α|Ψ|²Ψ strong-coupling → binary occupation; ∇²Ψ → nearest-neighbor exclusion PXP Hamiltonian (not assumed, derived) ‖T − H_PXP‖ = 0 II Same exclusion on 2D torus; spatial phase closure → winding number sectors Topological degeneracy (without Coulomb interaction); anyon braiding q-fold at ν = p/q; 2π/q phase (0.0% error) III ∇²Ψ + (1/c²)Ψ̈: simultaneous spatial and temporal phase closure Helical scars with spontaneous chirality Chirality 1.78 × 10⁻¹⁵ IV α ≠ 0 → amplitude–phase feedback; commutative operators projected onto constrained subspace Non-commutative algebra with integer eigenvalues j_max = ⌊L/2⌋ (exact) V ½A²|∇Φ|² (phase energy) persists where |∇A|² (amplitude) has decayed Topological phase persistence as structural origin of dark matter ⟨v_θ·r⟩ = 2.0000 ± 0.0003 VI Axiom 1.1 (discreteness) → ±1 projection of continuous phase; 2 axes × √2 diagonal Tsirelson bound S = 2√2 without Hilbert space Exact (analytic + numerical) VII (1/c²)Ψ̈ → 0 (NR limit): ED reduces to GP; ε = k²/(4λ) controls validity boundary Josephson effect (DC + AC); GP as low-energy ED; f_Φ̇ force channel (no GP counterpart) DC: R² > 0.99; AC: R² > 0.99; 4 falsifiable predictions at ε ~ 0.1 All code : https://github.com/Galileo-leo/existence-equation Part of the Existence Equation Evidence Paper series (EP I–VII).Parent work: The Existence Equation: The Grammar of Persistence (doi:10.5281/zenodo.18639317)
A finite ensemble of definite, equally real configurations looks like it must obey the Bell inequalities: definite values, counted, are the textbook picture of a local hidden-variable model. We show that the instinct fails, and exhibit the failure by literal enumeration. In the finite, timeless configuration ontology of the companion papers—where probability is counting, phase is stage-relative, and the population of an outcome class is proved to equal N|α|²—the CHSH quantity assembled from ratios of integer counts reaches the quantum value 2√2 to O(1/N); at N = 4.2×10⁶, counted |S| = 2.8284267. The instinct fails for three separable reasons, each with a counting formulation. Structural exclusion—which configurations exist—is relative to the instantiated measurement bases and fixes only the aligned-basis correlations. Configurations bear outcome records only for the devices their correlation structure contains, so no configuration answers two incompatible settings and, by Fine's theorem, no Bell inequality can be derived. And the skew-angle statistics are carried by the phase structure of the class—the same cross terms that carry two-slit interference. A control run makes the mechanism visible: inserting a sector record, the which-path analog, forces per-class summation, the cross terms never form, and counted |S| falls below the local bound. Marginal counts are computed for each wing from that wing's structure alone, so the counting form of no-signaling holds by construction and is tested exactly, including at small N. On the no-go ledger the ontology keeps locality and free settings; for the plain Bell scenario its operative escape is the absence of counterfactual values, with the denial of absolute outcomes required only in Wigner's-friend extensions. One in-model prediction distinguishes the framework from continuum quantum mechanics: | |S| − 2√2 | = O(1/N), with the residue's scale robust and its sign conditional on the model's integer-apportionment rule, which is flagged as a postulate. This paper is a demonstration and a disentangling, not a new theorem: given the companion results, the violation is guaranteed; what is shown is why a counting ontology is entitled to it.
Standard linear optics requires that the transmittance of an optic be independent of photon number: for a linear element the input–output relation a_out = t·a_in + r·b_in is an operator identity, so single-photon and bright-light transmission are equal as a theorem rather than as an approximation. We are not aware of a dedicated test of that equality with a controlled scatterer at the 10⁻⁴ level. We state a hypothesis in which the equality fails in the single-quantum sector by a fixed dimensionless coupling λ*, and specify the tabletop experiment that would exclude it. The observable is Δ = D_quantum − D_classical, where D is the half-difference of a two-arm log-ratio under an ABBA swap of a weak scatterer, measured once with counting detectors and once with photodiodes through identical geometry. Standard quantum mechanics fixes Δ = 0 exactly; the hypothesis predicts Δ = −λ*·(−p ln p), or −0.046·λ* at a 1% transmission deficit. The loss map is stated as a photon-number-dependent Kraus channel, K = Σ exp[−½λ*·I_R(n)]|n⟩⟨n| with P_R(n) = 1 − (1−p)^n, which is linear, completely positive, local and non-signalling; invariance of a remote marginal is verified explicitly on a two-mode squeezed vacuum to 3×10⁻¹⁷. An earlier thermal formulation of the same idea is excluded by published SNSPD efficiency data at 2 K by a factor of 2×10⁵ and is withdrawn. An attempt to derive the criterion distinguishing which optical elements incur the cost failed under independent adversarial review and is reported as a failure; the surviving readings are converted into five pre-registered experimental arms with their nulls stated in advance. A borrowed teaching bench at 780 nm reaches a total uncertainty of 2.9×10⁻⁴ per operating point at 2×10⁸ counts, giving 5σ sensitivity at λ* ≥ 0.031 and 95% exclusion to 0.013 at a 1% scatterer; an extended scan through the turnover at p = 36.8% reaches 0.0039 and 0.0016 respectively, subject to a costed high-loss error-budget row and seven stated pass criteria. Five signatures distinguish the effect from systematics, including a −p ln p scaling and a maximum located at p = 0.368. The cheapest arm needs no interferometer: the single-photon versus bright transmission of one 50/50 beam splitter at 10⁻³, which bounds one reading of the hypothesis below λ* = 0.003 in an afternoon’s run on a prepared bench. The protocol is pre-registered before any bench is borrowed. The result will be published in either direction; a null is reported as the best bound in this sector.
This record contains the preprint “Operational Auditability in Physics III: Auditability, No-Signaling, and the CHSH–Tsirelson Bound” (Version 1.0). The paper presents a compact operational framework based on explicit “held distinctions”, verification contours, and auditability requirements. Within this frame, it provides self-contained derivations of the CHSH classical bound and the Tsirelson bound, emphasizing which assumptions are operational (and therefore auditable) versus model-dependent. The manuscript also discusses no-signaling within the same contour-explicit approach and proposes a reproducibility template intended for heterogeneous checks and independent verification. Series note: Part III of a three-part series “Operational Auditability in Physics”.• Part I: Lorentz Symmetry as an Operational Invariant Under Contour Changes• Part II: Fluctuation Theorems as Conditional Holding-Equalities (Jarzynski, Crooks) Files:• PDF (readable preprint)• LaTeX sources (for reproducible rebuild) Keywords: Bell inequalities; CHSH; Tsirelson bound; no-signaling; reproducibility; operational foundations.