.zenodo.json

{
  "title": "Finite Contact Theory v0.36: The Next i — Equality, the Law Tower, and the Chromatic Reading",
  "version": "0.36.0",
  "upload_type": "publication",
  "publication_type": "preprint",
  "access_right": "open",
  "license": "cc-by-nc-sa-4.0",
  "creators": [
    {
      "name": "Douglas, Seth",
      "orcid": "0009-0007-4708-3252"
    }
  ],
  "description": "A finite reconstruction program for admissible reality. Chapters 1-9 recovered known structure from a finite-contact floor. Chapter 10, the program's first extension chapter, predicts a possible violation of Hilbert-space positivity and recovers nothing; Chapter 11 (this v0.11 release) proves the clean mixed-state exclusion that closes its clean core. Two things are published and held rigidly apart. (A) THE THEOREM, unconditional: a three-contact class function with a negative sign-sector eigenvalue (1 - 3r^2 - 2r^3 < 0 for r > 1/2) nonetheless keeps every physically accessible passive-linear-optical probability nonnegative. The accessible amplitudes are the monomials z_sigma = prod_i A[i][sigma(i)] of one complex 3x3 interferometer matrix; they obey the toric identity prod_even z = prod_odd z; and at the registered point r = 3/5 the exact inequality 152||z||^2 + 9|per A|^2 - 36|det A|^2 >= 0 holds for every complex 3x3 A (per A = sum z, det A = sum sgn(sigma) z), proven using only the toric relation and with equality only at A = 0. Because the form is degree-6 homogeneous, positivity holds for every passive-linear-optical transfer matrix, lossless or lossy; on the lossless unitary core U(3) the sharper strict (7/2)||z||^2 margin holds (the Fourier tritter saturating), while the (7/2) margin for arbitrary matrices is FALSE (an explicit -495 witness) and stays killed. So the sector is a lawful probabilistic model on the complete admitted grammar that lies OUTSIDE the positive-semidefinite Hilbert Gram cone: global Hilbert PSD fails while operational block positivity survives. (B) THE PREDICTION, conditional and experiment-open: on a received apparatus anchor r = 3/5 and the odd Z_2 identity-holonomy sector (Phi = pi), the three-state Gram discriminant is Delta_3 = 1 - 3r^2 - 2r^3 = (1-2r)(1+r)^2 = -64/125 < 0, where ordinary complex-Hilbert quantum mechanics forces Delta_3 = det G >= 0 (at r = 3/5 the PSD cone caps the cyclic phase at Phi <= arccos(5/27) ~ 79.3 deg while the extension reaches Phi = pi). The registered joint count vector (Delta_3, W, Q_3) = (-64/125, -128/1125, -12/125) both excludes the PSD Gram class and rejects the matched pairwise-only null (Q_3 = 0). This is a PREREGISTERED BET with a frozen protocol and kill conditions, NOT a discovery: the bridge premises (that a particle class carries Z_2 identity holonomy; that photons receive it -- the natural home is anyonic/topological matter, photons the clean-grammar long shot; that passive linear optics is the complete measurement grammar) are held open, and the decisive mixed-state / full-nuisance PSD-exclusion is an OPEN crux that has not been vetted by a quantum-optics expert. r = 3/5 is a received apparatus anchor, not a fundamental constant. This DOI is an archival / priority record of a mathematically closed conditional prediction, not an empirical discovery. One dependency-free script verifies the chapter from a clean clone in exact arithmetic: the core numbers, the foundational Fourier identity, positivity on rational toric witnesses, the unitary-core reduction and strict margin, the -495 kill of the (7/2)-universal, and separable-loss covariance, plus an independent adversarial descent over the full toric set. This v0.11 release adds Chapter 11, the clean mixed-state exclusion: the gauge-free raw-count witness W = P111 + D2 - 2/3 equals (2/9) det G for every partially-distinguishable Hilbert model at the Fourier tritter, so Gram positivity forces W >= 0 for pure and (by convexity, certified by the antisymmetrizer projector) mixed states, while the registered extension has W = -128/1125 < 0; hence no partially-distinguishable Hilbert model, pure or mixed, reproduces the registered counts, by the raw-count test P111 + D2 >= 2/3. This closes the clean mixed-state + mode-mismatch exclusion; multiphoton contamination, detector response, transfer-matrix uncertainty, and source drift remain the external experimental layer, and the bridge premises are unchanged. This v0.12 release adds Chapter 12, the exact quantum count regions: for n indistinguishable bosons in the n-mode Fourier interferometer the achievable region of count statistics is a simplex for n <= 4 (at n=3 the negative-Gram inequality P111 + D2 >= 2/3 is the complete boundary and the registered protocol reduces to tritter counts), central-projector positivity is insufficient at n=4 (six new raw-count laws), and a structural phase transition at n=5 produces an emergent logical qubit from permutation symmetry and counting alone, with a rebit-blindness theorem (single-shot cyclic counts cannot expose sigma_y) and a single-source real/complex/quaternionic counting no-go, both overcome by general passive networks; the resolution is a registered, experiment-open single-source conjugation-witness protocol (gap 5 sqrt2/256, about 1304 trials per setting) excluding a named real-internal-states + mode-only-optics model class, which does not falsify all real quantum mechanics and is not a performed experiment or a claim about nature. The region theorems are proof-backed and independently reproduced. This v0.13 release is a GOVERNANCE AND PRIOR-ART release with no new scientific claim and an unchanged live ceiling: it applies the Chapter-2 blind novelty protocol retroactively to the quantum-optics literature underlying Chapters 10-12, records a 15-reference must-cite list (Tichy, Shchesnovich, de Guise, Tillmann, Menssen, Brod-Galvao, Seron-Novo-Cerf, Bapat-Sunder, Drury, Dittel, Renou, McKague, and others), grades the partial-distinguishability formalism, the det-Gram positivity mechanism, the collective-phase and permutation-symmetry results, and the real-vs-complex witness as RECOVERY of standard results (surviving contributions narrowed to specific closed forms and the n=5 count-region geometry), logs the previously-missing related-work section as correction C-18, installs a release-checklist novelty gate, realigns the README front-page framing to the live ceiling, and names the Chapter-8 retained-interface corpus dependency in the claim register. This v0.14 release adds Chapter 13, FROM THE FLOOR TO THE INTERFACE: an exact finite forcing chain (twelve machine-checked rational-arithmetic checks) from three named hypotheses -- a ternary contact, future-readable order scars, internally-carried retention -- to the quaternionic interface that Chapter 8 starts from: exactly three mutually anticommuting involutive identity modes (a two-sided pincer: the order-reader cannot live in the two-mode algebra, and the carrier-parity reverse-oddtown bound caps the family at three, uniquely the pair-channels), whose oriented volume element is a central sqrt(-1), whose even sector is the quaternions, whose reflection symmetry forces exact 1/2 weights, with retention selecting the nonsplit double cover 2T = SL(2,3) over the split twin (given the named self-hosting axiom), and the minimal faithful receiver forced to be H with the 1+3 split and unique Euclidean form. The residual inputs are named as received: readability (the standing door, proven not-forced), measured ternary arity (with a conditional internal reading via the mod-4 phase plateau), the self-hosting axiom, and one orientation bit. Every ingredient is standard and cited (reverse oddtown = Babai-Frankl Ex. 1.1.5; Sarkar-van den Berg; Hurwitz-Radon; Clifford periodicity; Conway-Smith; Frobenius-Schur/Serre; Baez threefold way); the Moretti-Oppio quaternionic-to-complex reduction is engaged by name; the contribution is the composed derivation, graded INTERNAL-BLIND -- to our knowledge the first forcing of H from a retention/irreversibility hypothesis, where standard reconstructions derive complex quantum theory from reversibility. This v0.15 release adds Chapter 14, THE ATLAS OF FLOORS: an exact capability classification of generative floors on two independent, presentation-relative axes -- order-writability and residue-retention -- with all four cells exemplified and fenced by shipped theorems, quotient monotonicity in its safe scope, an exact CAR kernel (one complex fermionic mode inside every retained contact, the central i as its complex structure), the retention tower of the four-mark contact computed through third order by exact F_2 census (H^2 = C_2 unique, H^3 = C_2 x C_2 read by a gauge-invariant bracket witness, H^4 = C_2 with exactly one class; manufactured pentagon defects always removable), and the measurement obstruction relocated onto the double cover over its law quotient: no equivariant section exists (exhaustive over 4096), the retained bit is tomographically silent at law level yet certainty-grade to a scar reader, and promoting a registration into the law-state lifts prediction from exact chance to certainty -- the no-selector law and the measurement obstruction are the same fact. Presentation-relative and incomplete by stated scope; nature is not claimed to realize any cell.",
  "keywords": [
    "quantum foundations",
    "reconstruction of quantum theory",
    "Gram matrix positivity",
    "Hilbert space positivity",
    "identity holonomy",
    "linear optics",
    "Hong-Ou-Mandel",
    "tritter",
    "anyons",
    "preregistered prediction",
    "finite mathematics"
  ]
}