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v957_ccc_crossover_kinematics.py

verification/v957_ccc_crossover_kinematics.py

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"""v957 -- CCC.SEAM.KINEMATICS.01 (rounds DL-DLV, 2026-08-24): THE CCC
CROSSOVER KINEMATICS DICTIONARY -- the complete kinematic 2D -> 3D -> 4D
uplift of the seam and its thermal/holonomy dictionary, machine-checked
from corpus objects only.  ONE module from six probes (28/28 + 29/29 +
18/18 + 21/21 + 14/14 + 7/7 first-pass gates, zero fails; discovery
probes ccc_crossover_gates_probe.py, ccc_uplift_4d_probe.py,
ccc_fork_kms_holonomy_probe.py, ccc_kernel_gamma_kms_probe.py,
ccc_transfer_selector_probe.py, ccc_kappa_freeze_probe.py, notes DL-DLV,
2026-08-24, re-run identically at promotion, embedded BYTE-EXACT and
executed verbatim).

WHAT IS CERTIFIED [E] (exact identities on corpus objects; the CCC
reading itself stays [C], the cyclic interpretation of origin_theory is
NOT upgraded by this module):
  (1) RECIPROCAL STRUCTURE: the proven mu_4 Moebius stabiliser
      D_4 = <rho: z->iz, sigma: z->1/z> contains tau = rho^2 sigma:
      z -> -1/z with Omega * tau(Omega) = -1 identically (Penrose's
      reciprocal gauge as a stabiliser element), tau rho tau^{-1} =
      rho^{-1} (clock reversal = the Z_2 sheet parity), tau swaps the
      clock poles {0, inf} and fixes the marks +-i; the crossover locus
      |Omega| = |tau(Omega)| is the unit circle carrying all four marks.
  (2) LOCAL-SCALE RIGIDITY: on the 2D seam the clock alone leaves
      exactly ONE constant-curvature conformal modulus (the dilation
      family, Liouville-exact) and the reciprocal Z_2 kills it (unique
      zero at lambda = 1); Lie-algebra form: so(3,1) clock-commutant =
      2 with 1 boost, {clock, tau}-commutant = 0.
  (3) STINESPRING UNITARITY: the v221 transport (spectrum {1, (2/3)^6,
      (1/3)^6}) is CPTP, NOT unitary; its 9 Kraus operators give an
      exact isometry V^dag V = 1_3; ||T^n - P_star||_2 = (2/3)^{6n}
      exactly; iterated with fresh environments the global overlap is
      exactly invariant while the reduced trace distance decays at the
      seam rate and the environment retains the full distinguishability
      -- "entropy reset" = reduced channel, no information destroyed.
  (4) THE KINEMATIC UPLIFT: stereographic(Hopf(v)) = z1/z2 exactly (the
      seam sphere IS the Hopf base of S^3); the v492 deck diag(i, i^-1)
      acts freely (X = S^3/Z_4 = the lens boundary of the corpus A_3
      ALE XY = Z^4 is a smooth closed 3-manifold); clock diag(i, 1) and
      the reciprocal lift J = [[0,-1],[1,0]] normalise the deck and
      descend (J to tau, inverting the clock); the four marks lift to
      four Hopf fibre circles paired by the deck into the two Z_2 sheet
      orbits, Gauss linking number 1; conformal rigidity: the
      so(4,1)-commutant of the deck is 4-dimensional su(2)+u(1), ALL
      Killing, boost content 0 (infinitesimal Yamabe uniqueness with NO
      extra condition; control S^3 keeps 10 with 4 boosts); the full
      structure {deck, clock, J} leaves EXACTLY the Hopf fibre rotation;
      global uniqueness on the Obata solution manifold (boost family
      realised explicitly; deck-invariance defect bounded below over a
      200-axis scan, zero only at beta = 0); the 4D bridge: the
      inversion x -> x/|x|^2 is a conformal involution of the cone
      C^2/Z_4 (pullback |x|^{-4} flat, symbolic), fixes the unit lens
      pointwise, swaps the aeon ends, commutes with the deck; cone =
      cylinder e^{2s}(ds^2 + g), Omega_- Omega_+ = 1; Lorentzian
      shadow: (1/cos^2 T)(-dT^2 + g_{S^3}) is Einstein R_ab = 3 g_ab
      (symbolic Ricci), crossover T = pi/2 a spacelike round S^3,
      Omega_hat Omega_check = -1 with Omega_check = -cos T vanishing to
      first order.
  (5) KMS/MODULAR CLOSURE (discrete -> dynamics at the free level): the
      transport obeys detailed balance exactly; H_mod = -ln T exists
      with spectrum {0, 6 ln(3/2), 6 ln 3} exactly (the seam gap IS a
      modular energy); T = e^{-H_mod} (one clock tick = one unit of
      KMS time at beta = 1); discrete KMS/OS reflection symmetry and OS
      Gram positivity hold; the v526 normalisation beta_angle = 2 pi =
      1/(4 c3) is replicated exactly and equals the Gibbons-Hawking
      normalisation on a crossover fibre of radius 1/H.
  (6) HOLONOMY DICTIONARY: pi_1(X) = Z_4 with the v492 flat glue
      character chi(D) = i; the two clock-pole circles descend to the
      lens core geodesics with holonomy i (full mu_4); every seam
      string carries EXACTLY the 2-torsion chi(D^2) = -1, and D^2 = -1
      is trivial on the base while flipping the spinor coordinates --
      the v522 statement "gaugeable datum = the 2-torsion {1, (-1)^F};
      full wrap = fermion parity" in geometric form (typed [C]
      structural correspondence); mark strings link the pole strings
      once.
  (7) SELECTOR NECESSITY (the gamma-facing theorem): for the v512 mark
      family M(delta) = {+-1, +-e^{i delta}} the admissible reflection
      axes form the pair-exchanging V_4 for every delta != pi/2 and
      close to D_4 EXACTLY at delta = pi/2 -- the order-4 clock
      factorises into admissible reflections (rho = tau o s_mid) iff
      delta = pi/2; at operator level on the N = 16 Majorana seam ring
      (fermionic reordering signs kept, index-level, no Fock space) the
      free parent is Theta_a-real on ALL 16 axes (v521 side-blindness
      replicated) while the interacting mark family is Theta-real on
      exactly {k != 4: 2, k = 4: 4} axes and the clock-axis cuts are
      Theta-real ONLY at k = 4; asymmetric couplings break reality.
      Theta-reality being NECESSARY for reflection positivity, the
      UNIQUENESS half of the v534 selector (delta = pi/2, symmetric
      couplings) is DERIVED; the survival half (PD at positive
      coupling) and the sign bit stay v534's nonperturbative toy facts,
      cited -- reality is sign-blind (checked).
  (8) THE FROZEN GATE-6 KERNEL (feeds the preregistered search
      experiments/ccc-crossover-disc/, NO data touched): exactly two
      decay modes with rates ln(729/64) and ln 729 (ratio ln3/ln(3/2) =
      2.709511), frozen defect-class overlap table (+-1/sqrt2, +1/sqrt6)
      and (0, -2/sqrt6); disc radius theta_max = eta_rec/(eta_0 -
      eta_rec) ~= 1.16 deg (typed externals); kappa derived from the
      v526 KMS normalisation up to a declared convention band -- u_rec
      <= 8.3e-5 ticks across the WHOLE band, kernel contrast <= 3.3e-4:
      the template degenerates robustly to the sharp causal top-hat
      disc; freeze hashes v1/v2/v3 pinned and recomputed in-run.

HONEST FENCES.  The CCC/cyclic reading stays [C]; WOIT.OS.TWISTOR.01
stays [O] with all kill tests live (this module is kinematics + free
level + necessity direction ONLY -- no interacting A_hol, no OS field
reconstruction, no Einstein dynamics derived); the deck fork
(spacetime lens vs internal bundle) is decided only CONDITIONALLY on
v522's wrap = (-1)^F surviving the interacting level; the cosmology
fork (Starobinsky vs crossover epoch) is priced decidable (r in
[0.0033, 0.0048] vs future sigma(r) ~ 0.001) but NOT decided; the
preregistered disc search is a search target of the [C] reading -- its
null would NOT damage the compiler core.  External cosmography numbers
are typed external throughout.
"""

import base64
import hashlib
import io
import contextlib

from tfpt_constants import check, summary, reset

PROBES = {
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}


def _run_probe(fn):
    """decode byte-exact, verify hash, execute verbatim, return
    (rc, n_pass, n_total)."""
    npass_expect, sha_expect, *chunks = PROBES[fn]
    raw = base64.b64decode("".join(chunks))
    sha = hashlib.sha256(raw).hexdigest()
    if sha != sha_expect:
        return (99, 0, 0)
    g = {"__name__": f"v957_embed_{fn[:-3]}"}
    buf = io.StringIO()
    with contextlib.redirect_stdout(buf):
        exec(compile(raw, fn, "exec"), g)
        rc = g["main"]()
    passes = g.get("PASS", [])
    return (rc, sum(bool(x) for x in passes), len(passes))


def run():
    reset()
    import numpy as np
    import sympy as sp

    print("v957 -- CCC crossover kinematics dictionary (six probes"
          " embedded byte-exact + in-run recomputation)")

    # ------------------------------------------------------------------
    # S0/S1: the six probes, byte-exact and green as typed
    # ------------------------------------------------------------------
    for fn in PROBES:
        rc, np_, nt = _run_probe(fn)
        exp = PROBES[fn][0]
        check(f"probe {fn}: hash pinned, re-run green as typed "
              f"({np_}/{nt}, expected {exp}/{exp}, rc={rc})",
              int(rc == 0 and np_ == nt == exp), 1, exact=True)

    # ------------------------------------------------------------------
    # in-run recomputation (independent of the embedded sources)
    # ------------------------------------------------------------------
    RNG = np.random.default_rng(20260824)

    # (1) reciprocal structure
    zs = RNG.standard_normal(32) + 1j * RNG.standard_normal(32)
    check("tau(z) = -1/z satisfies Omega*tau(Omega) = -1 identically",
          int(all(np.isclose(z * (-1.0 / z), -1.0) for z in zs)), 1,
          exact=True)

    # (3) Stinespring: transport, isometry, exact contraction
    LAM2, LAM3 = (2.0 / 3.0) ** 6, (1.0 / 3.0) ** 6
    u2 = np.array([1.0, -1.0, 0.0]) / np.sqrt(2)
    u3 = np.array([1.0, 1.0, -2.0]) / np.sqrt(6)
    J = np.full((3, 3), 1.0 / 3.0)
    T = J + LAM2 * np.outer(u2, u2) + LAM3 * np.outer(u3, u3)
    kraus = [np.sqrt(T[i, j]) * np.outer(np.eye(3)[i], np.eye(3)[j])
             for i in range(3) for j in range(3)]
    V = np.zeros((27, 3))
    for a, K in enumerate(kraus):
        for i in range(3):
            V[i * 9 + a, :] += K[i, :]
    check("Stinespring V^dag V = 1_3 exactly (the v221 transport is a"
          " reduced channel of an isometry)",
          int(np.allclose(V.T @ V, np.eye(3))), 1, exact=True)
    ok_rate = all(np.isclose(
        np.linalg.norm(np.linalg.matrix_power(T, k) - J, 2), LAM2 ** k,
        rtol=1e-10) for k in range(1, 6))
    check("||T^n - P_star||_2 = (2/3)^{6n} exactly, n = 1..5",
          int(ok_rate), 1, exact=True)

    # (4) uplift core: Hopf identity + deck freeness + commutant
    vs = RNG.standard_normal((32, 2)) + 1j * RNG.standard_normal((32, 2))
    vs /= np.linalg.norm(vs, axis=1, keepdims=True)
    def hopf_stereo(v):
        w = 2 * v[0] * np.conj(v[1])
        h3 = abs(v[0]) ** 2 - abs(v[1]) ** 2
        return (w) / (1 - h3)
    check("stereographic(Hopf(v)) = z1/z2 exactly (the seam sphere IS"
          " the Hopf base)",
          int(all(np.isclose(hopf_stereo(v), v[0] / v[1]) for v in vs)),
          1, exact=True)
    DECK = np.diag([1j, -1j])
    free = all(not np.any(np.isclose(np.linalg.eigvals(
        np.linalg.matrix_power(DECK, k)), 1.0)) for k in (1, 2, 3))
    check("v492 deck acts freely on S^3 (lens crossover smooth)",
          int(free), 1, exact=True)

    def real_so4(M2):
        R = np.zeros((4, 4))
        for j in range(2):
            e = np.zeros(2, complex); e[j] = 1.0
            w = M2 @ e
            R[0, 2*j], R[1, 2*j], R[2, 2*j], R[3, 2*j] = (
                w[0].real, w[0].imag, w[1].real, w[1].imag)
            w = M2 @ (1j * e)
            R[0, 2*j+1], R[1, 2*j+1], R[2, 2*j+1], R[3, 2*j+1] = (
                w[0].real, w[0].imag, w[1].real, w[1].imag)
        return R

    def commutant_dims(g4s):
        basis, kind = [], []
        for a in range(4):
            for b in range(a + 1, 4):
                X = np.zeros((5, 5)); X[a, b], X[b, a] = 1., -1.
                basis.append(X); kind.append("rot")
        for a in range(4):
            X = np.zeros((5, 5)); X[a, 4], X[4, a] = 1., 1.
            basis.append(X); kind.append("boost")
        rows = []
        for g4 in g4s:
            g = np.eye(5); g[:4, :4] = g4
            gi = np.linalg.inv(g)
            rows.append(np.stack([((g @ B @ gi) - B).ravel()
                                  for B in basis], axis=1))
        A = np.vstack(rows)
        _, s, vt = np.linalg.svd(A)
        null = vt[np.sum(s > 1e-10):]
        boost = sum(abs(c[i]) for c in null
                    for i in range(10) if kind[i] == "boost")
        return null.shape[0], boost

    d_deck, b_deck = commutant_dims([real_so4(DECK)])
    d_ctrl, b_ctrl = commutant_dims([np.eye(4)])
    check("so(4,1) deck-commutant = 4 Killing fields with boost content"
          " 0 (Yamabe rigidity of the crossover); control S^3 keeps 10"
          " with 4 boosts",
          int(d_deck == 4 and b_deck < 1e-8 and d_ctrl == 10
              and b_ctrl > 1.0), 1, exact=True)

    # (5) KMS closure
    w, Vv = np.linalg.eigh(T)
    Hmod = Vv @ np.diag(-np.log(w)) @ Vv.T
    hev = np.sort(np.linalg.eigvalsh(Hmod))
    D2, D3 = 6 * np.log(1.5), 6 * np.log(3.0)
    check("spec(-ln T) = {0, 6 ln(3/2), 6 ln 3} exactly and"
          " T = e^{-H_mod} (one tick = one unit of KMS time)",
          int(np.allclose(hev, [0.0, D2, D3])
              and np.allclose(Vv @ np.diag(np.exp(-(-np.log(w)))) @ Vv.T,
                              T)), 1, exact=True)
    c3 = 1 / (8 * sp.pi)
    check("v526 normalisation replicated exactly: 1/(4 c3) = 2 pi ="
          " beta_angle (Gibbons-Hawking on the crossover fibre)",
          int(sp.simplify(1 / (4 * c3) - 2 * sp.pi) == 0), 1, exact=True)

    # (7) selector necessity core: D_4 closure only at delta = pi/2
    def adm_axes(delta):
        marks = np.array([0.0, np.pi, delta, delta + np.pi]) % (2*np.pi)
        cands = sorted({round(float((mi + mj) % (2*np.pi)), 12)
                        for mi in marks for mj in marks})
        n = 0
        for alpha in cands:
            img = (alpha - marks) % (2 * np.pi)
            if all(np.min(np.abs(((img[i] - marks + np.pi) % (2*np.pi))
                                 - np.pi)) < 1e-9 for i in range(4)):
                n += 1
        return n
    ok_generic = all(adm_axes(d) == 2 for d in (0.3, 0.9, 1.4, 2.2))
    check("M(delta) admissible reflections: V_4 (2 axes) generically,"
          " D_4 (4 axes) exactly at delta = pi/2 -- the clock"
          " factorisation exists only at mu_4",
          int(ok_generic and adm_axes(np.pi / 2) == 4), 1, exact=True)

    # (8) frozen kernel invariants
    check("frozen rate ratio ln3/ln(3/2) = 2.709511 (exact logs of"
          " 729/64 and 729)",
          float(D3 / D2), float(np.log(3) / np.log(1.5)), tol=1e-12)
    ETA_REC, ETA_0 = 280.3, 14165.0
    theta_deg = float(np.degrees(ETA_REC / (ETA_0 - ETA_REC)))
    check("frozen disc radius theta_max = eta_rec/(eta_0 - eta_rec) in"
          " [1.0, 1.3] deg (typed externals)",
          int(1.0 <= theta_deg <= 1.3), 1, exact=True)

    return summary("v957 CCC crossover kinematics dictionary")


if __name__ == "__main__":
    raise SystemExit(1 if run() else 0)
Recorded source fingerprint

4fb069e13d4e637ed0bc58a3a3bbcc44d1c1eaf1eaf91deaa33cef15167f46ce

Paper sections that cite this module

=150 2026-08-27 (CXXXI) (the external deep-review round — dimension / dynamics / gravity firewalls and the 4D construction ladder: the review diagnosis ``chiral [formula in source] D seam net [formula in source] local, interacting [formula in source] D quantum world'' is implemented as eight new contract IDs in tfpt_research_contracts plus one new load-bearing module. (1) DIMENSION.UPLIFT.FIREWALL.01 (standing rule, in force): no [formula in source] D theorem closes a [formula in source] D claim; every contract closure states the spacetime dimension of hypotheses AND conclusion; audit census recorded (SEAM.EQUIV.01 is [formula in source] D in and out — even fully proved it is a boundary building block, not the 4D theory; the v957 kinematic uplift does not close it; the anomaly-inflow bulk is invertible/topological, never to be silently equated with physical spacetime); the realistic route ordering (seam as boundary module [formula in source] genuine 4D Euclidean lattice [formula in source] OS package [formula in source] chirality/no-mirror [formula in source] only then BW/CHM [formula in source] entanglement gravity [formula in source] bulk–seam equivalence) is registered as the programme skeleton. (2) SEAM.BULK4D.RECON.01 : the previously implicit seam [formula in source] bulk theorem made explicit (4D local algebras/Schwinger functions; locality/microlocality, Poincar\'e covariance [formula in source] spectrum condition, spin-statistics [formula in source] CPT, both helicities, clustering, nontrivial S-matrix, unique operator dictionary). (3) the dynamics split DYN.MARKOV.EMBED.01 / DYN.UNITARY.DILATION.01 (``three meanings of dynamics'': relaxation [formula in source] / dissipative semigroup [formula in source] / unitary [formula in source] ): the finite kernel half of MARKOV.EMBED is executed \ as v971_markov_embedding_generator.py ( [formula in source] , sympy-exact) — [formula in source] of the v221 seam kernel is an EXACT classical Markov generator: [formula in source] by spectral calculus, row sums symbolically zero, off-diagonals exactly [formula in source] (the reviewer's independently verified numbers), uniformization certificate [formula in source] entrywise [formula in source] [formula in source] positivity-preserving doubly stochastic for all [formula in source] , [formula in source] (gap [formula in source] ), negative control: second eigenvalue [formula in source] gives [formula in source] — provably NOT embeddable; the field level and the local size-consistent unitary dilation (Stinespring [formula in source] Lieb–Robinson [formula in source] OS continuation) stay ; binding precision: the shared F_transfer relaxation shape is a universal CONTRACTION CLASS, not one physical clock (v723/v724/v777). (4) QFT4D.OS.RECON.01 \ (the genuine 4D Euclidean lattice OS package) with the binding phrasing rule: the v381 all-orders leg is a local perturbative construction under the stated EG/BRST hypotheses (Duch weak adiabatic limit cited, hypotheses unverified for the concrete model; no confinement / mass gap / asymptotic charged states / nonperturbative Higgs vacuum / full S-matrix follows) — tfpt_2 and tfpt_5 phrasing restricted accordingly. (5) CHIRAL4D.NOMIRROR.01 \ (explicit GW/overlap chiral lattice operator; local gauge-invariant measure, perturbative [formula in source] global anomaly freedom, no Witten [formula in source] anomaly, no mirrors, correct index/charges, stable continuum limit; Mastropietro arXiv:2303.02790 as calibration). (6) GRAV.NONCIRCULAR.01 (standing rule, in force): BW is a theorem WITHIN a local Poincar\'e-covariant QFT (Mund/Morinelli counterexample landscape cited), never a generator of Lorentz spacetime from a modular flow; every BW/CHM use declares assumption-vs-result; audit census: the entanglement-equilibrium Einstein derivation (v323/v358/v359) is typed ASSUMPTION (conditional on the 4D package, never citable as evidence for it), QG.AMB.01 correctly declared, the seam KMS [formula in source] chain dimension-typed, the intrinsic-BW programme the honest result-direction attempt. (7) OBS.TRANSDUCTION.01: the transduction principle (internal eigenvalue [formula in source] nonvanishing projection [formula in source] [formula in source] physical coupling [formula in source] observable signature; without the middle arrow neither non-observation falsifies nor observation confirms; minimal model machine-checked at exploration level in fo01, uniform functional blind to [formula in source] , character channel recovers [formula in source] to [formula in source] ; the ACT [formula in source] Planck birefringence proximity typed coincidence-level pending the shared-action proof). (8) PRED.JOINTLIKELIHOOD.01 : evidence reorganized from hit-counting into overdetermined relation bundles (flavor sum rule; [formula in source] , [formula in source] ; one normalized axion action; character-resolved transfer) with the statistical demand (joint likelihood, atom-induced covariance, effective dof, prespecified null [formula in source] formula grammar, real holdout); the v100 ``13/13, [formula in source] '' statement retyped as a look-elsewhere quantifier under its declared null — the 2026-06-09 freeze protects FUTURE measurements, it does not retroactively make historically known data blind. Docs corrected in the same change: docs/OPEN_PROBLEMS.md (the Einstein-derivation overstatement rewritten to the conditional Jacobson-route typing with the explicit does-NOT-follow list; ``zero open internal mechanisms'' fixed to match the contract scope fence — ledger wins; the all-orders phrasing restricted) and docs/FALSIFICATION.md (the null-model section retitled and rescoped, freeze and kill tests unchanged). Ledger [formula in source] rows; suite [formula in source] modules; bash build.sh audit and the manifest regeneration are the joint exit gate)

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