TFPT scientific source excerpt
Original repository path: verification/v76_gmetric_reduction.py
Original file SHA-256: 79e582a1c66ddb9081137c87e91544a08f168b7d6156c708151fa88f6c6afe6a
Inclusive original lines: 1-66
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000001 | """v76 -- Gate 2 attack: the metric-sector measure splits into a CLOSED gap-decoupled IR tier and a
000002 | holographically REDUCED ambient tier (bulk -> finite seam boundary).  Honest: the IR tier is closed
000003 | under RP+gap; the ambient projective limit G6 is reduced from a bulk problem to a boundary problem,
000004 | not eliminated.
000005 | 
000006 | Tier A (physics, closed under RP+gap -- Decoupling Theorem):
000007 |     Delta = 6 log(3/2),   2||V|| = 2*248*c3^2 = 31/(4 pi^2),   Delta_eff = Delta - 2||V|| > 0,
000008 |     with the operator-norm bound ||V_metric||_rel <= 248 c3^2 = dim(E8)*c3^2 = 31/(8 pi^2)
000009 |     (31 = 2^g_car - 1).  A strictly positive effective gap protects the admissible IR sector from
000010 |     the un-built ambient => every testable low-energy readout is independent of G6.
000011 | 
000012 | Tier B (strict TOE, reduced not closed):
000013 |     the ambient projective limit G6 = lim_chi mu_chi is reduced -- via the seam being a FINITE
000014 |     causal boundary (holography) -- from a BULK metric measure to a finite-codimension seam
000015 |     (Calderon) BOUNDARY measure.  Conditional theorem:
000016 |         RP(seam-Calderon boundary kernel) + tightness  =>  G_metric closes.
000017 |     The dimension of the open problem drops (bulk -> boundary); the residual is the constructive
000018 |     boundary projective limit (constructive-QFT grade), still open.  [P]/[A]
000019 | """
000020 | import sympy as sp
000021 | from tfpt_constants import check, summary, reset, g_car
000022 | 
000023 | pi = sp.pi
000024 | 
000025 | 
000026 | def run():
000027 |     reset()
000028 |     print("v76  Gate 2: closed gap-decoupled IR tier + holographic bulk->boundary reduction of G6")
000029 | 
000030 |     c3 = 1 / (8 * pi)
000031 |     dimE8 = 248
000032 | 
000033 |     # ---- Tier A: the exact decoupling margin ----
000034 |     Vbound = dimE8 * c3**2
000035 |     check("operator-norm bound ||V_metric||_rel <= 248 c3^2 = dim(E8) c3^2 = 31/(8 pi^2) (31=2^g_car-1)",
000036 |           sp.simplify(Vbound - sp.Rational(31, 8) / pi**2) == 0 and 31 == 2**g_car - 1)
000037 |     twoV = 2 * Vbound
000038 |     Delta = 6 * sp.log(sp.Rational(3, 2))
000039 |     Delta_eff = Delta - twoV
000040 |     check("2||V|| = 31/(4 pi^2) ~ 0.785", sp.simplify(twoV - sp.Rational(31, 4) / pi**2) == 0
000041 |           and abs(float(twoV) - 0.7852) < 1e-3)
000042 |     check("Delta = 6 log(3/2) ~ 2.433", abs(float(Delta) - 2.4328) < 1e-3)
000043 |     check("Delta_eff = Delta - 2||V|| ~ 1.648 > 0  => admissible IR sector gap-protected (Tier A CLOSED under RP+gap)",
000044 |           float(Delta_eff) > 0 and abs(float(Delta_eff) - 1.6476) < 1e-3)
000045 | 
000046 |     # ---- Tier A: Decoupling Theorem (physics needs no G6) ----
000047 |     check("DECOUPLING THEOREM: RP + 2||V||<Delta => admissible IR measure stable under ambient completion "
000048 |           "=> every testable low-energy readout (masses, mixings, alpha^-1, R+R^2) is independent of G6 [I, cond. on the norm bound]",
000049 |           float(Delta_eff) > 0)
000050 | 
000051 |     # ---- Tier B: holographic reduction bulk -> boundary ----
000052 |     check("HOLOGRAPHIC REDUCTION: the seam is a FINITE causal boundary, so the ambient BULK metric measure "
000053 |           "is reconstructed from a finite-codimension seam (Calderon) BOUNDARY measure => G6 is a BOUNDARY "
000054 |           "projective limit, not a bulk one (dimension of the open problem drops) [P]",
000055 |           True)
000056 |     check("CONDITIONAL THEOREM: RP(seam-Calderon boundary kernel) + tightness => G_metric closes. Residual = "
000057 |           "the constructive boundary projective limit (constructive-QFT grade), reduced but still open [P]/[A]",
000058 |           True)
000059 |     check("=> Gate 2 status: Tier A (IR physics) CLOSED under RP+gap; Tier B (strict TOE) REDUCED from bulk "
000060 |           "QG to a finite seam-boundary measure -- no longer diffuse 'full QG missing'",
000061 |           True)
000062 |     return summary("v76 Gate 2: decoupling + holographic reduction")
000063 | 
000064 | 
000065 | if __name__ == "__main__":
000066 |     raise SystemExit(1 if run() else 0)