TFPT scientific source excerpt
Original repository path: verification/v990_wj_transduction_mechanism.py
Original file SHA-256: d365bdab9884798ceb0cce13462a2d9bd8675ad9ea44b843a612eb6268bf099b
Inclusive original lines: 1-102
Line numbers below refer to the original source.
This bounded excerpt is source evidence; it is not a new proof/checker run.
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000001 | """v990 -- FTRANSFER.GENERATING.01 + OBS.TRANSDUCTION.01 [O update:
000002 | content shadow + finite W[J] derivative identities + transduction
000003 | shadow executed; contracts stay Open].
000004 | 
000005 | [OMITTED: non-scientific conversation or execution metadata]
000006 | content of tfpt4d_content_candidate_probe (not imported):
000007 | 
000008 |   [E] Z6-CENTRE 6Y TABLE: Q -> 1, u^c -> 2, d^c -> 2, L -> 3,
000009 |         e^c -> 0 (6Y mod 6); T4 anomaly bookkeeping exact on the
000010 |         real one-generation content; drop-L mutant fires.
000011 | 
000012 |   [E/N] W[J] AT DIM 96 (2 sites, 1 quantum Z6, species Q + e^c):
000013 |         dW/dJ = <O> (thermal mean); Hessian = Kubo connected
000014 |         correlator.  Probe diffs ~6e-11 / ~1e-7.
000015 | 
000016 |   [N] TRANSDUCTION SHADOW d2W/dJ dtheta: dynamical-link mixed is
000017 |         nonzero on the seam-coupled link (~-9e-3 in the probe);
000018 |         decoupled e^c control is EXACTLY 0.  Frozen-link companion:
000019 |         Q-staggered transduces, e^c control stays 0.
000020 | 
000021 | HONEST SCOPE (firewall): 1+1D 2-site Hamiltonian ring; Z6 centre
000022 | shadow (u^c and d^c share charge 2); finite W[J], not the 4D
000023 | generating functional.  Contracts stay [O].  No marker move.
000024 | Python-only / Wolfram mirror deferred.
000025 | 
000026 | Provenance: experiments/tfpt-discovery/tfpt4d_content_candidate_probe.py
000027 | (ALL PASS; not imported).
000028 | """
000029 | from fractions import Fraction as F
000030 | 
000031 | import numpy as np
000032 | 
000033 | from tfpt_constants import check, summary, reset
000034 | 
000035 | GEN = [
000036 |     ("Q",   3, 2, F(1, 6)),
000037 |     ("u^c", 3, 1, F(-2, 3)),
000038 |     ("d^c", 3, 1, F(1, 3)),
000039 |     ("L",   1, 2, F(-1, 2)),
000040 |     ("e^c", 1, 1, F(1, 1)),
000041 | ]
000042 | CHARGES = [int(6 * g[3]) % 6 for g in GEN]
000043 | 
000044 | NS = 2
000045 | DL = 6
000046 | OMEGA = np.exp(2j * np.pi / 6)
000047 | Z1 = np.diag(OMEGA ** np.arange(6)).astype(complex)
000048 | X1 = np.roll(np.eye(6), 1, axis=0).astype(complex)
000049 | LAM_E, W_HOP, MASS = 1.0, 0.7, 0.5
000050 | BETA, THETA0, MU_Q = 0.35, 0.7, 0.5
000051 | EPS_J, EPS_TH = 1.0e-4, 1.0e-4
000052 | W_SZ = np.diag([1.0, -1.0])
000053 | W_ANN = np.array([[0.0, 1.0], [0.0, 0.0]], dtype=complex)
000054 | 
000055 | 
000056 | def anomaly_sums(fields):
000057 |     y3 = sum(c * w * y ** 3 for _, c, w, y in fields)
000058 |     su2y = sum(c * y for _, c, w, y in fields if w == 2)
000059 |     su3y = sum(w * y for _, c, w, y in fields if c == 3)
000060 |     grav = sum(c * w * y for _, c, w, y in fields)
000061 |     witten = sum(c for _, c, w, y in fields if w == 2)
000062 |     return y3, su2y, su3y, grav, witten
000063 | 
000064 | 
000065 | def w_ferm(alpha, n_modes, dl):
000066 |     out = np.array([[1.0]], dtype=complex)
000067 |     for j in range(n_modes):
000068 |         if j < alpha:
000069 |             out = np.kron(out, W_SZ)
000070 |         elif j == alpha:
000071 |             out = np.kron(out, W_ANN)
000072 |         else:
000073 |             out = np.kron(out, np.eye(2))
000074 |     return np.kron(np.eye(dl), out)
000075 | 
000076 | 
000077 | def log_tr_exp(A):
000078 |     ev = np.linalg.eigvalsh(0.5 * (A + A.conj().T))
000079 |     m = float(ev.max())
000080 |     return m + float(np.log(np.sum(np.exp(ev - m))))
000081 | 
000082 | 
000083 | def kubo_connected(Xe, Ye, p, evals):
000084 |     lam = -BETA * evals
000085 |     dlam = lam[None, :] - lam[:, None]
000086 |     psi = np.ones_like(dlam, dtype=complex)
000087 |     mask = np.abs(dlam) > 1e-12
000088 |     psi[mask] = (np.exp(dlam[mask]) - 1.0) / dlam[mask]
000089 |     x_mean = complex(np.dot(p, np.diag(Xe)))
000090 |     y_mean = complex(np.dot(p, np.diag(Ye)))
000091 |     acc = np.sum(p[:, None] * psi * Xe * Ye.T)
000092 |     return acc - x_mean * y_mean
000093 | 
000094 | 
000095 | def thermal_pack(Hm):
000096 |     evals, evecs = np.linalg.eigh(0.5 * (Hm + Hm.conj().T))
000097 |     lam = -BETA * evals
000098 |     lam_s = lam - lam.max()
000099 |     ww = np.exp(lam_s)
000100 |     p = ww / ww.sum()
000101 |     return evals, evecs, p
000102 |