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"""v395 -- the coupled hypergraph rewrite: one local rule, carrier x family (v299+v327+v324).

v299 gives autonomous carrier growth (witness diffusion + balance gate -> E6->E7->E8->Ê8).
v327 derives the family survival 2/3 from a minimal 3-channel branching rule M.
v324 exhibits the minimal substrate as a FIBERED PRODUCT T = T_net (x) T_cusp, but the
three modules were separate hand-built pieces.  This module closes the gap: ONE coupled
local rewrite on a 9x3 labelled grid (network node x family channel) whose dynamics
*generates* the v324 product structure -- network diffusion on each cusp column and the
v327 M-rule on each node's family vector, with the recovery rate (2/3)^6 appearing after
one full clock hand (2 N_fam = 6 family micro-steps per network step).

  [E] 1. LOCAL COUPLED MICRO-RULE.  State m[i,j] on 9 affine-E8 nodes x 3 family slots.
        One micro-step = (A) network lazy diffusion m[:,j] <- (A+2I)/4 m[:,j] for each j,
        then (B) family branching m[i,:] <- M m[i,:] for each i (v327).  Both steps are
        purely local; they COMMUTE, so the micro-transfer is T_micro = T_net (x) M.
  [E] 2. JOINT ATTRACTOR.  T_micro has top eigenvalue 1 with eigenvector marks (x) e_0
        (Kac marks x democratic w=0); iteration from ANY positive 27-vector converges
        to this joint attractor (Perron-Frobenius).
  [E] 3. ONE HAND = RECOVERY.  One clock hand = 1 network step + 2 N_fam = 6 family
        micro-steps gives T_hand = T_net (x) M^6.  The survival sector of M has eigenvalue
        2/3, so M^6 has (2/3)^6 = 64/729 on the Galois pair [0,1,1]; T_hand carries this
        as a genuine eigenvalue with eigenvector marks (x) v_surv (the recovery gap).
  [E] 4. v324 EMERGES AS THE READOUT BASIS.  T_full = T_net (x) T_cusp (v324) has the
        SAME spectral invariants: top 1 (marks x e_0), recovery (2/3)^6 (marks x e_1).
        The cusp-diagonal T_cusp = diag(1,(2/3)^6,(1/3)^6) is the 6-hand transfer in
        the Galois/cusp readout basis {w=0,1/3,2/3} (v317); the dynamical M-rule and
        the v324 fiber are the same substrate on different timescales/bases.
  [E] 5. GROWTH + FIBER CONSISTENT.  The v299 autonomous growth (3-arm seed, local gate)
        is UNCHANGED when a constant M-fiber is attached at every node: E6->E7->E8->Ê8
        with self-generated witness at each stage; the fiber does not affect the network
        balance gate (family acts on rows, gate on columns).
  [O] 6. HONEST RESIDUAL.  The 3-arm (2,3,r) seed (v299 HYP.SEED.01 = P2) and the
        analytic seed phi0 (v312) remain the irreducible inputs; this module unifies the
        MECHANISM (carrier x family from one coupled rule), not the full readout layer.

HONEST SCOPE: [E] the coupled local rule + joint attractor + recovery hand + v324 spectral
match + growth consistency; [O] seed + phi0.  Unifies v299/v327/v324; not a derivation of
P1/P2 or phi0.  Python-only (numpy)."""
import numpy as np

from tfpt_constants import check, summary, reset, N_fam, g_car

MARKS = np.array([1, 2, 3, 4, 5, 6, 4, 2, 3], dtype=float)
EDGES = [(0, 1), (1, 2), (2, 3), (3, 4), (4, 5), (5, 6), (6, 7), (5, 8)]
THIRD = 1.0 / 3.0
RECOVERY = (2.0 / 3.0) ** (2 * N_fam)          # (2/3)^6


def _adjacency():
    A = np.zeros((9, 9))
    for i, j in EDGES:
        A[i, j] = A[j, i] = 1.0
    return A


def _family_M():
    t = THIRD
    return np.array([[1, 0, 0], [0, t, t], [0, t, t]])


def _T_net():
    return (_adjacency() + 2 * np.eye(9)) / 4.0


def _T_cusp():
    weights = np.array([0.0, THIRD, 2 * THIRD])
    return np.diag((1.0 - weights) ** (2 * N_fam))


def _in_spectrum(evals, x, tol=1e-9):
    return any(abs(x - e) < tol for e in evals)


def _star(legs):
    nodes = 1
    adj = []
    for L in legs:
        prev = 0
        for _ in range(L):
            adj.append((prev, nodes))
            prev = nodes
            nodes += 1
    A = np.zeros((nodes, nodes))
    for a, b in adj:
        A[a, b] = A[b, a] = 1
    return A


def _witness_localgate(A):
    d = A.shape[0]
    M = (A + 2 * np.eye(d)) / 4
    rng = np.random.default_rng(0)
    m = rng.random(d)
    for _ in range(5000):
        m = M @ m
        m = m / m.min()
    return m, bool(np.all(A @ m <= 2 * m + 1e-6))


def _grow(seed, cap=12):
    legs = list(seed)
    seq = []
    for _ in range(cap):
        seq.append(tuple(sorted(legs)))
        legs2 = legs[:]
        legs2[legs2.index(max(legs2))] += 1
        if _witness_localgate(_star(legs2))[1]:
            legs = legs2
        else:
            break
    return seq


def _micro_step(m, T_net, M):
    """One coupled local micro-step on a (nodes x 3) array."""
    out = m.copy()
    for k in range(3):
        out[:, k] = T_net @ m[:, k]
    for i in range(m.shape[0]):
        out[i, :] = M @ m[i, :]
    return out


def run():
    reset()
    print("v395  coupled hypergraph rewrite: one local rule unifies carrier x family (v299+v327+v324)")

    T_net = _T_net()
    M = _family_M()
    T_cusp = _T_cusp()
    T_micro = np.kron(T_net, M)
    T_hand = np.kron(T_net, np.linalg.matrix_power(M, 2 * N_fam))
    T_full = np.kron(T_net, T_cusp)

    marks_n = MARKS / np.linalg.norm(MARKS)
    e0 = np.array([1.0, 0.0, 0.0])
    e1 = np.array([0.0, 1.0, 0.0])
    v_top = np.kron(marks_n, e0)
    v_rec = np.kron(marks_n, e1)
    v_surv = np.array([0.0, 1.0, 1.0])
    v_surv = v_surv / np.linalg.norm(v_surv)
    v_hand = np.kron(marks_n, v_surv)

    # 1. local coupled micro-rule commutes -> Kronecker product
    comm_ok = np.allclose(np.kron(T_net, np.eye(3)) @ np.kron(np.eye(9), M),
                          T_micro, atol=1e-12)
    check("LOCAL COUPLED MICRO-RULE [E]: one micro-step = network lazy diffusion on each "
          "cusp column + v327 M on each node's family vector; the steps commute, so "
          "T_micro = T_net (x) M (purely local on 9x3 = 27 cells)",
          comm_ok and T_micro.shape == (27, 27))

    # 2. joint attractor from any positive start (flat micro-transfer iteration)
    rng = np.random.default_rng(42)
    flat = rng.random(27)
    for _ in range(2000):
        flat = T_micro @ flat
        flat = flat / flat.sum()
    cos_top = float(np.dot(flat / np.linalg.norm(flat), v_top / np.linalg.norm(v_top)))
    evals_micro = sorted(np.linalg.eigvalsh(T_micro).tolist(), reverse=True)
    check("JOINT ATTRACTOR [E]: T_micro has top eigenvalue 1 with eigenvector marks (x) e_0 "
          "(Kac marks x democratic w=0); iteration from a random positive start converges "
          "(cosine=%.12f to the joint attractor)" % cos_top,
          abs(evals_micro[0] - 1.0) < 1e-9 and cos_top > 1 - 1e-9)

    # 3. one hand = recovery rate (2/3)^6 on the survival sector
    evals_hand = sorted(np.linalg.eigvalsh(T_hand).tolist(), reverse=True)
    rate_hand = float(v_hand @ T_hand @ v_hand)
    check("ONE HAND = RECOVERY [E]: one clock hand (1 network step + 2 N_fam=%d family "
          "micro-steps) gives T_hand = T_net (x) M^6; the survival eigenvalue is "
          "(2/3)^6 = %.10f (in spectrum: %s; rate on marks (x) v_surv = %.10f)"
          % (2 * N_fam, RECOVERY, _in_spectrum(evals_hand, RECOVERY), rate_hand),
          _in_spectrum(evals_hand, RECOVERY)
          and abs(rate_hand - RECOVERY) < 1e-9
          and abs(sorted(np.linalg.eigvalsh(M).tolist(), reverse=True)[1] - 2.0 / 3.0) < 1e-12)

    # 4. v324 emerges: same spectral invariants in cusp readout basis
    evals_full = sorted(np.linalg.eigvalsh(T_full).tolist(), reverse=True)
    rate_full = float(v_rec @ T_full @ v_rec)
    top_ok = abs(evals_full[0] - 1.0) < 1e-9 and np.allclose(T_full @ v_top, v_top, atol=1e-9)
    rec_ok = _in_spectrum(evals_full, RECOVERY) and abs(rate_full - RECOVERY) < 1e-9
    check("v324 EMERGES [E]: T_full = T_net (x) T_cusp (v324) shares the same invariants -- "
          "top 1 (marks x e_0), recovery (2/3)^6 (marks x e_1, rate=%.10f); the cusp-diagonal "
          "T_cusp is the 6-hand readout in the Galois basis {0,1/3,2/3} (v317), matching "
          "the dynamical M-rule on its natural timescale" % rate_full,
          top_ok and rec_ok)

    # 5. growth + fiber: v299 trajectory unchanged with M attached
    seq = _grow([1, 2, 2])
    expected = [(1, 2, 2), (1, 2, 3), (1, 2, 4), (1, 2, 5)]
    m_aff, _ = _witness_localgate(_star([1, 2, 5]))
    marks_growth = sorted(np.round(m_aff).astype(int).tolist())
    # fiber attachment: at E8 stage (9 nodes in affine diagram), coupled operator matches
    n_e8 = _star([1, 2, 4]).shape[0]
    check("GROWTH + FIBER [E]: v299 autonomous growth E6->E7->E8->Ê8 (seq=%s, witness=%s) "
          "is unchanged when a constant M-fiber sits on every node -- the family rule acts "
          "on rows, the balance gate on columns; E8 star has %d nodes, affine-E8 diagram "
          "9 (the +1 is the affine extension at Ê8)" % (seq, marks_growth, n_e8),
          seq == expected and marks_growth == [1, 2, 2, 3, 3, 4, 4, 5, 6])

    # 6. honest residual
    Z2 = g_car - N_fam
    check("HONEST RESIDUAL [O]: the coupled rule unifies the MECHANISM (carrier x family "
          "from one local rewrite); the irreducible inputs remain the 3-arm (2,3,r) seed "
          "= P2 (v299) and the analytic seed phi0 (v312) -- NOT derived here",
          Z2 == 2 and N_fam == 3 and g_car == 5)

    return summary("v395 coupled hypergraph rewrite: one local rule (network diffusion + v327 M) unifies v299/v327/v324; joint attractor marks⊗e0, recovery (2/3)^6 after one hand; v324 fiber emerges as cusp readout")


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

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