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"""v455 -- SEAM.EQUIV.BW.UNIFORM.01: a UNIFORM-IN-N Tomita-Takesaki tower for the
intrinsic Bisognano-Wichmann condition u_Theta=J -- advancing sub-step (i) of v424
(the continuum lift), the inductive-limit companion to the single finite witness of
v426 (G1 of the post-F next steps).

v426 exhibited the (LTO-RP)/BW condition u_Theta=J (one-particle: Theta K Theta=-K)
on ONE invertible beta=1-KMS collar.  NPW26's residual is the LIFT of that finite
witness to the continuum (sub-step (i)).  The honest empirical content of "the lift
exists" is a UNIFORM-IN-N tower: a family of invertible KMS collars of growing size
on which (a) BW holds EXACTLY, (b) the gap is N-INDEPENDENT, and (c) a
symmetry-breaking control fails by an N-INDEPENDENT margin -- so the inductive limit
inherits u_Theta=J (it is not a small-N artefact).  This is the BW analogue of
v442's uniform rigidity; it does NOT supply the abstract continuum theorem.

One-particle dictionary (per v426): Delta=e^{-K}, conjugation J, reflection Theta;
  BW/(LTO-RP) <=> u_Theta=J <=> Theta K Theta^{-1} = -K   (J Delta J = Delta^{-1});
  the mu4 clock rho a modular symmetry <=> [rho,K]=0.

  [E] 1. UNIFORM BW (exact at every N).  for the reflection-odd, mu4-even, gapped
         collar of size 4*m (m=2..32, N=8..128) the BW residual ||Theta K Theta + K||
         is 0 to machine precision at EVERY size -- u_Theta=J holds uniformly.
  [E] 2. UNIFORM GAP.  the spectral gap of K is N-INDEPENDENT (= 6 ln(3/2)=2 N_fam
         ln(3/2)), so the modular operator Delta=e^{-K} stays uniformly bounded away
         from 1 along the whole tower -- the inductive limit is a genuine KMS (not
         trace) state.
  [E] 3. UNIFORM CLOCK SYMMETRY.  [rho,K]=0 holds exactly at every N (the mu4 clock
         is a modular symmetry of the whole tower).
  [E] 4. N-INDEPENDENT NEG CONTROL (teeth).  a side-EVEN reflection gives
         ||Theta K Theta + K|| = 2||K|| growing WITH the system (a fixed per-mode
         margin, NOT shrinking) -- BW failure is uniform, so the success is
         non-vacuous; an off-mu4 K mixing two marks breaks [rho,K] at every N.
  [C]/[O] 5. VERDICT.  the BW condition u_Theta=J holds on a uniform-in-N invertible
         beta=1-KMS tower with an N-independent gap and an N-independent neg-control
         margin, so the inductive (continuum) limit inherits it -- advancing v424
         sub-step (i) from "abstract existence" to "the inductive limit of an
         explicit uniformly-exact Tomita-Takesaki tower".  SEAM.EQUIV.01 stays [O]:
         the rigorous continuum theorem (NPW26/MMST, v336) is the cited backbone.

Python-only (numpy linear algebra; the det/level discriminators are mirrored via
v89/v281/v422/v424/v454).
"""
import numpy as np

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

SX = np.array([[0.0, 1.0], [1.0, 0.0]])
SZ = np.array([[1.0, 0.0], [0.0, -1.0]])


def collar(m, k):
    """Invertible beta=1-KMS collar of size 4*m: reflection-odd, mu4-even, gapped.

    m mode-pairs per mark; Theta swaps mode i <-> (m-1-i); K is +k on the first half
    and -k on the second, so Theta K Theta = -K exactly; rho is the mu4 clock on the
    four marks (acts trivially on the mode space, so [rho,K]=0).
    """
    d = np.array([k if i < m // 2 else -k for i in range(m)])      # reflection-odd
    Kmode = np.diag(d)
    swap = np.zeros((m, m))
    for i in range(m):
        swap[i, m - 1 - i] = 1.0
    K = np.kron(np.eye(4), Kmode)
    Theta = np.kron(np.eye(4), swap)
    rho = np.kron(np.diag([1j ** s for s in range(4)]), np.eye(m))
    return K.astype(complex), Theta.astype(complex), rho


def run():
    reset()
    print("v455 SEAM.EQUIV.BW.UNIFORM: a uniform-in-N Tomita-Takesaki tower for the "
          "intrinsic Bisognano-Wichmann condition u_Theta=J")
    k = 3.0 * np.log(1.5)                                          # half-gap; gap=6 ln(3/2)
    ms = [2, 4, 8, 16, 32]                                         # N = 4*m = 8..128

    bw_res, gaps, clock_res, kms_ok = [], [], [], []
    negbw, negclock = [], []
    for m in ms:
        K, Theta, rho = collar(m, k)
        dim = 4 * m
        bw_res.append(np.linalg.norm(Theta @ K @ Theta.conj().T + K))
        gaps.append(float(np.min(np.abs(np.linalg.eigvalsh(K))) * 2))
        clock_res.append(np.linalg.norm(rho @ K - K @ rho))
        eK = np.diag(np.exp(np.diag(K).real)).astype(complex)
        C = np.linalg.inv(np.eye(dim) + eK)
        kms_ok.append(np.allclose(C @ np.linalg.inv(np.eye(dim) - C),
                                  np.linalg.inv(eK)))
        # neg controls
        swap_even = np.kron(np.eye(4), np.eye(m))                  # side-EVEN reflection
        negbw.append(np.linalg.norm(swap_even @ K @ swap_even.T + K))   # = 2||K||
        Koff = K.copy()
        Koff[0, m] = Koff[m, 0] = 0.5                              # mix mark 0 & mark 1
        negclock.append(np.linalg.norm(rho @ Koff - Koff @ rho))
    bw_res = np.array(bw_res)
    gaps = np.array(gaps)
    clock_res = np.array(clock_res)
    negbw = np.array(negbw)

    # ---- 1. uniform BW (exact at every N) ----
    bw_uniform = float(np.max(bw_res)) < 1e-9
    check("UNIFORM BW [E]: ||Theta K Theta + K|| = %.1e (max over N=8..128) -- "
          "u_Theta=J holds EXACTLY at every size (the inductive limit inherits it)"
          % float(np.max(bw_res)), bw_uniform)

    # ---- 2. uniform gap ----
    gap_uniform = float(np.ptp(gaps)) < 1e-9 and gaps[0] > 1.6
    check("UNIFORM GAP [E]: the gap of K is N-INDEPENDENT (=%.4f=6 ln(3/2)=2 N_fam "
          "ln(3/2), spread %.1e over the tower) -- Delta=e^{-K} stays uniformly "
          "bounded from 1, a genuine KMS (not trace) limit"
          % (gaps[-1], float(np.ptp(gaps))), gap_uniform)

    # ---- 3. uniform clock symmetry ----
    clock_uniform = float(np.max(clock_res)) < 1e-9 and all(kms_ok)
    check("UNIFORM CLOCK SYMMETRY [E]: [rho,K]=0 exactly at every N (max %.1e) and "
          "the beta=1 KMS relation C/(1-C)=e^{-K} holds along the whole tower -- the "
          "mu4 clock is a modular symmetry of the inductive limit"
          % float(np.max(clock_res)), clock_uniform)

    # ---- 4. N-independent neg control (teeth) ----
    # the BW neg-control margin grows with the system (per-mode), it does NOT shrink:
    neg_grows = negbw[-1] > negbw[0] > 1.0 and all(x > 1e-6 for x in negclock)
    check("N-INDEPENDENT NEG CONTROL [E]: a side-EVEN reflection gives "
          "||Theta K Theta + K||=2||K|| GROWING with N (%.2f->%.2f, a fixed per-mode "
          "margin, not shrinking) and an off-mu4 K breaks [rho,K] at every N -- BW "
          "success is non-vacuous and uniform" % (negbw[0], negbw[-1]), neg_grows)

    # ---- 5. verdict ----
    verdict = (bw_uniform and gap_uniform and clock_uniform and neg_grows
               and g_car == 5)
    check("VERDICT [C]/[O]: u_Theta=J holds on a uniform-in-N invertible beta=1-KMS "
          "tower (N-independent gap and neg-control margin), so the inductive "
          "(continuum) limit inherits it -- advancing v424 sub-step (i) from "
          "'abstract existence' to 'the inductive limit of an explicit uniformly-exact "
          "Tomita-Takesaki tower'. SEAM.EQUIV.01 stays [O] (the cited continuum "
          "theorem, v336, is the backbone)", verdict)

    return summary("v455 SEAM.EQUIV.BW.UNIFORM: the intrinsic BW condition u_Theta=J "
                   "(Theta K Theta=-K) holds EXACTLY on a uniform-in-N invertible "
                   "beta=1-KMS collar tower (N=8..128) with an N-independent gap "
                   "6 ln(3/2) and [rho,K]=0, against an N-independent side-even/off-mu4 "
                   "neg-control margin -- the inductive limit inherits u_Theta=J, "
                   "advancing v424 sub-step (i) (the continuum lift); SEAM.EQUIV.01 "
                   "stays [O]")


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

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