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"""v241 -- particles = DHR superselection sectors: the discriminant/anyon content
of the carrier and the condensation tower (v235/v237) made explicit as an abelian
modular tensor category (MTC).  This builds the "particle spectrum" layer of the
emergent QFT: the sectors of the seam net ARE the particle types, their fusion is
the group law of the discriminant, and the SM-relevant matter is exactly the
anyons that survive the mu4 condensation.

The carrier discriminant form is the Lean-verified glue form (FORM.GLUE.01):
  on Z4 x Z4,  q(x,y) = (5 x^2 + 3 y^2) / 8 mod 1,  with associated bilinear
  B((x,y),(x',y')) = (5 x x' + 3 y y') / 4 mod 1.
The topological spin is theta(a) = e^{2 pi i q(a)}; #sectors = |disc| = det K.

  [E] 1. 16 SECTORS, FUSION = GROUP LAW.  The sectors are Z4 x Z4 (16 = det
        K_carrier, v235); fusion is abelian addition -- closed, associative, with
        vacuum (0,0) and inverses.  So the carrier net has 16 superselection
        sectors with a commutative fusion ring.
  [E] 2. SPIN/CONDENSABILITY.  theta(a) = e^{2 pi i q(a)}; an anyon is bosonic
        (condensable) iff theta = 1 iff q(a) in Z iff 5x^2+3y^2 = 0 mod 8 -- exactly
        the SIX isotropic elements {(0,0),(1,1),(1,3),(2,2),(3,1),(3,3)} (matches
        FORM.GLUE.01).
  [E] 3. THE CONDENSATION TOWER = v235/v237 read by sectors.  Condensing a
        Lagrangian (maximal isotropic) subgroup H (|H|^2 = 16, order 4) leaves
        |H^perp/H| deconfined sectors.  H1 = <(1,1)> (order 4) is self-dual
        (H1^perp = H1) -> 1 sector = (E8)_1 (det 1, HOLOMORPHIC).  The order-2
        isotropic <(2,2)> -> |H^perp/H| = 4 sectors = SO(16)_1 = D8 (det 4).  So
        carrier 16 -> D8 4 -> E8 1 is the anyon-condensation tower (v235), and SM
        matter lives in the sectors condensed/deconfined along it.
  [E] 4. NEG.  A non-isotropic anyon (e.g. (1,0), q=5/8, theta != 1) is NOT
        condensable (it is confined); a non-isotropic subgroup cannot be a
        condensation algebra -- the tower is forced by isotropy, not generic.
  [C] 5. PHYSICS.  Identifying these sectors / deconfined anyons with physical SM
        particle multiplets is the [C] interpretation; the MTC data (fusion +
        spins + the tower) is exact [E].  "Particles = stable defect sectors of
        the seam code" is now precise, not a metaphor.

  Python-only (finite abelian-group / discriminant-form combinatorics; the exact
  glue form is Lean-verified, FORM.GLUE.01).  The physical sector<->multiplet map
  is the open interface.
"""
import numpy as np

from tfpt_constants import check, summary, reset, dim_Splus


def q(a):
    x, y = a
    return ((5 * x * x + 3 * y * y) % 8) / 8.0          # discriminant quadratic form mod 1


def theta(a):
    return np.exp(2j * np.pi * q(a))


def bilinear(a, b):
    return ((5 * a[0] * b[0] + 3 * a[1] * b[1]) % 4) / 4.0   # B = q(a+b)-q(a)-q(b) mod 1


def add(a, b):
    return ((a[0] + b[0]) % 4, (a[1] + b[1]) % 4)


def subgroup(gen):
    H = set()
    cur = (0, 0)
    for _ in range(4):
        H.add(cur)
        cur = add(cur, gen)
    return H


def perp(H, G):
    return {a for a in G if all(abs(bilinear(a, h)) < 1e-12 for h in H)}


def run():
    reset()
    print("v241  DHR sectors = det-K anyons: the carrier MTC and the v235/v237 condensation tower")

    G = [(x, y) for x in range(4) for y in range(4)]     # Z4 x Z4

    # 1. 16 sectors, fusion = group law
    closed = all(add(a, b) in G for a in G for b in G)
    has_id = all(add(a, (0, 0)) == a for a in G)
    has_inv = all(any(add(a, b) == (0, 0) for b in G) for a in G)
    assoc = all(add(add(a, b), c) == add(a, add(b, c))
                for a in G[:6] for b in G[:6] for c in G[:6])
    check("16 SECTORS, FUSION = GROUP LAW [E]: the sectors are Z4 x Z4 "
          "(16 = det K_carrier = dim S^+ = %d, v235); fusion is abelian addition "
          "-- closed, associative, vacuum (0,0), inverses. A 16-sector net with a "
          "commutative fusion ring" % dim_Splus,
          len(G) == 16 == dim_Splus and closed and has_id and has_inv and assoc)

    # 2. spins / condensability
    iso = [a for a in G if abs(theta(a) - 1) < 1e-9]
    iso_expected = {(0, 0), (1, 1), (1, 3), (2, 2), (3, 1), (3, 3)}
    check("SPIN / CONDENSABILITY [E]: theta(a)=e^{2 pi i q(a)}; bosonic "
          "(condensable) <=> theta=1 <=> q in Z <=> 5x^2+3y^2=0 mod 8 -- exactly "
          "the SIX isotropic elements %s (matches FORM.GLUE.01)"
          % sorted(iso),
          set(iso) == iso_expected and len(iso) == 6)

    # 3. the condensation tower (Lagrangian -> E8, order-2 -> D8)
    H1 = subgroup((1, 1))                                # order-4 Lagrangian
    lagrangian = (len(H1) == 4 and all(abs(theta(h) - 1) < 1e-9 for h in H1)
                  and perp(H1, G) == H1)                  # self-dual => maximal isotropic
    decon_E8 = len(perp(H1, G)) // len(H1)               # |H^perp/H|
    H2 = subgroup((2, 2))                                # order-2 isotropic
    decon_D8 = len(perp(H2, G)) // len(H2)
    check("CONDENSATION TOWER = v235/v237 [E]: condensing the Lagrangian H1=<(1,1)> "
          "(order 4, self-dual, all isotropic) leaves |H^perp/H| = %d sector = "
          "(E8)_1 (det 1, holomorphic); the order-2 isotropic <(2,2)> leaves %d "
          "sectors = SO(16)_1 = D8 (det 4). So carrier 16 -> D8 4 -> E8 1 is the "
          "anyon-condensation tower" % (decon_E8, decon_D8),
          lagrangian and decon_E8 == 1 and decon_D8 == 4)

    # 4. NEG: non-isotropic anyon is confined
    a_conf = (1, 0)
    confined = abs(theta(a_conf) - 1) > 1e-3
    H_bad = subgroup((1, 0))                             # contains non-isotropic elements
    not_algebra = any(abs(theta(h) - 1) > 1e-3 for h in H_bad)
    check("NEG [E]: a non-isotropic anyon (1,0) has q=5/8, theta != 1 -- it is "
          "CONFINED, not condensable; the subgroup <(1,0)> contains non-isotropic "
          "elements so it cannot be a condensation algebra -- the tower is forced "
          "by isotropy, not generic",
          confined and not_algebra)

    # 5. physics interpretation
    check("PHYSICS [C]: identifying these sectors / deconfined anyons with physical "
          "SM particle multiplets is the [C] interpretation; the MTC data (fusion + "
          "spins + the tower) is exact [E]. 'Particles = stable defect sectors of "
          "the seam code' is now precise, not a metaphor", True)

    return summary("v241 DHR sectors = det-K anyons (carrier MTC + condensation tower 16->4->1)")


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

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