"""v94 -- Sheet Diamond & Winding Line (review round 2026-06-11): the flavor operators live on ONE two-parameter surface; the winding channel and the quark-ratio Pluecker readings are canonicalised. [I] + honest corrections. Validated from the second review round. What is genuinely NEW (the review's points 5, 7-9, 14-18 already exist as v74/v81/v88/v89/v92/v75 and are not duplicated here): [I] 1. SHEET DIAMOND. M(s,t) = R + Q diag(s,t,t) carries all four flavor operators as distinguished points: R = M(0,0), K = M(1,-1), L = M(2,0), F = M(1,1), with the two global invariants det M(s,t) = 3st^2 + 9st + 6s + t^2 + 5t + 8, det B_M(s,t) = 6st + 12s + 3t^2 + 15t + 16. The mass-transport pencil K + xQ is the CUT (s,t) = (1+x, x-1), on which det B factorises as (3x+2)(3x+5) -- the v81 master cover. [I] 2. BUILT-IN NEGATIVE CONTROLS. The factorisation is special to that cut: the diagonal cut t = s gives 9s^2+27s+16 with disc = 153 -- the SAME non-square discriminant as the R-direction control of v85 (anchor-first coherence) -- and the R->L cut t = 0 is linear (degenerate direction). [I] 3. WINDING LINE SYNCHRONISATION. On R_s = R + s*1 e_1^T: det R_s = 8 + 2s, det B_{R_s} = 16 + 4s = 2 det R_s for ALL s -- anchor area and torsion volume run synchronously on the whole winding channel, not just at the endpoints. Each of the three closure conditions alone fixes the physical value: tr R_s = 15 = dim A3 => s = 6, det R_s = 20 = det L => s = 6, (R_s^T a)_1 = 30 = h(E8) => s = 6. [I] 4. COFACTOR SEAM NORMAL (typed as repackaging: the cross product of columns 2,3 IS the first adjugate row by construction; the content is the integer readings). n = r_2 x r_3 = (5,-9,6) is the common first adjugate row of R and L (columns 2,3 are winding-invariant), n.1 = 2 = |Z2| (the per-winding determinant increment, hence det R_s = 8 + 2s), n^T R = (8,0,0), n^T L = (20,0,0), n.a = 8, n.(a+6*1) = 20: the normal annihilates the stable columns and selects the first generation as the only open torsion channel. [I/N] 5. REALITY -- the review's "Reality Selector" CORRECTED. The spectrum of R_s becomes real at s* ~ 2.825 (disc sign change between s=2 and s=3), NOT at s=6: reality does not select the winding value (the triple lock does). Honest statement: the winding line CROSSES the reality threshold, and at the physical s = 6 the spectrum is real positive with disc chi_L = 39200 = 2^5 5^2 7^2 = 2 (10*14)^2. [I] 6. F-CORNER AUDIT (extends v80's det B_F = 52): det F = 32 = 2^5, chi_F = (lam-2)(lam^2-13lam+16), B_F = [[37,43],[53,63]] with sum = 196 = 14^2 = (dim G2)^2, tr = 100, 43+53 = 96 = 2 Omega_adm. Audit fingerprints, not load-bearing. [I] 7. RIGHT-PLUECKER CANONICALISATION (load-bearing improvement): with Pi_R(M) = minors of (M1 | Ma), Pi_R(Q) = (0,4,5), Pi_R(K) = (12,12,-2), Pi_R(R) = (8,12,4), Pi_R(L) = (20,30,10) = 10*(2,3,1), the canonical quark-ratio readings become c_u/c_d = g_car ||Pi_L(K)||_1 / (N_fam^2 Delta_Q) (11, left) c_t/c_b = N_fam / ||Pi_R(K)||_1 (26, right) -- BOTH ratio integers now live in the SAME operator K (left block = flavor orientation, right block = transport propagation); the older readings Pl(L)_13 = 26 and 2*Delta_Q = 26 become corollaries. Sum Pi_R(L) = 60 = cascade start closes the loop to v91. [I] 8. FIREWALL REJECTION (honest): the review's rule "all small rational factors must be adjacent spine quotients" is FALSE as stated -- the load-bearing 16/7, 7/6 (lepton c's), 5/6 (gamma_car), 8/7 (m_mu/m_tau prefactor) are not adjacent quotients of (2,3,4,5). The adjacent-quotient ladder stays what v74 typed it as: an exact observation on the recurring glue/misalignment factors, NOT a hard admissibility filter. """ import sympy as sp from tfpt_constants import check, summary, reset s, t, x, lam = sp.symbols('s t x lambda') R = sp.Matrix([[1, 3, 0], [1, 5, 2], [2, 5, 3]]) Q = sp.Matrix([[3, 1, 0], [3, 2, 0], [3, 2, 1]]) SIG = sp.diag(1, -1, -1) K = R + Q * SIG L = R + Q * (sp.eye(3) + SIG) F = R + Q ONE = sp.Matrix([1, 1, 1]) A = sp.Matrix([1, 1, 2]) def anchor_block(M): return sp.Matrix([[(ONE.T * M * ONE)[0], (ONE.T * M * A)[0]], [(A.T * M * ONE)[0], (A.T * M * A)[0]]]) def pi_left(M): blk = sp.Matrix.vstack((ONE.T * M), (A.T * M)) return [blk[:, [i, j]].det() for i, j in ((0, 1), (0, 2), (1, 2))] def pi_right(M): blk = sp.Matrix.hstack(M * ONE, M * A) return [blk[[i, j], :].det() for i, j in ((0, 1), (0, 2), (1, 2))] def run(): reset() print("v94 sheet diamond & winding line (review 2026-06-11, validated subset)") # 1. the diamond and its two global invariants M = R + Q * sp.diag(s, t, t) check("diamond corners: R=M(0,0), K=M(1,-1), L=M(2,0), F=M(1,1)", M.subs({s: 0, t: 0}) == R and M.subs({s: 1, t: -1}) == K and M.subs({s: 2, t: 0}) == L and M.subs({s: 1, t: 1}) == F) check("det M(s,t) = 3st^2+9st+6s+t^2+5t+8 (exact)", sp.expand(M.det() - (3*s*t**2 + 9*s*t + 6*s + t**2 + 5*t + 8)) == 0) dB = sp.expand(anchor_block(M).det()) check("det B_M(s,t) = 6st+12s+3t^2+15t+16 (exact)", sp.expand(dB - (6*s*t + 12*s + 3*t**2 + 15*t + 16)) == 0) check("mass-transport pencil = the cut (s,t)=(1+x,x-1): det B -> " "(3x+2)(3x+5) (the v81 master cover)", sp.factor(sp.expand(dB.subs({s: 1 + x, t: x - 1}))) == (3*x + 2)*(3*x + 5)) # 2. built-in negative controls diag_cut = sp.expand(dB.subs(t, s)) check("NEGATIVE CONTROL: diagonal cut t=s gives 9s^2+27s+16, disc = 153 " "non-square -- the SAME control discriminant as v85's R-direction", diag_cut == 9*s**2 + 27*s + 16 and sp.discriminant(diag_cut, s) == 153 and not sp.sqrt(153).is_rational) check("NEGATIVE CONTROL: R->L cut t=0 is linear 12s+16 (degenerate " "direction, no cover)", sp.expand(dB.subs(t, 0)) == 12*s + 16) # 3. winding line synchronisation + triple lock Rs = R + s * ONE * sp.Matrix([[1, 0, 0]]) check("winding line: det R_s = 8+2s AND det B_{R_s} = 16+4s = 2 det R_s " "for ALL s (anchor area / torsion volume synchronised)", sp.expand(Rs.det() - (8 + 2*s)) == 0 and sp.expand(anchor_block(Rs).det() - 2*Rs.det()) == 0) check("triple lock: tr=15=dim A3, det=20=det L, (R_s^T a)_1=30=h(E8) " "EACH alone give s=6=|R+(A3)|", sp.solve(Rs.trace() - 15, s) == [6] and sp.solve(Rs.det() - 20, s) == [6] and sp.solve((Rs.T * A)[0] - 30, s) == [6]) # 4. cofactor seam normal n = R[:, 1].cross(R[:, 2]) check("cofactor seam normal n = (5,-9,6) = first adjugate row of R AND " "of L (columns 2,3 winding-invariant)", list(n) == [5, -9, 6] and R.adjugate()[0, :].T == n and L.adjugate()[0, :].T == n) check("n.1 = 2 = |Z2| (the per-winding determinant increment); " "n^T R = (8,0,0), n^T L = (20,0,0): only generation 1 is an open " "torsion channel", (n.T * ONE)[0] == 2 and list(n.T * R) == [8, 0, 0] and list(n.T * L) == [20, 0, 0]) # 5. reality, corrected chi = sp.expand((lam * sp.eye(3) - Rs).det()) disc = sp.discriminant(chi, lam) check("disc(s) = 17s^4-18s^3+709s^2+588s-7996; sign change between s=2 " "and s=3 => reality threshold s* ~ 2.825, NOT 6: reality does NOT " "select the winding value (honest correction of the review)", sp.expand(disc - (17*s**4 - 18*s**3 + 709*s**2 + 588*s - 7996)) == 0 and disc.subs(s, 2) < 0 and disc.subs(s, 3) > 0) check("at the physical s=6: disc chi_L = 39200 = 2^5 5^2 7^2 = " "2(10*14)^2, spectrum real (R at s=0 is complex: disc = -7996 < 0)", disc.subs(s, 6) == 39200 and 39200 == 2 * (10 * 14)**2 and disc.subs(s, 0) == -7996) # 6. F-corner audit BF = anchor_block(F) check("F-corner audit: det F = 32 = 2^5; chi_F = (lam-2)(lam^2-13lam+16); " "B_F = [[37,43],[53,63]], det 52 = dim F4 (v80), sum 196 = 14^2 = " "(dim G2)^2, tr 100, 43+53 = 96 = 2 Omega_adm [AUDIT]", F.det() == 32 and sp.factor(sp.expand((lam * sp.eye(3) - F).det())) == (lam - 2) * (lam**2 - 13*lam + 16) and BF == sp.Matrix([[37, 43], [53, 63]]) and BF.det() == 52 and sum(BF) == 196 and BF.trace() == 100 and BF[0, 1] + BF[1, 0] == 96) # 7. right-Pluecker canonicalisation check("right-Pluecker block: Pi_R(Q)=(0,4,5), Pi_R(K)=(12,12,-2), " "Pi_R(R)=(8,12,4), Pi_R(L)=(20,30,10)=10(2,3,1), sum 60 = cascade " "start", pi_right(Q) == [0, 4, 5] and pi_right(K) == [12, 12, -2] and pi_right(R) == [8, 12, 4] and pi_right(L) == [20, 30, 10] and sum(pi_right(L)) == 60) nL = sum(abs(v) for v in pi_left(K)) nR = sum(abs(v) for v in pi_right(K)) check("CANONICAL ratio readings: ||Pi_L(K)||_1 = 11 and ||Pi_R(K)||_1 = " "26 -- BOTH quark-ratio integers live in the SAME operator K " "(left = orientation, right = propagation)", nL == 11 and nR == 26) check("c_u/c_d = g_car*11/(N_fam^2 Delta_Q) = 55/117 and c_t/c_b = " "N_fam/||Pi_R(K)||_1 = 3/26; Pl(L)_13 = 26 and 2*Delta_Q = 26 " "become corollaries", sp.Rational(5 * nL, 9 * 13) == sp.Rational(55, 117) and sp.Rational(3, nR) == sp.Rational(3, 26) and pi_left(L)[1] == 26 and 2 * 13 == 26) # 8. firewall rejection (honest) spine = [2, 3, 4, 5] adj = {sp.Rational(spine[i], spine[i+1]) for i in range(3)} \ | {sp.Rational(spine[i+1], spine[i]) for i in range(3)} offenders = [sp.Rational(16, 7), sp.Rational(7, 6), sp.Rational(5, 6), sp.Rational(8, 7)] check("FIREWALL REJECTED as a hard rule: load-bearing 16/7, 7/6 (lepton " "c's), 5/6 (gamma_car), 8/7 are NOT adjacent spine quotients -- " "the v74 quotient ladder stays an observation, not a filter", all(r not in adj for r in offenders)) return summary("v94 sheet diamond") if __name__ == "__main__": raise SystemExit(1 if run() else 0)