{ "_provenance": { "box1eq_de": "/phys_lbl3_qed_parents/vp/box1eq_de_symbolic.json \u2014 exact rational w'-DE connection A(w',d) of the 8-master 1-loop box (mass-w' line) family, reconstructed from 46 exact-rational Kira samples (0 mismatches). ROUND 2: the ONLY input of the fixed-eps computation (analytic formula; the kernel is solved from the w'->inf vacuum boundary, no numeric seed).", "box1eq_bnd_w5": "/phys_lbl3_qed_parents/vp/box1eq_masters_bnd_e20_out.json \u2014 1-LOOP AMFlow Laurent values of the 8 box masters at w'=5. ROUND 2: live CROSS-CHECK only (round 1 used them as transport seeds).", "Kn": "/phys_lbl3_qed_parents/vp/amflow_box1_Kn20_e20_out.json \u2014 1-LOOP AMFlow threshold Taylor coefficients K_n(eps) at w'=1. ROUND 2: cross-check for the live arc-VoP Cauchy coefficients. 2026-07-05: K_2^(1) demoted from 'single shipped numeric input' to CROSS-CHECK ONLY \u2014 the evaluator derives it at runtime from the exact parametric 2-fold (K2_threshold_eps01; verified vs this string to its full 120 digits, the LBL3VP build spec); ALL of Kn is now held-out gate data, no shipped numeric inputs remain.", "sigvp_de": "/phys_lbl3_qed_parents/vp/sigvp_de_symbolic.json \u2014 symbolic w-DE for the 4-master Sigma_VP system. ROUND 2: RETIRED from the computation (the spectral density is closed-form / Gamma_1(6) one-fold now); kept for provenance.", "sigvp_bnd_w5": "/phys_lbl3_qed_parents/vp/sigvp_bnd_w5_e20_out.json \u2014 2-LOOP AMFlow Laurent boundary values of the Sigma_VP masters at w=5. ROUND 2: RETIRED (round-1 transport seed); kept for provenance.", "note": "ball midpoints re-printed at 120 significant digits; source files carry ~300. Round-2 rederivation notes: /lbl3vp/r2-eichler/ (v1b_orders.py = 3-body density validation, v2*.py = kernel closed forms)." }, "sigvp_de": { "masters": [ [ 1, 2, 1, 1, 0 ], [ 1, 1, 1, 1, 0 ], [ 1, 0, 1, 0, 0 ], [ 1, 1, 1, 0, 0 ] ], "var": "w", "dim_var": "d", "A": [ [ "(d*w**3 - 5*d*w**2 - 33*d*w - 27*d - 4*w**3 + 34*w**2 + 264*w + 90)/(2*w**4 - 14*w**3 - 42*w**2 + 54*w)", "(3*d*w + 9*d - 10*w - 30)/(2*w**3 - 20*w**2 + 18*w)", "(-8*d**3*w**2 - 96*d**3*w - 24*d**3 - d**2*w**4 + 2*d**2*w**3 + 56*d**2*w**2 + 894*d**2*w + 201*d**2 + 4*d*w**4 - 8*d*w**3 - 128*d*w**2 - 2424*d*w - 516*d - 4*w**4 + 8*w**3 + 96*w**2 + 2040*w + 420)/(8*d*w**6 - 72*d*w**5 - 48*d*w**4 + 496*d*w**3 - 600*d*w**2 + 216*d*w - 40*w**6 + 360*w**5 + 240*w**4 - 2480*w**3 + 3000*w**2 - 1080*w)", "(2*d**2*w**3 + 26*d**2*w**2 + 30*d**2*w + 6*d**2 - 13*d*w**3 - 121*d*w**2 - 159*d*w - 27*d + 18*w**3 + 138*w**2 + 198*w + 30)/(2*w**6 - 18*w**5 - 12*w**4 + 124*w**3 - 150*w**2 + 54*w)" ], [ "(6*w - 6)/(w**2 - 9*w)", "(d*w - 4*w + 6)/(w**2 - 9*w)", "(-2*d**3 - d**2*w + 19*d**2 + 4*d*w - 52*d - 4*w + 44)/(2*d*w**3 - 20*d*w**2 + 18*d*w - 10*w**3 + 100*w**2 - 90*w)", "(2*d**2*w + 2*d**2 - 11*d*w - 9*d + 14*w + 10)/(2*w**3 - 20*w**2 + 18*w)" ], [ "0", "0", "0", "0" ], [ "0", "0", "(2 - d)/(2*w**2 - 2*w)", "(d*w + d - 4*w - 2)/(2*w**2 - 2*w)" ] ], "n_samples": 36, "mismatches": 0 }, "box1eq_de": { "masters": [ [ 1, 1, 1, 1 ], [ 1, 0, 0, 0 ], [ 0, 1, 0, 0 ], [ 1, 0, 1, 0 ], [ 0, 1, 0, 1 ], [ 1, 1, 1, 0 ], [ 1, 1, 0, 1 ], [ 0, 1, 1, 1 ] ], "var": "wp", "dim_var": "d", "A": [ [ "(d*w - 5*w)/(w**2 + 1)", "(-12*d*w**3 - 9*d*w**2 - 9*d*w - 6*d + 24*w**3 + 18*w**2 + 18*w + 12)/(6*w**7 - 4*w**6 + 36*w**5 - 20*w**4 + 54*w**3 - 16*w**2 + 24*w)", "(9*d*w**3 + 33*d*w**2 + 12*d*w + 24*d - 18*w**3 - 66*w**2 - 24*w - 48)/(12*w**6 - 8*w**5 + 72*w**4 - 40*w**3 + 108*w**2 - 32*w + 48)", "(3*d*w - 9*w)/(w**4 + 5*w**2 + 4)", "(-3*d*w - 3*d + 9*w + 9)/(6*w**4 - 4*w**3 + 12*w**2 - 4*w + 6)", "(12 - 3*d)/(2*w**2 + 2)", "(-2*d*w + 2*d + 8*w 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