{ "row": 35, "line": { "name": "L1", "x": "17/2", "z": "5/3", "mt2": "1", "variable": "y", "connection": "row35_data.json (A_entries)" }, "what": "the canonical-basis census of the 35 non-elliptic diagonal blocks of the line connection: each block run through the eps-factoriser by itself; 29 admit a rational rotation T(eps, y) to an eps-factorised dlog form eps * Atilde(y), 6 stop (the engine's stop string verbatim, its class by name); sector 481 (rows 54-59, n = 6): the maximal-cut curve is elliptic (j non-constant in z5); the eps^0 block is reducible to first order -- six exact hyperexponential factors, see the sector_481 entry", "form": { "T_Atilde": "the engine's string matrices in (eps, x), x == y on the line, nested lists COLUMN-major (json[j][i] = M[i][j]); rational literals as p//q; verbatim from the engine's out file", "identity": "T A T^-1 + (dT/dy) T^-1 == eps * Atilde, A the block of the line connection at d = 4 - 2 eps", "residues": "row-major nested lists (json[i][j] = R[i][j]) of exact rationals p/q: the residue matrix of Atilde at each rational pole (letters.poles, the same order), Rinf the residue at infinity, quad_kernels[q] the (U y + V)/q(y) term of the quadratic letter q (U, V row-major)", "dlog_form": "Atilde(y) == sum_p residues[p]/(y - p) + sum_q (U_q y + V_q)/q(y) exactly; Rinf == -(sum_p residues[p] + sum_q U_q / lead(q))", "alphabet_letters": "each rational pole named by the alphabet letter whose restriction to this line vanishes there (quadratic_alphabet_letter: the letter whose restriction is the quadratic factor)", "sector_487_entry": "the sector-487 entry carries, beside the OK-block keys, basis_change (the cut-IBP dictionary C over the served four, the transcribed rotation, S = T_transcribed . C written as this block's T, det C, the receipts by sha256, the engine report) and served_basis_stop (the stop entry of the served basis, kept beside as the record); letters.quadratic_alphabet_letters states the two-variable form of each quadratic factor as a restriction check to this line only", "sector_481": "the sector-481 entry beside blocks[] (the sector is not in blocks[]: not run through the eps-factoriser; census.elliptic_not_run names it): the label, the maximal-cut curve statement in the served text's words, eps0_block_chain = the first-order factorisation receipt of the served block on this line at d = 4 in y (verdict, size, remainder_rank, the six chain factors verbatim -- exponents per singular factor as [factor, exponent] pairs (search labels; the canonical exponents are the residues of rate_u_prime_over_u, rate_partial_fractions), degree_bound, P (the polynomial vector), n_solutions_at_this_exponent, rate_u_prime_over_u, rate_partial_fractions -- the search_log, the bounds EB / NB / MAXCOMBO, the versions, the wall; the input by basename + sha256), rays (the two mass-scaling rays P and E: the ray block receipts and their chain receipts by sha256, verdicts), controls (the S-vs-N block control, the thimble receipts with their digit figures, the built-in C1-C4 of the served script), provenance_scripts (the block extractor and the ray config maker, as text; not runnable from this bundle); every receipt named by its vendored sha256 and its original sha256" }, "check_points": [ [ "1/223", "29/211" ], [ "5/6", "17/139" ] ], "eps_free_shift": "1/97", "census": { "n_blocks": 35, "n_ok": 29, "n_stopped": 6, "ok_sectors": [ 262, 294, 98, 321, 322, 326, 327, 353, 354, 355, 358, 359, 161, 167, 384, 388, 416, 420, 422, 423, 225, 227, 231, 455, 480, 484, 485, 486, 487 ], "stopped_by_class": { "Moser-irreducible": [ 417, 449 ], "eps^0 obstruction": [ 421, 453, 482, 483 ] }, "elliptic_not_run": { "sector": 481, "rows": [ 54, 59 ], "n": 6 }, "line_text": "29 OK / 6 stopped (2 Moser-irreducible + 4 eps^0) / 1 elliptic" }, "sources": { "engine": { "Normalize.jl": "4c5772a76f92d0d291a55c5427d55cc6e55798a1133d0d59a9fd4074bef54ea0", "Fuchsia.jl": "8a8c7369f13e5dcb7e27ecad8cd1bc2d2e07cde3a6d3bef5f8a1841347ef76f2" }, "runner_sha256": "6e497c73cda9a1da9c7d1ab3c1a11f2b0e18558c9be02ebed9ceacbc61b859d5", "verifier_sha256": "857543b36073fe1047e5e62ac16b78f0263dfb753f3d24d94876cf2e510f2a84", "out_files": "the engine's out file per block (blocks[*].source: file name + sha256)", "receipt_sha256_16": "a675806bd6068dec", "alphabet_census_sha256_16": "cd1b7bf207d0d5e0", "p1c_receipt_sha256_16": "875b7217badfe6e2", "live_receipt_sha256_16": "e9ba6a61677fdec5" }, "blocks": [ { "sector": 262, "n": 1, "rows": [ 0 ], "masters": [ "wpairT4[0,1,1,0,0,0,0,0,1]" ], "ok": true, "stop_class": "OK", "stop": "", "T": [ [ "1" ] ], "Atilde": [ [ "0" ] ], "letters": { "engine_string": "(String[], Dict{String, Any}(\"inf\" => [0]))", "poles": [], "alphabet_letters": {}, "algebraic_factors": [], "quadratic_alphabet_letter": null, "residues": {}, "Rinf": [ [ "0" ] ], "quad_kernels": {} }, "source": { "file": "out_b262.json", "sha256": "b344b82f864f85902a84df435de6aeb77af2a5e77d8f88fbdd3eae0263dd4e32" } }, { "sector": 294, "n": 1, "rows": [ 1 ], "masters": [ "wpairT4[0,1,1,0,0,1,0,0,1]" ], "ok": true, "stop_class": "OK", "stop": "", "T": [ [ "1" ] ], "Atilde": [ [ "0" ] ], "letters": { "engine_string": "(String[], Dict{String, Any}(\"inf\" => [0]))", "poles": [], "alphabet_letters": {}, "algebraic_factors": [], "quadratic_alphabet_letter": null, "residues": {}, "Rinf": [ [ "0" ] ], "quad_kernels": {} }, "source": { "file": "out_b294.json", "sha256": "20fcb30bbeb3826d3b8c6e4e0c4133eb79b646d98f210478ee0494a0c5040e0c" } }, { "sector": 98, "n": 1, "rows": [ 2 ], "masters": [ "wpairT4[0,1,0,0,0,1,1,0,0]" ], "ok": true, "stop_class": "OK", "stop": "", "T": [ [ "1" ] ], "Atilde": [ [ "0" ] ], "letters": { "engine_string": "(String[], Dict{String, Any}(\"inf\" => [0]))", "poles": [], "alphabet_letters": {}, "algebraic_factors": [], "quadratic_alphabet_letter": null, "residues": {}, "Rinf": [ [ "0" ] ], "quad_kernels": {} }, "source": { "file": "out_b98.json", "sha256": "8a2d6a8cdf6dcbce7023ee747d81c2b36984dd6db2bf569f06096b40d10188e1" } }, { "sector": 321, "n": 2, "rows": [ 3, 4 ], "masters": [ "wpairT4[1,0,0,0,0,0,1,0,1]", "wpairT4[1,-1,0,0,0,0,1,0,1]" ], "ok": true, "stop_class": "OK", "stop": "", "T": [ [ "((-2875//162*eps^2 + 125//6*eps - 125//27)//(eps^4 - 2*eps^3 + 11//9*eps^2 - 2//9*eps)*x^2 + (625//81*eps - 125//27)//(eps^3 - 2*eps^2 + 11//9*eps - 2//9)*x + 125//162//(eps^2 - eps + 2//9))//(x^3 + 3*x^2 + 3*x + 1)", "(115//81//(eps^2 - eps + 2//9)*x^3 + 115//9//(eps^2 - 2//3*eps)*x^2 - 115//9//(eps^2 - 4//3*eps + 1//3)*x - 115//81//(eps^2 - eps + 2//9))//(x^3 + 3*x^2 + 3*x + 1)" ], [ "((875//27*eps - 250//27)//(eps^3 - eps^2 + 2//9*eps)*x^2 - 125//27//(eps^2 - eps + 2//9)*x)//(x^4 + 4//3*x^3 - 2*x^2 - 4*x - 5//3)", "(-115//27//(eps^2 - eps + 2//9)*x^3 + (-805//27*eps + 230//27)//(eps^3 - eps^2 + 2//9*eps)*x^2 + 230//27//(eps^2 - eps + 2//9)*x)//(x^4 + 4//3*x^3 - 2*x^2 - 4*x - 5//3)" ] ], "Atilde": [ [ "(-2*x + 4)//(x^2 + x)", "-138//25//(x^2 + x)" ], [ "50//23//(x^2 + x)", "(-x - 3)//(x^2 + x)" ] ], "letters": { "engine_string": "([\"x\", \"x - (-1)\"], Dict{String, Any}(\"0\" => [4 50//23; -138//25 -3], \"inf\" => [2 0; 0 1], \"-1\" => [-6 -50//23; 138//25 2]))", "poles": [ "0", "-1" ], "alphabet_letters": { "0": "y", "-1": "y + 1" }, "algebraic_factors": [], "quadratic_alphabet_letter": null, "residues": { "0": [ [ "4", "50/23" ], [ "-138/25", "-3" ] ], "-1": [ [ "-6", "-50/23" ], [ "138/25", "2" ] ] }, "Rinf": [ [ "2", "0" ], [ "0", "1" ] ], "quad_kernels": {} }, "source": { "file": "out_b321.json", "sha256": "d6b1de692192ecb932d31cfd1ffc1639c9a9b9805a7738d55c96f1fc5157846c" } }, { "sector": 322, "n": 2, "rows": [ 5, 6 ], "masters": [ "wpairT4[0,1,0,0,0,0,1,0,1]", "wpairT4[-1,1,0,0,0,0,1,0,1]" ], "ok": true, "stop_class": "OK", "stop": "", "T": [ [ "1", "0" ], [ "0", "1//(x - 5//3)" ] ], "Atilde": [ [ "0", "0" ], [ "0", "0" ] ], "letters": { "engine_string": "(String[], Dict{String, Any}(\"inf\" => [0 0; 0 0]))", "poles": [], "alphabet_letters": {}, "algebraic_factors": [], "quadratic_alphabet_letter": null, "residues": {}, "Rinf": [ [ "0", "0" ], [ "0", "0" ] ], "quad_kernels": {} }, "source": { "file": "out_b322.json", "sha256": "205d7761acf01a6ea9c85c77eb06833d2625848c0838d10b8bf557b2a7a3ab33" } }, { "sector": 326, "n": 3, "rows": [ 7, 8, 9 ], "masters": [ "wpairT4[0,1,1,0,0,0,1,0,1]", "wpairT4[-1,1,1,0,0,0,1,0,1]", "wpairT4[0,1,1,0,0,-1,1,0,1]" ], "ok": true, "stop_class": "OK", "stop": "", "T": [ [ "1", "(17//4*x + 323//48)//(x + 31//12)", "0" ], [ "0", "1//(x + 31//12)", "0" ], [ "0", "0", "1" ] ], "Atilde": [ [ "0", "0", "0" ], [ "0", "0", "0" ], [ "0", "0", "0" ] ], "letters": { "engine_string": "(String[], Dict{String, Any}(\"inf\" => [0 0 0; 0 0 0; 0 0 0]))", "poles": [], "alphabet_letters": {}, "algebraic_factors": [], "quadratic_alphabet_letter": null, "residues": {}, "Rinf": [ [ "0", "0", "0" ], [ "0", "0", "0" ], [ "0", "0", "0" ] ], "quad_kernels": {} }, "source": { "file": "out_b326.json", "sha256": "7a6cc5b831f66f5cd305aaffb045c35c2bbdf6e174cffb8f7fa42d51e2c65983" } }, { "sector": 327, "n": 2, "rows": [ 10, 11 ], "masters": [ "wpairT4[1,1,1,0,0,0,1,0,1]", "wpairT4[1,1,1,0,0,-1,1,0,1]" ], "ok": true, "stop_class": "OK", "stop": "", "T": [ [ "((1//3*eps - 1//3)//(eps - 1//3)*x^3 + 1//3*x^2 + (9*eps - 7//3)//(eps - 1)*x + (-5//3*eps - 5//3)//(eps - 1))//(x^2 + (6*eps - 8//3)//(eps - 1)*x + (5*eps - 5//3)//(eps - 1))", "((-7//18*eps + 7//18)//(eps - 1//3)*x^3 + (-2//9*eps + 7//54)//(eps - 1//3)*x^2 + (-17//2*eps + 14//9)//(eps - 1)*x + (10//9*eps + 10//9)//(eps - 1))//(x^2 + (6*eps - 8//3)//(eps - 1)*x + (5*eps - 5//3)//(eps - 1))" ], [ "(-2*x^2 + 2*x)//(x^2 + (6*eps - 8//3)//(eps - 1)*x + (5*eps - 5//3)//(eps - 1))", "(7//3*x^2 - 4//3*x)//(x^2 + (6*eps - 8//3)//(eps - 1)*x + (5*eps - 5//3)//(eps - 1))" ] ], "Atilde": [ [ "(-28//3*x^2 - 925//18*x - 1421//54)//(x^3 + 37//6*x^2 + 143//18*x + 25//9)", "(175//18*x - 2//3)//(x^2 + x)" ], [ "-8//(x + 1)", "(25//3*x^3 + 350//9*x^2 + 475//27*x - 25//9)//(x^4 + 37//6*x^3 + 143//18*x^2 + 25//9*x)" ] ], "letters": { "engine_string": "([\"x\", \"x - (-1)\"], Dict{String, Any}(\"_algebraic_factors\" => [\"18*x^2 + 93*x + 50\", \"18*x^2 + 93*x + 50\"], \"0\" => [0 0; -2//3 -1], \"inf\" => [28//3 8; -175//18 -25//3], \"-1\" => [-34//3 -8; 187//18 22//3]))", "poles": [ "0", "-1" ], "alphabet_letters": { "0": "y", "-1": "y + 1" }, "algebraic_factors": [ "18*x^2 + 93*x + 50" ], "quadratic_alphabet_letter": "x*y + y**2 - 2*y*z + z**2", "residues": { "0": [ [ "0", "0" ], [ "-2/3", "-1" ] ], "-1": [ [ "-34/3", "-8" ], [ "187/18", "22/3" ] ] }, "Rinf": [ [ "28/3", "8" ], [ "-175/18", "-25/3" ] ], "quad_kernels": { "18*x^2 + 93*x + 50": { "U": [ [ "36", "0" ], [ "0", "36" ] ], "V": [ [ "93", "0" ], [ "0", "93" ] ] } } }, "source": { "file": "out_b327.json", "sha256": "592d3a5349ca3cb18199e3b12fa44fcd7aa3e3e52e444ea996eedc609d04aa74" } }, { "sector": 353, "n": 1, "rows": [ 12 ], "masters": [ "wpairT4[1,0,0,0,0,1,1,0,1]" ], "ok": true, "stop_class": "OK", "stop": "", "T": [ [ "1" ] ], "Atilde": [ [ "-1//(x - 5//3)" ] ], "letters": { "engine_string": "([\"x - (5//3)\"], Dict{String, Any}(\"5//3\" => [-1], \"inf\" => [1]))", "poles": [ "5/3" ], "alphabet_letters": { "5/3": "y - z" }, "algebraic_factors": [], "quadratic_alphabet_letter": null, "residues": { "5/3": [ [ "-1" ] ] }, "Rinf": [ [ "1" ] ], "quad_kernels": {} }, "source": { "file": "out_b353.json", "sha256": "1a0fd4600f052e0713e0242e7dc69031c3f7ae8d5625cd21f635e80f1def282a" } }, { "sector": 354, "n": 2, "rows": [ 13, 14 ], "masters": [ "wpairT4[0,1,0,0,0,1,1,0,1]", "wpairT4[-1,1,0,0,0,1,1,0,1]" ], "ok": true, "stop_class": "OK", "stop": "", "T": [ [ "1", "(35//12*x + 175//24)//(x + 7//2)" ], [ "0", "1//(x + 7//2)" ] ], "Atilde": [ [ "0", "0" ], [ "0", "0" ] ], "letters": { "engine_string": "(String[], Dict{String, Any}(\"inf\" => [0 0; 0 0]))", "poles": [], "alphabet_letters": {}, "algebraic_factors": [], "quadratic_alphabet_letter": null, "residues": {}, "Rinf": [ [ "0", "0" ], [ "0", "0" ] ], "quad_kernels": {} }, "source": { "file": "out_b354.json", "sha256": "67cbb5f0495a54678d6fde05314a3031bb251f79d115855272b3f0273bd09a67" } }, { "sector": 355, "n": 2, "rows": [ 15, 16 ], "masters": [ "wpairT4[1,1,0,0,0,1,1,0,1]", "wpairT4[1,1,-1,0,0,1,1,0,1]" ], "ok": true, "stop_class": "OK", "stop": "", "T": [ [ "(2261//96//(eps^2 - 1//3*eps)*x^3 + (436373//4608*eps - 241927//3072)//(eps^3 - 5//6*eps^2 + 1//6*eps)*x^2 + (56993027//27648*eps^2 - 74787097//55296*eps + 5383441//18432)//(eps^4 - 11//6*eps^3 + eps^2 - 1//6*eps)*x + (248734871//82944*eps^2 - 295279817//165888*eps + 50341165//165888)//(eps^4 - 11//6*eps^3 + eps^2 - 1//6*eps))//(x^2 + (-161//12*eps + 67//24)//(eps - 1)*x + (-173//12*eps + 91//24)//(eps - 1))", "(-1989//64//(eps^2 - 1//2*eps)*x^3 + (-7735//512*eps^2 + 199121//1024*eps - 70941//1024)//(eps^4 - 11//6*eps^3 + eps^2 - 1//6*eps)*x^2 + (-2194309//3072*eps^2 + 5854511//6144*eps - 526201//2048)//(eps^4 - 11//6*eps^3 + eps^2 - 1//6*eps)*x + (-14907113//9216*eps^2 + 23914631//18432*eps - 4920565//18432)//(eps^4 - 11//6*eps^3 + eps^2 - 1//6*eps))//(x^2 + (-161//12*eps + 67//24)//(eps - 1)*x + (-173//12*eps + 91//24)//(eps - 1))" ], [ "(133//16//(eps^2 - eps)*x^3 + 32319//256//(eps^2 - eps)*x^2 + 430787//768//(eps^2 - eps)*x + 16320829//27648//(eps^2 - eps))//(x^2 + (-161//12*eps + 67//24)//(eps - 1)*x + (-173//12*eps + 91//24)//(eps - 1))", "(-117//16//(eps^2 - eps)*x^3 - 28431//256//(eps^2 - eps)*x^2 - 126321//256//(eps^2 - eps)*x - 1595269//3072//(eps^2 - eps))//(x^2 + (-161//12*eps + 67//24)//(eps - 1)*x + (-173//12*eps + 91//24)//(eps - 1))" ] ], "Atilde": [ [ "(x^4 - 275//24*x^3 - 8731//96*x^2 - 288629//1728*x - 502747//5184)//(x^5 + 697//48*x^4 + 3353//48*x^3 + 230227//1728*x^2 + 548299//5184*x + 74825//2592)", "(624//133*x^2 + 1898//133*x + 143//6)//(x^4 + 13*x^3 + 601//12*x^2 + 6163//108*x + 1025//54)" ], [ "(-2128//117*x^2 - 19418//351*x - 194579//2106)//(x^4 + 13*x^3 + 601//12*x^2 + 6163//108*x + 1025//54)", "(-x^2 - 167//6*x + 196//9)//(x^4 + 13*x^3 + 601//12*x^2 + 6163//108*x + 1025//54)" ] ], "letters": { "engine_string": "([\"x - (-73//48)\", \"x - (-41//6)\", \"x - (-1)\"], Dict{String, Any}(\"_algebraic_factors\" => [\"18*x^2 + 93*x + 50\", \"18*x^2 + 93*x + 50\", \"18*x^2 + 93*x + 50\", \"18*x^2 + 93*x + 50\"], \"-73//48\" => [-1 0; 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0 0 0 0; 0 0 0 0; -2//3 0 0 -2//3]))", "poles": [], "alphabet_letters": {}, "algebraic_factors": [ "18*x^2 + 93*x + 203", "18*x^2 + 93*x + 50" ], "quadratic_alphabet_letter": "x*y + y**2 - 2*y*z + z**2", "residues": {}, "Rinf": [ [ "8/3", "0", "0", "8/3" ], [ "0", "0", "0", "0" ], [ "0", "0", "0", "0" ], [ "-2/3", "0", "0", "-2/3" ] ], "quad_kernels": { "18*x^2 + 93*x + 203": { "U": [ [ "-108", "0", "0", "0" ], [ "0", "-36", "0", "0" ], [ "0", "0", "0", "0" ], [ "0", "0", "0", "0" ] ], "V": [ [ "-279", "-1989/2", "0", "0" ], [ "18", "-93", "0", "0" ], [ "0", "0", "0", "0" ], [ "0", "0", "0", "0" ] ] }, "18*x^2 + 93*x + 50": { "U": [ [ "60", "0", "0", "-48" ], [ "0", "36", "0", "0" ], [ "0", "0", "0", "0" ], [ "12", "0", "0", "12" ] ], "V": [ [ "155", "0", "-561/2", "-124" ], [ "0", "93", "0", "0" ], [ "12", "0", "0", "-24" ], [ "31", "0", "-561/4", "31" ] ] } }, "quadratic_alphabet_letters": { "18*x^2 + 93*x + 50": { "form": "x*y + y**2 - 2*y*z + z**2", "restriction_to_the_line_equals_q_up_to_the_integer_scale": true, "scale": "18", "note": "the served letter of the first quadratic (the alphabet letter whose restriction to this line is this factor)" }, "18*x^2 + 93*x + 203": { "form": "x*y + y**2 - 2*y*z + z**2 + x", "restriction_to_the_line_equals_q_up_to_the_integer_scale": true, "scale": "18", "note": "a restriction check of the two-variable form to this line only" } } }, "source": { "file": "out_b487_g.json", "sha256": "5a5556dd0c29e4205e14e079e943f91b275175bbb43155e61555c2728db0089e" }, "basis_change": { "their_masters": [ 1, 1, 1, -1, -1, 1, 1, 1, 1 ], "in_place_of": [ 1, 1, 1, -2, 0, 1, 1, 1, 1 ], "served_four": [ "wpairT4[1,1,1,0,0,1,1,1,1]", "wpairT4[1,1,1,-1,0,1,1,1,1]", "wpairT4[1,1,1,-2,0,1,1,1,1]", "wpairT4[1,1,1,0,-1,1,1,1,1]" ], "their_basis_order": [ "1,1,1,0,0,1,1,1,1", "1,1,1,-1,0,1,1,1,1", "1,1,1,0,-1,1,1,1,1", "1,1,1,-1,-1,1,1,1,1" ], "C_rows_in_their_basis_order_over_the_served_four": { "1,1,1,0,0,1,1,1,1": [ "1", "0", "0", "0" ], "1,1,1,-1,0,1,1,1,1": [ "0", "1", "0", "0" ], "1,1,1,0,-1,1,1,1,1": [ "0", "0", "0", "1" ], "1,1,1,-1,-1,1,1,1,1": [ "(-78*d*y**2 + 39*d*y + 741*d + 312*y**2 - 156*y - 2964)/(250*d - 868)", "(54*d*y - 923*d - 228*y + 3100)/(250*d - 868)", "(66*d - 198)/(125*d - 434)", "(156*d*y + 403*d - 624*y - 1612)/(375*d - 1302)" ] }, "C_variables": "(d, y): the cut-IBP dictionary rows as the P1 receipt writes them; y == x on the line, d = 4 - 2 eps in T", "det_C": "-66*(d - 3)/(125*d - 434)", "T_transcribed": [ [ "289*x/8 + 3179/24", "0", "17*x/2 + 527/24", "0" ], [ "85/12 - 17*x/4", "0", "17/4", "0" ], [ "0", "17/2", "0", "0" ], [ "0", "289/8", "0", "17/2" ] ], "T_transcribed_source": "the sympy matrix literal of p1c_make_blocks.py with r1 = r2 = 1 and the line's (X, Z) = (17/2, 5/3)", "S": "T = S = T_transcribed . C, the transformation FROM THE SERVED BASIS (written above as this block's T, column-major); det S = 918731*(2*eps - 1)*(18*x^2 + 93*x + 203)/(192*(125*eps - 33))", "identity_asserted_symbolically": "S A S^-1 + (dS/dy) S^-1 == eps * Atilde over Q(eps)(y), A the served block of rows 75-78 at d = 4 - 2 eps", "p1_receipt_sha256": "20e002d2037532dcdda5b76d8076a7a9e7ca8dc20644f36c5f98dd93a0eb7dab", "p1c_receipt_sha256": "875b7217badfe6e2540af6689817f094a05833abcbcb28e5ece5e9e6dfe500a8", "live_receipt_sha256": "e9ba6a61677fdec5f35bbab3439a58bb9e700e493b53fbdaa5206f7a5dce19f7", "engine_report": { "already_epsform": "true", "fuchsian_input": "true" }, "engine_t_factor_s": 6.00022292137146, "engine_t_parse_s": 1.8643851280212402, "engine_T_relative_to_the_g_block": "identity", "verifier_verdict_at_the_two_census_points": "PASS", "verifier_points": [ { "eps": "1/223", "d": "890/223", "y": "29/211", "identity_TAT_plus_dTT_eq_eps_Atilde": true, "Atilde_eps_free": true }, { "eps": "5/6", "d": "7/3", "y": "17/139", "identity_TAT_plus_dTT_eq_eps_Atilde": true, "Atilde_eps_free": true } ] }, "served_basis_stop": { "stop_class": "Moser-irreducible", "stop": "input not Fuchsian and Moser reduction failed: all higher-order poles are stuck (no kernel/cokernel shear reduces rank) \u2014 Moser-irreducible or needs full Barkatou pencil", "source": { "file": "out_b487.json", "sha256": "db92d1a79daf5831aa0685faac0294707c02c4e8ca56acefe2efa40a68bb7d8d" }, "note": "in the basis carrying [1,1,1,-2,0,1,1,1,1]" } } ], "sector_481": { "sector": 481, "n": 6, "rows": [ 54, 55, 56, 57, 58, 59 ], "masters": [ "wpairT4[1,0,0,0,0,1,1,1,1]", "wpairT4[1,-1,0,0,0,1,1,1,1]", "wpairT4[1,0,-1,0,0,1,1,1,1]", "wpairT4[1,0,0,-1,0,1,1,1,1]", "wpairT4[1,0,0,0,-1,1,1,1,1]", "wpairT4[1,-2,0,0,0,1,1,1,1]" ], "label": "sector 481 (rows 54-59, n = 6): the maximal-cut curve is elliptic (j non-constant in z5); the eps^0 block is reducible to first order -- six exact hyperexponential factors on this line, on the other served line and along the two mass-scaling rays; not run through the eps-factoriser (census.elliptic_not_run unchanged)", "maximal_cut_curve": { "statement": "(sector $481$) has an elliptic maximal-cut curve: its fibrewise curve has non-constant $j$ (an order-two Picard--Fuchs operator in the fibre variable $z_5$; $j$ non-constant along the mass-scaling ray as well), while its $\\eps^0$ differential-equation block is reducible to first order.", "source": "the served section text (the statement object STATEMENT_SEC481_20260910T021848Z.json, pair c_L213_is_elliptic, TO)" }, "eps0_block_chain": { "schema": "P2_REDUCIBILITY_v1", "recipe": "report_C3.md L135-142 (sys_factor): hyperexponential vector solutions prod f_i^{e_i} P, quotient by a rational gauge, iterate; L508-511 (blocktri)", "mode": "--served", "line": "L1", "stamp_utc": "2026-09-10T01:56:29Z", "stamp_end_utc": "2026-09-10T01:59:14Z", "script_of_record": { "file": "p2_reducibility.py", "sha256": "2eb65015d73bce5992bb8590e28724f9692caad36d54353d0d76106f5b053ef4", "vendored_as": "vendor_row35_sec481/scripts/p2_reducibility.py (as text; re-cut)", "vendored_sha256": "96e5690908a6c8856f14fa111732a15f5fe48c304bfd8e9946a9708fc4584ea4" }, "served_script": { "file": "qqww-t4-sec481-chain.py", "note": "the succession of the script of record served beside this file (pinned by the bundle MANIFEST.sha256, not here): --line L1 re-runs this chain on the served connection and compares it factor by factor with --reference" }, "bounds": { "EB": 3, "NB": 12, "MAXCOMBO": 20000 }, "sympy": "1.14.0", "python_flint": "0.8.0", "input": { "file": "row35_data.json", "sha256": "6acf455def67385491ef9be8734c223129c811854503d810abbd4b71a8dea9fc", "rows": [ 54, 55, 56, 57, 58, 59 ], "masters": [ "wpairT4[1,0,0,0,0,1,1,1,1]", "wpairT4[1,-1,0,0,0,1,1,1,1]", "wpairT4[1,0,-1,0,0,1,1,1,1]", "wpairT4[1,0,0,-1,0,1,1,1,1]", "wpairT4[1,0,0,0,-1,1,1,1,1]", "wpairT4[1,-2,0,0,0,1,1,1,1]" ], "d": 4, "variable": "y", "note": "the SERVED L1 line block in y at d = 4 (L1: (x,z) = (17/2, 5/3); L2: (17/2, 7/4)); NOT the ray object" }, "verdict": "REDUCIBLE_TO_FIRST_ORDER", "size": 6, "remainder_rank": 0, "bounded_search_used": true, "n_factors": 6, "chain": [ { "exponents": [ [ "y + 1", "0" ], [ "y - 5/3", "-1" ], [ "y + 25/6", "0" ], [ "y + 41/6", "-1" ], [ "y**2 + 31*y/6 + 25/9", "0" ], [ "y**2 + 31*y/6 + 203/18", "0" ], [ "y**2 + 358*y/15 + 19801/225", "0" ], [ "y**2 - 203*y/15 - 7751/900", "0" ], [ "y**8 + 62*y**7/3 - 342646*y**6/2925 - 131506681*y**5/35100 - 67297324561*y**4/3290625 - 2168467309253*y**3/78975000 + 94394655040817*y**2/1895400000 + 161064076435621*y/1421550000 + 799655341918027/17058600000", "0" ] ], "degree_bound": 12, "P": [ "3455275/3394594", "166050*y**2/1697297 + 857925*y/1697297 + 1057265/969884", "166050*y**2/1697297 + 857925*y/1697297 - 5674645/1697297", "-83025*y**2/1697297 - 1751465*y/3394594 + 5049500/5091891", "9825*y/14263 - 131685/399364", "y**2 + 31*y/6 + 7292141/845712" ], "n_solutions_at_this_exponent": 2, "rate_u_prime_over_u": "0", "rate_partial_fractions": "0", "exponents_note": "search labels; the canonical exponents are the residues of rate_u_prime_over_u (rate_partial_fractions)" }, { "exponents": [ [ "y + 1", "0" ], [ "y - 5/3", "-1" ], [ "y + 25/6", "0" ], [ "y + 41/6", "-1" ], [ "y**2 + 31*y/6 + 25/9", "0" ], [ "y**2 + 31*y/6 + 203/18", "0" ], [ "y**2 + 358*y/15 + 19801/225", "0" ], [ "y**2 - 203*y/15 - 7751/900", "0" ], [ "y**8 + 62*y**7/3 - 342646*y**6/2925 - 131506681*y**5/35100 - 67297324561*y**4/3290625 - 2168467309253*y**3/78975000 + 94394655040817*y**2/1895400000 + 161064076435621*y/1421550000 + 799655341918027/17058600000", "0" ] ], "degree_bound": 12, "P": [ "2057*y**2/30339 + 63767*y/182034 + 296765447/895607280", "2057*y**2/30339 + 63767*y/182034 + 20927918/55975455", "-2057*y**2/60678 - 10764281*y/74633940 - 9587677/89560728", "384659*y/9951192 + 23464199/298535760", "y**4 + 31*y**3/3 + 1123318904*y**2/31097475 + 36355446571*y/746339400 + 40821792233/1990238400" ], "n_solutions_at_this_exponent": 1, "rate_u_prime_over_u": "0", "rate_partial_fractions": "0", "exponents_note": "search labels; the canonical exponents are the residues of rate_u_prime_over_u (rate_partial_fractions)" }, { "exponents": [ [ "y + 1", "0" ], [ "y - 5/3", "-1" ], [ "y + 25/6", "0" ], [ "y + 41/6", "-1" ], [ "y + 61/30", "-1" ], [ "y**2 + 31*y/6 + 25/9", "0" ], [ "y**2 + 31*y/6 + 203/18", "0" ], [ "y**2 + 358*y/15 + 19801/225", "-3/2" ], [ "y**2 - 203*y/15 - 7751/900", "0" ], [ "y**8 + 62*y**7/3 - 342646*y**6/2925 - 131506681*y**5/35100 - 67297324561*y**4/3290625 - 2168467309253*y**3/78975000 + 94394655040817*y**2/1895400000 + 161064076435621*y/1421550000 + 799655341918027/17058600000", "0" ] ], "degree_bound": 12, "P": [ "2057*y**6/30339 + 56602469*y**5/24877980 + 2986975871*y**4/149267880 + 12657661049*y**3/8396318250 - 47354425510073*y**2/83963182500 - 2163210782548343*y/1259447737500 - 3345455320615507/4534011855000", "2057*y**6/30339 + 4877147*y**5/2073165 + 576620297*y**4/24877980 + 185428945867*y**3/4198159125 - 540307851787*y**2/1554873750 - 147073487167904*y/104953978125 - 10985515638908767/11335029637500", "-2057*y**6/60678 - 7123391*y**5/6219495 - 7546871761*y**4/746339400 + 664013999*y**3/839631825 + 5012534854327*y**2/16792636500 + 57591954695572*y/62972386875 + 2073320657210429/4534011855000", "y**8 + 80002718*y**7/2073165 + 4684430587*y**6/9951192 + 12848863346551*y**5/7463394000 - 727282537228693*y**4/111950910000 - 22727616229175459*y**3/335852730000 - 1167731043094610783*y**2/6297238687500 - 282182710863314533*y/1511337285000 - 2084210494211147567/45340118550000" ], "n_solutions_at_this_exponent": 1, "rate_u_prime_over_u": "(-27000*y**2 - 443925*y - 1085385)/(6750*y**3 + 174825*y**2 + 921600*y + 1207861)", "rate_partial_fractions": "-45*(15*y + 179)/(225*y**2 + 5370*y + 19801) - 30/(30*y + 61)", "exponents_note": "search labels; the canonical exponents are the residues of rate_u_prime_over_u (rate_partial_fractions)" }, { "exponents": [ [ "y + 1", "0" ], [ "y - 5/3", "-1" ], [ "y + 25/6", "0" ], [ "y + 41/6", "-1" ], [ "y**2 + 31*y/6 + 25/9", "0" ], [ "y**2 + 31*y/6 + 203/18", "0" ], [ "y**2 + 358*y/15 + 19801/225", "-1" ], [ "y**2 - 203*y/15 - 7751/900", "0" ], [ "y**4 + 23839*y**3/2460 - 593969*y**2/24600 - 35191943*y/138375 - 82136051/664200", "-1" ], [ "y**8 + 62*y**7/3 - 342646*y**6/2925 - 131506681*y**5/35100 - 67297324561*y**4/3290625 - 2168467309253*y**3/78975000 + 94394655040817*y**2/1895400000 + 161064076435621*y/1421550000 + 799655341918027/17058600000", "0" ] ], "degree_bound": 12, "P": [ "-34969*y**5/39852 - 7728149*y**4/239112 - 769318*y**3/2025 - 235690325651*y**2/134500500 - 5909021720371*y/2017507500 - 561553568059/807003000", "34969*y**5/398520 + 27310789*y**4/11955600 + 190546081*y**3/59778000 - 110555437663*y**2/538002000 - 1508302525609*y/1614006000 - 9001475197/17933400", "y**8 + 119939*y**7/3321 + 153468103*y**6/398520 + 52785020221*y**5/59778000 - 14209086797273*y**4/1793340000 - 5543780988269297*y**3/107600400000 - 35060157025397653*y**2/322801200000 - 28771143526745249*y/322801200000 - 6780924165148021/193680720000" ], "n_solutions_at_this_exponent": 1, "rate_u_prime_over_u": "(-22416750000*y**6 - 713880540000*y**5 - 7104044857500*y**4 - 22253186319300*y**3 + 36048124921680*y**2 + 310784999701500*y + 424443943864020)/(4483350000*y**7 + 169129822500*y**6 + 1950100515000*y**5 + 5613139581525*y**4 - 36878841616680*y**3 - 268968953188242*y**2 - 522026500615080*y - 203296993231375)", "rate_partial_fractions": "-30*(15*y + 179)/(225*y**2 + 5370*y + 19801) - 6*(2214000*y**3 + 16091325*y**2 - 26728605*y - 140767772)/(3321000*y**4 + 32182650*y**3 - 80185815*y**2 - 844606632*y - 410680255) + 6/(6*y + 25)", "exponents_note": "search labels; the canonical exponents are the residues of rate_u_prime_over_u (rate_partial_fractions)" }, { "exponents": [ [ "y + 1", "0" ], [ "y - 5/3", "-1" ], [ "y + 41/6", "-1" ], [ "y**2 + 31*y/6 + 25/9", "0" ], [ "y**2 + 31*y/6 + 203/18", "0" ], [ "y**2 + 358*y/15 + 19801/225", "-1" ], [ "y**2 - 203*y/15 - 7751/900", "-3/2" ], [ "y**3 + 389*y**2/30 + 7984*y/225 + 811/90", "-1" ], [ "y**8 + 62*y**7/3 - 342646*y**6/2925 - 131506681*y**5/35100 - 67297324561*y**4/3290625 - 2168467309253*y**3/78975000 + 94394655040817*y**2/1895400000 + 161064076435621*y/1421550000 + 799655341918027/17058600000", "0" ] ], "degree_bound": 12, "P": [ "10285*y**6/76046 + 318835*y**5/152092 - 115667167*y**4/4562760 - 29174103937*y**3/82129680 - 1201036258169*y**2/1026621000 - 6494032364039*y/6159726000 - 315703322407/1108750680", "y**7 + 217*y**6/12 - 1836854377*y**5/11406900 - 539884972897*y**4/164259360 - 1070189754318503*y**3/61597260000 - 9970495873433093*y**2/246389040000 - 46198664066659631*y/1108750680000 - 92228389124509387/6652504080000" ], "n_solutions_at_this_exponent": 1, "rate_u_prime_over_u": "(-637875000*y**7 - 14084887500*y**6 - 5200301250*y**5 + 1244615155875*y**4 + 7532494561800*y**3 + 16019665095630*y**2 + 13697500603290*y + 3464112917763)/(91125000*y**8 + 2214337500*y**7 - 4631883750*y**6 - 387619144875*y**5 - 2879272566225*y**4 - 8109717090210*y**3 - 9208788254728*y**2 - 4219831151423*y - 622351469305)", "rate_partial_fractions": "-30*(15*y + 179)/(225*y**2 + 5370*y + 19801) - 90*(30*y - 203)/(900*y**2 - 12180*y - 7751) - 2*(675*y**2 + 5835*y + 7984)/(450*y**3 + 5835*y**2 + 15968*y + 4055) + 1/(y + 1)", "exponents_note": "search labels; the canonical exponents are the residues of rate_u_prime_over_u (rate_partial_fractions)" }, { "exponents": [ [ "y - 5/3", "-1" ], [ "y + 41/6", "-1" ], [ "y**2 + 31*y/6 + 25/9", "-1" ], [ "y**2 + 31*y/6 + 203/18", "2" ], [ "y**2 + 358*y/15 + 19801/225", "-1" ], [ "y**2 - 203*y/15 - 7751/900", "-1" ], [ "y**8 + 62*y**7/3 - 342646*y**6/2925 - 131506681*y**5/35100 - 67297324561*y**4/3290625 - 2168467309253*y**3/78975000 + 94394655040817*y**2/1895400000 + 161064076435621*y/1421550000 + 799655341918027/17058600000", "1" ] ], "degree_bound": 0, "P": [ "1" ], "n_solutions_at_this_exponent": 1, "rate_u_prime_over_u": "(80583461712000000000*y**17 + 3538957026852000000000*y**16 + 23949694094771520000000*y**15 - 961359188719143600000000*y**14 - 17249080553731082836800000*y**13 - 37068759397534421419200000*y**12 + 1459459071149998890609964800*y**11 + 16664185357169083047021866400*y**10 + 79836721112225002660157608272*y**9 + 162518576510913552016114756824*y**8 - 77587769940584664318811709832*y**7 - 980295511737772494279778118274*y**6 - 1356460662483848525337164965707*y**5 + 711441417856413444468729615711*y**4 + 3202906278750177520490509242378*y**3 + 2537910999812567872654688027628*y**2 + 665878946794566758051478344073*y + 21529768301048510732648925135)/(20145865428000000000*y**18 + 936782742402000000000*y**17 + 8381854332596880000000*y**16 - 220372971386790960000000*y**15 - 4913038053384769613520000*y**14 - 21781780703119573055640000*y**13 + 320823092715751784321114400*y**12 + 5108360850149302968090116400*y**11 + 32704051440869469524368975968*y**10 + 109925547892295696783415708840*y**9 + 150518054203653990879824998914*y**8 - 236893571854832809789384761459*y**7 - 1287613705901985257682434666004*y**6 - 1720426910852097275676501621915*y**5 + 384757104377160124088573383776*y**4 + 3381638360249353346556776766999*y**3 + 3560007648814659489554153945676*y**2 + 1563898277515440083210052723615*y + 255368665382665802380738067750)", "rate_partial_fractions": "6*(12*y + 31)*(1895400000*y**6 + 29378700000*y**5 - 242420931000*y**4 - 3812096412000*y**3 - 9533713742568*y**2 + 5112554718357*y + 10391230737782)/(17058600000*y**8 + 352544400000*y**7 - 1998311472000*y**6 - 63912246966000*y**5 - 348869330524224*y**4 - 468388938798648*y**3 + 849551895367353*y**2 + 1932768917227452*y + 799655341918027) + 6*(12*y + 31)/(18*y**2 + 93*y + 203) - 3*(12*y + 31)/(18*y**2 + 93*y + 50) - 30*(15*y + 179)/(225*y**2 + 5370*y + 19801) - 60*(30*y - 203)/(900*y**2 - 12180*y - 7751) - 6/(6*y + 41) - 3/(3*y - 5)", "exponents_note": "search labels; the canonical exponents are the residues of rate_u_prime_over_u (rate_partial_fractions)" } ], "search_log": [ { "size": 6, "singular_factors": [ [ "y + 1", 1 ], [ "y - 5/3", 1 ], [ "y + 25/6", 1 ], [ "y + 41/6", 1 ], [ "y**2 + 31*y/6 + 25/9", 1 ], [ "y**2 + 31*y/6 + 203/18", 1 ], [ "y**2 + 358*y/15 + 19801/225", 1 ], [ "y**2 - 203*y/15 - 7751/900", 1 ], [ "y**8 + 62*y**7/3 - 342646*y**6/2925 - 131506681*y**5/35100 - 67297324561*y**4/3290625 - 2168467309253*y**3/78975000 + 94394655040817*y**2/1895400000 + 161064076435621*y/1421550000 + 799655341918027/17058600000", 1 ] ], "pole_order_at_infinity": 3, "fuchsian": false, "candidate_exponents": [ [ "0", "1" ], [ "-1", "0" ], [ "0", "1" ], [ "-1", "0" ], [ "0" ], [ "0", "2" ], [ "-3/2", "0" ], [ "-3/2", "0" ], [ "0", "1" ] ], "infinity_rational_exponents": "irregular at infinity: degree bound NB", "n_combinations": 256, "combinations_tried": 7 }, { "size": 5, "singular_factors": [ [ "y + 1", 1 ], [ "y - 5/3", 1 ], [ "y + 25/6", 1 ], [ "y + 41/6", 1 ], [ "y**2 + 31*y/6 + 25/9", 1 ], [ "y**2 + 31*y/6 + 203/18", 1 ], [ "y**2 + 358*y/15 + 19801/225", 1 ], [ "y**2 - 203*y/15 - 7751/900", 1 ], [ "y**8 + 62*y**7/3 - 342646*y**6/2925 - 131506681*y**5/35100 - 67297324561*y**4/3290625 - 2168467309253*y**3/78975000 + 94394655040817*y**2/1895400000 + 161064076435621*y/1421550000 + 799655341918027/17058600000", 1 ] ], "pole_order_at_infinity": 3, "fuchsian": false, "candidate_exponents": [ [ "0", "1" ], [ "-1", "0" ], [ "0", "1" ], [ "-1", "0" ], [ "0" ], [ "0", "2" ], [ "-3/2", "0" ], [ "-3/2", "0" ], [ "0", "1" ] ], "infinity_rational_exponents": "irregular at infinity: degree bound NB", "n_combinations": 256, "combinations_tried": 7 }, { "size": 4, "singular_factors": [ [ "y + 1", 1 ], [ "y - 5/3", 1 ], [ "y + 25/6", 1 ], [ "y + 41/6", 1 ], [ "y + 61/30", 1 ], [ "y**2 + 31*y/6 + 25/9", 1 ], [ "y**2 + 31*y/6 + 203/18", 1 ], [ "y**2 + 358*y/15 + 19801/225", 1 ], [ "y**2 - 203*y/15 - 7751/900", 1 ], [ "y**8 + 62*y**7/3 - 342646*y**6/2925 - 131506681*y**5/35100 - 67297324561*y**4/3290625 - 2168467309253*y**3/78975000 + 94394655040817*y**2/1895400000 + 161064076435621*y/1421550000 + 799655341918027/17058600000", 1 ] ], "pole_order_at_infinity": 4, "fuchsian": false, "candidate_exponents": [ [ "0", "1" ], [ "-1", "0" ], [ "0", "1" ], [ "-1", "0" ], [ "-1", "0" ], [ "0" ], [ "0", "2" ], [ "-3/2", "0" ], [ "-3/2", "0" ], [ "0", "1" ] ], "infinity_rational_exponents": "irregular at infinity: degree bound NB", "n_combinations": 512, "combinations_tried": 3 }, { "size": 3, "singular_factors": [ [ "y + 1", 1 ], [ "y - 5/3", 1 ], [ "y + 25/6", 1 ], [ "y + 41/6", 1 ], [ "y**2 + 31*y/6 + 25/9", 1 ], [ "y**2 + 31*y/6 + 203/18", 1 ], [ "y**2 + 358*y/15 + 19801/225", 1 ], [ "y**2 - 203*y/15 - 7751/900", 1 ], [ "y**4 + 23839*y**3/2460 - 593969*y**2/24600 - 35191943*y/138375 - 82136051/664200", 1 ], [ "y**8 + 62*y**7/3 - 342646*y**6/2925 - 131506681*y**5/35100 - 67297324561*y**4/3290625 - 2168467309253*y**3/78975000 + 94394655040817*y**2/1895400000 + 161064076435621*y/1421550000 + 799655341918027/17058600000", 1 ] ], "pole_order_at_infinity": 4, "fuchsian": false, "candidate_exponents": [ [ "0", "1" ], [ "-1", "0" ], [ "0", "1" ], [ "-1", "0" ], [ "0" ], [ "0", "2" ], [ "-1", "0" ], [ "-3/2", "0" ], [ "-1", "0" ], [ "0", "1" ] ], "infinity_rational_exponents": "irregular at infinity: degree bound NB", "n_combinations": 512, "combinations_tried": 5 }, { "size": 2, "singular_factors": [ [ "y + 1", 1 ], [ "y - 5/3", 1 ], [ "y + 41/6", 1 ], [ "y**2 + 31*y/6 + 25/9", 1 ], [ "y**2 + 31*y/6 + 203/18", 1 ], [ "y**2 + 358*y/15 + 19801/225", 1 ], [ "y**2 - 203*y/15 - 7751/900", 1 ], [ "y**3 + 389*y**2/30 + 7984*y/225 + 811/90", 1 ], [ "y**8 + 62*y**7/3 - 342646*y**6/2925 - 131506681*y**5/35100 - 67297324561*y**4/3290625 - 2168467309253*y**3/78975000 + 94394655040817*y**2/1895400000 + 161064076435621*y/1421550000 + 799655341918027/17058600000", 1 ] ], "pole_order_at_infinity": 2, "fuchsian": false, "candidate_exponents": [ [ "0", "1" ], [ "-1", "0" ], [ "-1", "0" ], [ "0" ], [ "0", "2" ], [ "-1", "0" ], [ "-3/2", "0" ], [ "-1", "0" ], [ "0", "1" ] ], "infinity_rational_exponents": "irregular at infinity: degree bound NB", "n_combinations": 256, "combinations_tried": 1 }, { "size": 1, "singular_factors": [ [ "y - 5/3", 1 ], [ "y + 41/6", 1 ], [ "y**2 + 31*y/6 + 25/9", 1 ], [ "y**2 + 31*y/6 + 203/18", 1 ], [ "y**2 + 358*y/15 + 19801/225", 1 ], [ "y**2 - 203*y/15 - 7751/900", 1 ], [ "y**8 + 62*y**7/3 - 342646*y**6/2925 - 131506681*y**5/35100 - 67297324561*y**4/3290625 - 2168467309253*y**3/78975000 + 94394655040817*y**2/1895400000 + 161064076435621*y/1421550000 + 799655341918027/17058600000", 1 ] ], "pole_order_at_infinity": 1, "fuchsian": true, "candidate_exponents": [ [ "-1" ], [ "-1" ], [ "-1" ], [ "2" ], [ "-1" ], [ "-1" ], [ "1" ] ], "infinity_rational_exponents": [ "4" ], "n_combinations": 1, "combinations_tried": 1 } ], "wall_s": 152.781, "receipt_wall_s": 164.489, "receipt": { "file": "P2_REDUCIBILITY_s2live_L1_20260910T015629Z.json", "vendored_sha256": "c1101be41ad04ca7c3973af493a43b9ee945d92ea729dff812a6c99107b68bcc", "original_sha256": "a0e2ca3ad58b9627c34ae476b1fdcbe3ec1fd1bb0e3d9b6d0ebd5c545b28bfdb", "where": "vendor_row35_sec481/lines/" } }, "rays": { "P": { "block": { "file": "P2_SEC481_BLOCK_p2live_S_20260910T011946Z.json", "vendored_sha256": "e316f787c2012917e65f139df7c8e854089da5b835b93bb7ba268bfed9345f79", "original_sha256": "9127798a545deb9180b1ba66b35b5b56e1990e02ed3b24abdf203715adae09e1" }, "chain_receipt": { "file": "P2_REDUCIBILITY_p2live_R_20260910T012246Z.json", "vendored_sha256": "1413f2430f9ab7ca8c90c883315c7d4fa2aaab20a3f282f6f8a391a2872367cb", "original_sha256": "1f0966cdba0269534791a289cf217c27eeb73d0b3ed2886034b994274a304964", "verdict": "REDUCIBLE_TO_FIRST_ORDER", "n_factors": 6, "remainder_rank": 0, "wall_s": 72.939 }, "ray": { "name": "P", "s_t_mW2_per_lam": [ "67/8", "-25/9", "13/60" ], "mt2": 1, "mode": "sym", "lam": "lam", "d": "symbolic", "note": "(s,t,mW2) = lam * ray; RAY=P is the ray through the physical point P of the audited external computation (its report_C3.md L70/L149/L496); RAY=E passes through that computation's point E = the served base point (x, y, z) = (17/2, 1/3, 5/3) at lam = 1" } }, "E": { "block": { "file": "P2_SEC481_BLOCK_p2liveE_S_20260910T012441Z.json", "vendored_sha256": "08f55706a9db2ba5c0d51bcfeda4e49230c6522efd7ce758b809f5f8ff724b1b", "original_sha256": "a55fa907ab779fc531ec4cd3a2dee743fd89e601c3e777f89d49d48aec40ff1b" }, "chain_receipt": { "file": "P2_REDUCIBILITY_p2liveE_R_20260910T012556Z.json", "vendored_sha256": "cb6a66b41086c11f97bf80c864cff8b971c5614f93380ec4f5c5be7d15217691", "original_sha256": "ac0fbc4280da4f74ec264bc90ac7920c653b898ccd133e6a89177a40d4c16143", "verdict": "REDUCIBLE_TO_FIRST_ORDER", "n_factors": 6, "remainder_rank": 0, "wall_s": 70.348 }, "ray": { "name": "E", "s_t_mW2_per_lam": [ "-17/2", "-1/3", "-5/3" ], "mt2": 1, "mode": "sym", "lam": "lam", "d": "symbolic", "note": "(s,t,mW2) = lam * ray; RAY=P is the ray through the physical point P of the audited external computation (its report_C3.md L70/L149/L496); RAY=E passes through that computation's point E = the served base point (x, y, z) = (17/2, 1/3, 5/3) at lam = 1" } } }, "controls": { "S_vs_N": { "file": "P2_S_VS_N_p2live_20260910T012100Z.json", "vendored_sha256": "635666269f0cf3ea39f3aec3c47f7d75fe3d151bc177331af4af1754368472e3", "original_sha256": "e8e070407c018a7b69a9762a4e2acbd08ed37a0f2f7c8538005cc00707b9601d", "all_available_pairs_equal": true, "note": "the symbolic ray block (S) against three numeric-kinematics blocks (N1-N3) at lam = 1, 1/4, 4: equal at d = 4 and at generic d" }, "thimble": { "file": "P2_THIMBLE_s2live_TH_20260910T020155Z.json", "vendored_sha256": "ce0bfd36104017248892b47add37690bb91e2753f146b99416b981752b9f2ec4", "original_sha256": "ce0bfd36104017248892b47add37690bb91e2753f146b99416b981752b9f2ec4", "verdict": "OK", "DE_certified_digits": { "y_1o3": 39.37, "y_2o5": 39.29 }, "dps": 40 }, "thimble_vs_chain": { "file": "P2_THIMBLE_VS_CHAIN_s2live_XC_20260910T021554Z.json", "vendored_sha256": "606088a4c09abed1c36d757d87179b88bd09d56ce82accfd4de42a44d80ac0e4", "original_sha256": "bd0fcdc21b7a8037b7789a6bced6fc30ba8edfd613d5274e4bf6a15403c008da", "PASS": true, "thimble_in_chain_solution_space_digits": 39.89, "last_factor_closed_form_digits": 39.04, "planted_fail": { "perturbed_H1": 20.61, "wrong_exponent": 1.61 }, "gauge_upper_triangular_exact": true, "diagonal_equals_chain_rates_exact": true, "note": "the L1 chain receipt is the chain input of this control (the same factors on L2 by the L2 receipt)" }, "built_in_C1_to_C4": "qqww-t4-sec481-chain.py --controls (a planted reducible 3x3 chain; the Legendre companion, irreducible; a half-integer triangular 2x2; Legendre (+) a 1x1 factor)" }, "provenance_scripts": [ { "file": "p2_extract_block.py", "vendored_sha256": "51dea9bba09be5bb3dee610bb36a1360658d12af7bfa8fc1937987c0ae127656", "original_sha256": "c82452c47082748672d76cc3603f77768bf08f8c20124bcd62a9f1bbf93d8ef6", "runnable_from_this_bundle": false }, { "file": "p2_make_config.py", "vendored_sha256": "f470c0f68ab3e84836e793b90a6e40755b2d8dfb9f23bce3ab53cd3b023696cb", "original_sha256": "727099b4d45d18ae70df6b7f81d655fade1f6b3d2686b02169f9df4eef351d7a", "runnable_from_this_bundle": false } ] } }