files / problems / kissing-5d / compute / q4 / dual_exact.json
{
"bv_self_tests": [
{
"name": "gegenbauer_n5_matches_delsarte",
"ok": true
},
{
"name": "P_k_n_at_1",
"ok": true
},
{
"name": "P2_n4",
"ok": true
},
{
"name": "Q0",
"ok": true
},
{
"name": "Q1",
"ok": true
},
{
"name": "Q_k(u,u,1)=(1-u^2)^k",
"ok": true
},
{
"name": "S0(1,1,1)=J",
"ok": true
},
{
"name": "Sk(1,1,1)=0 for k>=1",
"ok": true
},
{
"name": "S0_d1_entries",
"ok": true
},
{
"name": "p4_half",
"ok": true
},
{
"name": "psd_J",
"ok": true
},
{
"name": "psd_off",
"ok": true
},
{
"name": "psd_diag",
"ok": true
}
],
"delsarte_1point": {
"numerical_deg12": 46.336869215638316,
"rational_den1000_certified": false,
"rational_bound": 46.337,
"comment": "Odlyzko\u2013Sloane continuum number \u224846.34. A 1-point dual cannot go below that, hence cannot exclude 41\u201344."
},
"levenshtein_as_bv": {
"name": "Levenshtein_L5_as_BV",
"bound": "48",
"float_bound": 48.0,
"certified": true,
"unrestricted": true,
"F_k": "zero",
"comment": "F_k=0 reduces BV to Delsarte; L_5(5,1/2)=48",
"excludes": []
},
"diagonal_grid": {
"1": {
"success": false,
"grid_bound": null,
"note": "diagonal F_k on a finite grid; residue until lifted"
},
"2": {
"success": false,
"grid_bound": null,
"note": "diagonal F_k on a finite grid; residue until lifted"
},
"3": {
"success": false,
"grid_bound": null,
"note": "diagonal F_k on a finite grid; residue until lifted"
},
"4": {
"success": true,
"grid_bound": 85.55555555555556,
"note": "diagonal F_k on a finite grid; residue until lifted"
}
},
"slsqp_grid": {
"2": {
"success": false,
"grid_bound": 23.356708617777265,
"message": "Iteration limit reached",
"note": "Cholesky F_k on a subsampled grid; residue"
}
},
"constant_putinar": {
"1": {
"success": false,
"numerical_bound": null,
"certified": null
},
"2": {
"success": false,
"numerical_bound": null,
"certified": null
},
"3": {
"success": false,
"numerical_bound": null,
"certified": null
},
"4": {
"success": false,
"numerical_bound": null,
"certified": null
}
},
"sos_dictionary": {
"5": {
"success": false,
"numerical_bound": null,
"certified": null,
"n_g_blocks": 122
},
"6": {
"success": true,
"numerical_bound": 40.38461538461541,
"certified": null,
"n_g_blocks": 130
}
},
"p4_span": {
"3": {
"system_ok": null,
"reason": "all 34 nonnegative kernel vectors have h not \u2264 0 on I",
"float_bound": null,
"certified": null
},
"4": {
"system_ok": null,
"reason": "all 81 nonnegative kernel vectors have h not \u2264 0 on I",
"float_bound": null,
"certified": null
},
"5": {
"system_ok": null,
"reason": "all 148 nonnegative kernel vectors have h not \u2264 0 on I",
"float_bound": null,
"certified": null
}
},
"putinar_sdp": {
"error": "No module named 'cvxpy'"
},
"rank1_ansatz": {
"tried": 6,
"hits": [
{
"alpha": "0",
"sample_max_g": "0",
"sample_max_g_float": 0.0,
"certified": false,
"note": "rank-1 all-ones F0; sample of D' only, not a theorem"
},
{
"alpha": "1/100",
"sample_max_g": "49/1600",
"sample_max_g_float": 0.030625,
"certified": false,
"note": "rank-1 all-ones F0; sample of D' only, not a theorem"
},
{
"alpha": "1/10",
"sample_max_g": "49/160",
"sample_max_g_float": 0.30625,
"certified": false,
"note": "rank-1 all-ones F0; sample of D' only, not a theorem"
},
{
"alpha": "1/4",
"sample_max_g": "49/64",
"sample_max_g_float": 0.765625,
"certified": false,
"note": "rank-1 all-ones F0; sample of D' only, not a theorem"
},
{
"alpha": "1/2",
"sample_max_g": "49/32",
"sample_max_g_float": 1.53125,
"certified": false,
"note": "rank-1 all-ones F0; sample of D' only, not a theorem"
},
{
"alpha": "1",
"sample_max_g": "49/16",
"sample_max_g_float": 3.0625,
"certified": false,
"note": "rank-1 all-ones F0; sample of D' only, not a theorem"
}
]
},
"lift_attempts": {
"1": {
"certified": false,
"hit": null
},
"2": {
"certified": false,
"hit": null
},
"3": {
"certified": false,
"hit": null
},
"4": {
"certified": false,
"hit": null
}
},
"best_certified_unrestricted": {
"source": "Levenshtein_L5_as_BV",
"bound": "48",
"float_bound": 48.0,
"certified": true,
"unrestricted": true,
"excludes": []
},
"excludes_any_k": [],
"certified_below_44": false,
"comment": "Exact S_k^5 matrices over Q, replayed by q4/bv.py self-tests. 1-point Delsarte is the Odlyzko\u2013Sloane number \u224846.34 and cannot exclude 41\u201344. Tried: constant-multiplier Putinar at d=1..4; diagonal and Cholesky grid duals; exact p4-span kernel at d=3,4,5 (nonnegative kernel vectors exist, none make h\u22640 on I); square dictionary LP at d=5,6 (d=6 numerical 40.38 did not snap to an identity over Q); floating Putinar SDP at d=5 (solver hit the dummy cut 40, grid_ok false). Nothing certified below 44. Mittelmann\u2013Vallentin s_14(5)=44.998\u2026 is the published upper bound and the numerical floor of this hierarchy at degree 14, so a dual <44 would need d>14 or a different hierarchy, and would still need an exact SOS/Putinar certificate."
}