Datasets:
Formats:
csv
Languages:
English
Size:
< 1K
Tags:
mathematics
information-theory
quantum-information
representation-theory
bosonic-memory
task-relative-compression
File size: 8,809 Bytes
e740887 | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 | {
"project": "ORYNTHRA-H6",
"version": "1.0.0",
"date": "2026-10-09",
"core_scope": "Finite task quotients and phase-registered conserved-spectrum representation implementation",
"not_a_general_file_compressor": true,
"formal_statements_with_supplied_proofs": 19,
"regression_tests": {
"passed": 44,
"total": 44,
"percentage": 100,
"meaning": "Release test pass rate, not correctness probability"
},
"exhaustive_six_label_permutations": {
"checked": 720,
"total": 720
},
"exact_symbolic_gram_identities": 2,
"claims": [
{
"label": "prop:counting",
"number": "3.1",
"type": "proposition",
"title": "No shortening of every finite string",
"proof_status": "Proof supplied in manuscript; not independently or formally certified",
"novelty_status": "Inherited foundation, standard consequence, or candidate combination; see prior-art audit"
},
{
"label": "thm:quotient",
"number": "4.3",
"type": "theorem",
"title": "Minimal future-compatible task quotient",
"proof_status": "Proof supplied in manuscript; not independently or formally certified",
"novelty_status": "Inherited foundation, standard consequence, or candidate combination; see prior-art audit"
},
{
"label": "thm:linear",
"number": "5.1",
"type": "theorem",
"title": "Closure-rank compression",
"proof_status": "Proof supplied in manuscript; not independently or formally certified",
"novelty_status": "Inherited foundation, standard consequence, or candidate combination; see prior-art audit"
},
{
"label": "thm:sixwing",
"number": "6.1",
"type": "theorem",
"title": "Six-wing activation law",
"proof_status": "Proof supplied in manuscript; not independently or formally certified",
"novelty_status": "Inherited foundation, standard consequence, or candidate combination; see prior-art audit"
},
{
"label": "cor:nonsubmod",
"number": "6.2",
"type": "corollary",
"title": "Unbounded failure of submodular budgeting",
"proof_status": "Proof supplied in manuscript; not independently or formally certified",
"novelty_status": "Inherited foundation, standard consequence, or candidate combination; see prior-art audit"
},
{
"label": "prop:storage",
"number": "7.1",
"type": "proposition",
"title": "Storage-only photon cutoff",
"proof_status": "Proof supplied in manuscript; not independently or formally certified",
"novelty_status": "Inherited foundation, standard consequence, or candidate combination; see prior-art audit"
},
{
"label": "thm:packing",
"number": "8.2",
"type": "theorem",
"title": "Spectral branch packing",
"proof_status": "Proof supplied in manuscript; not independently or formally certified",
"novelty_status": "Inherited foundation, standard consequence, or candidate combination; see prior-art audit"
},
{
"label": "cor:onemode",
"number": "8.3",
"type": "corollary",
"title": "The one-mode obstruction",
"proof_status": "Proof supplied in manuscript; not independently or formally certified",
"novelty_status": "Inherited foundation, standard consequence, or candidate combination; see prior-art audit"
},
{
"label": "thm:deficit",
"number": "9.1",
"type": "theorem",
"title": "Exact representation-deficit law",
"proof_status": "Proof supplied in manuscript; not independently or formally certified",
"novelty_status": "Inherited foundation, standard consequence, or candidate combination; see prior-art audit"
},
{
"label": "prop:gap",
"number": "10.1",
"type": "proposition",
"title": "Generator defect bound",
"proof_status": "Proof supplied in manuscript; not independently or formally certified",
"novelty_status": "Inherited foundation, standard consequence, or candidate combination; see prior-art audit"
},
{
"label": "prop:robustone",
"number": "10.2",
"type": "proposition",
"title": "One-mode robust obstruction",
"proof_status": "Proof supplied in manuscript; not independently or formally certified",
"novelty_status": "Inherited foundation, standard consequence, or candidate combination; see prior-art audit"
},
{
"label": "thm:symmetric",
"number": "11.1",
"type": "theorem",
"title": "Full-permutation photon threshold",
"proof_status": "Proof supplied in manuscript; not independently or formally certified",
"novelty_status": "Inherited foundation, standard consequence, or candidate combination; see prior-art audit"
},
{
"label": "prop:simplex",
"number": "12.1",
"type": "proposition",
"title": "Vacuum-complement orthogonality",
"proof_status": "Proof supplied in manuscript; not independently or formally certified",
"novelty_status": "Inherited foundation, standard consequence, or candidate combination; see prior-art audit"
},
{
"label": "cor:unitary",
"number": "13.1",
"type": "corollary",
"title": "Universal finite-dimensional coherent control",
"proof_status": "Proof supplied in manuscript; not independently or formally certified",
"novelty_status": "Inherited foundation, standard consequence, or candidate combination; see prior-art audit"
},
{
"label": "prop:meanstore",
"number": "14.1",
"type": "proposition",
"title": "Minimum uniform storage energy",
"proof_status": "Proof supplied in manuscript; not independently or formally certified",
"novelty_status": "Inherited foundation, standard consequence, or candidate combination; see prior-art audit"
},
{
"label": "prop:weighted",
"number": "14.2",
"type": "proposition",
"title": "Uniform equivariant mean-energy optimum",
"proof_status": "Proof supplied in manuscript; not independently or formally certified",
"novelty_status": "Inherited foundation, standard consequence, or candidate combination; see prior-art audit"
},
{
"label": "prop:query-energy",
"number": "15.1",
"type": "proposition",
"title": "Necessary query-energy bound",
"proof_status": "Proof supplied in manuscript; not independently or formally certified",
"novelty_status": "Inherited foundation, standard consequence, or candidate combination; see prior-art audit"
},
{
"label": "prop:nonresonance",
"number": "16.1",
"type": "proposition",
"title": "Rationally independent frequencies",
"proof_status": "Proof supplied in manuscript; not independently or formally certified",
"novelty_status": "Inherited foundation, standard consequence, or candidate combination; see prior-art audit"
},
{
"label": "prop:gapenergy",
"number": "16.2",
"type": "proposition",
"title": "Energy-gap stability of the commutator obstruction",
"proof_status": "Proof supplied in manuscript; not independently or formally certified",
"novelty_status": "Inherited foundation, standard consequence, or candidate combination; see prior-art audit"
}
],
"candidate_contributions": [
"Task-to-spectrum representation packing workflow",
"Exact optimum 2(1-C/M) for the stated covariance metric",
"Natural-permutation resource frontier and exact deficit plateau",
"Six-wing unbounded high-order activation construction"
],
"physical_assumptions": [
"Degenerate modes for H proportional to total photon number",
"Arbitrary unitaries within invariant photon-number sectors",
"Exact physical group representation for the main deficit theorem",
"Phase-registered logical action, including arbitrary logical superpositions",
"Ideal preparation and readout; external phase reference not charged",
"No uncharged correlated side information in memory bounds"
],
"explicit_negative_results": [
"H6 is not exact arbitrary-state one-photon-loss correcting",
"Number twirling destroys exact H6 label distinguishability",
"A nondegenerate register spectrum excludes exact energy-conserving nonabelian logical action"
],
"global_novelty_verified": false,
"external_peer_review": false,
"proof_assistant_verified": false,
"hardware_validated": false,
"physical_energy_density_record": null,
"proposed_not_delivered": [
"Loss-correcting spectral packing characterization",
"Reference-inclusive optimal code",
"Learned multimodal compression benchmark",
"Restricted optical control synthesis and noisy hardware comparison"
]
}
|