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Merged
Mister-Meeseeks merged 7 commits into from
Oct 16, 2026
Merged

Research: exact star-decoder hierarchies, target budgets, and COPY bounds #669

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d581e77
Prove asymmetric hypercube star obstruction and local puncture threshold
the-missionary-company Oct 13, 2026
308f1e6
Record completed seed-48 sprint result and review link
the-missionary-company Oct 13, 2026
8bcbaaf
Prove global-star rigidity and exact two-target puncture geometry
the-missionary-company Oct 13, 2026
76f007a
Determine complete graph-star hierarchies with independent exact checks
the-missionary-company Oct 13, 2026
7d52602
Prove uniform star-code weight gap and optimal three-target geometry
the-missionary-company Oct 13, 2026
697e4d3
Prove fourth-weight optimizers and weighted copy obstruction
the-missionary-company Oct 13, 2026
8f4600b
Prove fifth weights, exact forest target budgets, and odd native bounds
the-missionary-company Oct 13, 2026
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200 changes: 200 additions & 0 deletions research/asymmetric-hypercube-decoder/BLOCK-RESULTS.json
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Original file line number Diff line number Diff line change
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{
"cases": [
{
"accepted_supports": 4,
"all_accepted_slices_unsigned": true,
"all_codewords_enumerated": true,
"all_rank3_support14_spaces_in_one_block": true,
"allowed_ports": 16,
"codewords": 8,
"constant_weight8_planes": 4,
"geometry": "complementary",
"global_stars": 51,
"k": 3,
"logical_4_plus_4_supports": 4900,
"negative_controls": [
"projected two-point star is not shortened codeword",
"even 4+4 affine slices with varying core rejected"
],
"p": 5,
"ports": 80,
"quadruples_per_block": [
70,
70
],
"rank3_support14_spaces": 0,
"shortened_dimension": 3,
"universal_pair_histogram": {
"1": 4,
"3": 2
},
"weight_eight_words": 6,
"weight_histogram": {
"0": 1,
"8": 6,
"16": 1
}
},
{
"all_codewords_enumerated": true,
"all_rank3_support14_spaces_in_one_block": true,
"allowed_ports": 32,
"codewords": 64,
"constant_weight8_planes": 8,
"fixed_core_per_block_supports": 512,
"geometry": "four_cycle",
"global_stars": 51,
"includes_both_3_4_orientations": true,
"k": 3,
"negative_controls": [
"rank3 constant-weight8 four-cycle passes block parity but fails full code"
],
"p": 5,
"ports": 80,
"rank3_support14_candidates_admitted": 0,
"rank3_support14_spaces": 0,
"shortened_dimension": 6,
"shortened_dimension_histogram": {
"1": 512
},
"universal_pair_histogram": {
"1": 8,
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},
"weight_eight_words": 12,
"weight_histogram": {
"0": 1,
"8": 12,
"16": 38,
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}
},
{
"accepted_supports": 16,
"all_accepted_slices_unsigned": true,
"all_codewords_enumerated": true,
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"allowed_ports": 32,
"codewords": 2048,
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"geometry": "complementary",
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"k": 4,
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"projected two-point star is not shortened codeword",
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],
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1820,
1820
],
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"universal_pair_histogram": {
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},
"weight_eight_words": 76,
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}
},
{
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"geometry": "four_cycle",
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],
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"rank3_support14_spaces": 480,
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"shortened_dimension_histogram": {
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},
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},
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}
},
{
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"geometry": "complementary",
"global_stars": 939,
"k": 5,
"logical_4_plus_4_supports": 1293121600,
"negative_controls": [
"projected two-point star is not shortened codeword",
"even 4+4 affine slices with varying core rejected"
],
"p": 7,
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35960,
35960
],
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},
{
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"fixed_core_per_block_supports": 131072,
"geometry": "four_cycle",
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"k": 5,
"negative_controls": [
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],
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"rank3_support14_candidates_admitted": 0,
"shortened_dimension": 66,
"shortened_dimension_histogram": {
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}
}
],
"scope": "Full-generator complementary-block and four-cycle shortenings for k=3,4,5 at q=2. Full word enumeration only when dimension<=22. Complementary 4+4 candidates use exact syndrome meet-in-the-middle; cycle support candidates have fixed core signs separately in each block. Case counts overlap and are not global distinct-subcode counts.",
"status": "PASS"
}
106 changes: 106 additions & 0 deletions research/asymmetric-hypercube-decoder/BOUNDARY-RESULTS.json
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{
"arithmetic": "exact F2 integer bitsets",
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15,
240,
3840,
61440,
983040,
15728640
],
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"extended_weight_distribution": {
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"16": 15,
"18": 32,
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"4": 6,
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},
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"global_degree_at_most_two_generators": 51,
"global_nonempty_rank": 40,
"global_ports": 80,
"global_rank": 40,
"negative_controls": [
"the graph-only slice space rejects valid shortened words",
"every weight-four E word is a single unsigned block",
"distinct weight-four E words have disjoint supports",
"the k=3 global empty star is already in the nonempty span"
],
"residual_graph_rank": 8,
"residual_graph_words": 256,
"residual_ports": 24,
"scope": "Complete finite linear-space audit of the k=3,p=5 shortening at all five original pairs. Every shortening basis vector is checked; linearity extends containment and quotient agreement to its full span. All residual E words are enumerated. This is not an enumeration of every global codeword or rank-three subcode; the proof in HIGHER-WEIGHTS.md supplies the third-weight conclusion.",
"shortening_cases": [
{
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"avoided_port_count": 32,
"selected_pair": 0,
"shortening_basis_sha256": "583dd87859755b8839ebf64fc4791401708060c93235586b5988cbfc9041da92",
"shortening_rank": 18,
"slice_basis_sha256": "898105a106a456c8756c2cb8bc7933fa9fe95a416908b80d840a559ce6af5a4d",
"slice_projection_ranks": [
10,
10
]
},
{
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"avoided_port_count": 32,
"selected_pair": 1,
"shortening_basis_sha256": "5b799813e6e3005ec41e287b55afabd32e8705df9809ea727a143f9b4fee6423",
"shortening_rank": 18,
"slice_basis_sha256": "935a684e5de50c1ff0328ceacecc2b96b6f9fdfb26afc3cdfc4f617b1a950c3c",
"slice_projection_ranks": [
10,
10
]
},
{
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"avoided_port_count": 32,
"selected_pair": 2,
"shortening_basis_sha256": "61753ecabc8e0aac1482fbc6a4c23f6e7090209940c5056ea138a1875b23b74f",
"shortening_rank": 18,
"slice_basis_sha256": "2ff8a65de9f350a47db24db117a5f9b95e5fa4f0662c187d433406c4f0549066",
"slice_projection_ranks": [
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]
},
{
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"selected_pair": 3,
"shortening_basis_sha256": "c3f2f744b45df7ec5aa26112084c5b7b54000dbbf5ad30e123f286b10ad9b209",
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"slice_basis_sha256": "ffc2f874bea8e4a7d1c2d0e615188cb4b1745c338bab8ce1a9c56a8eff197ab8",
"slice_projection_ranks": [
10,
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]
},
{
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"selected_pair": 4,
"shortening_basis_sha256": "97fc780bf5a73c052c38bc09e5fd48e0d32febd16fab0f77f040fb1b273ad038",
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"slice_basis_sha256": "ae2121fa4c42049fcfdf757fb8d0f870837d32480ee4aa98ce9a6991dd784dd2",
"slice_projection_ranks": [
10,
10
]
}
],
"status": "PASS",
"unsigned_block_rank": 6,
"unsigned_graph_intersection_rank": 4
}
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