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Certify P111/P112 block-rank lower bound nine and exact binary broadcast rate #1744

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Merged
Mister-Meeseeks merged 3 commits into from
Oct 14, 2026
Merged

Certify P111/P112 block-rank lower bound nine and exact binary broadcast rate #1744

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f1b590e
Prove P112 fitting rank nine over all characteristic-two fields
Tuafo Oct 14, 2026
a9ae627
Strengthen P112 certificate to block rank and nonlinear broadcast
Tuafo Oct 14, 2026
7803398
Certify the selected P111 corollary by exact root reflection
Tuafo Oct 14, 2026
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110 changes: 110 additions & 0 deletions research/p112-characteristic-two-minrank/P111-VERIFIED.json
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Original file line number Diff line number Diff line change
@@ -0,0 +1,110 @@
{
"status": "PASS_SELECTED_P111_BLOCK_RANK_AND_BINARY_BROADCAST_9D",
"prototype_sha256": "327d2a868043e846381aa58a33053c24425e8cad522ff401b10ec8af1d649a3f",
"selected_word_sha256": "e3e301e62bc2b41dbf1ceac0acf3d35824ebeab1848c5a2142d4577b109da52f",
"vertices": 111,
"required_zero_unordered_edges": 2870,
"binary_gram_entries": 12321,
"reflection": "negate coordinate 1, using zero-based coordinate indices",
"P112_to_P111_witness_map": {
"2": 12,
"10": 16,
"16": 26,
"32": 38,
"34": 40,
"57": 63,
"68": 69,
"70": 71,
"78": 74,
"84": 84,
"100": 99,
"102": 97,
"108": 107,
"110": 109
},
"cliques": [
[
12,
26,
63,
71,
74,
84,
99,
97
],
[
16,
26,
63,
71,
74,
84,
107,
109
],
[
12,
16,
26,
38,
40,
63,
71,
84
],
[
26,
38,
63,
69,
71,
84,
99,
107
]
],
"odd_incidence": [
40,
69,
97,
109
],
"induced_witness_vertices": 14,
"outside_messages_fixed_for_entropy_argument": 97,
"all_field_block_rank_lower_bound": "9*d for every positive integer d",
"characteristic_two_block_rank_and_binary_broadcast": "exactly 9*d",
"corruption_controls": [
{
"control": "P111 source bytes changed",
"outcome": "REJECTED",
"reason": "source SHA-256"
},
{
"control": "reflection map vertex changed",
"outcome": "REJECTED",
"reason": "coordinate-one sign reflection into selected P111"
},
{
"control": "root norm changed",
"outcome": "REJECTED",
"reason": "integer E8 root coordinates"
},
{
"control": "induced required-zero edge omitted",
"outcome": "REJECTED",
"reason": "exact induced four-isolates-plus-Petersen fitting graph"
},
{
"control": "binary diagonal changed",
"outcome": "REJECTED",
"reason": "nine-coordinate binary labels"
},
{
"control": "binary labels truncated to eight coordinates",
"outcome": "REJECTED",
"reason": "odd binary diagonal"
}
],
"scope": "Finite embedding and upper-bound checks plus the same written Petersen rank/entropy reduction. No new native word, paid supplier saving or multiplication-exponent improvement."
}
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