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Research: sharp 27-deletion boundary for one-sided E8 masked rigidity #1609

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Merged
Mister-Meeseeks merged 1 commit into from
Oct 14, 2026
Merged

Research: sharp 27-deletion boundary for one-sided E8 masked rigidity #1609

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132 changes: 132 additions & 0 deletions research/masked-e8-puncture-threshold/CERTIFICATE.json
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Original file line number Diff line number Diff line change
@@ -0,0 +1,132 @@
{
"census": {
"counts_by_rank": [
1,
63,
1281,
10395,
33411,
36435,
8821
],
"maximum_proper_flat": 36,
"rank6_flats": 8821,
"rank6_size_histogram": {
"10": 5040,
"13": 2016,
"16": 1008,
"21": 666,
"30": 63,
"36": 28
},
"rank6_supports_sha256": "33b3b5d35229e378c2e68c47a8e09cb0d9dce06484902b8b161abb288d0b3863"
},
"first_failure_deletions": 27,
"geometry_sha256": "499909f15616b21ed34b704054685a0c90c244fb81819ba458e076b8dd97308c",
"no_new_kappa": true,
"prime": 65537,
"rank_certificate": "Integer root minors have absolute value at most 4096 by squared row norm eight and Hadamard; 65537 exceeds this bound.",
"rigid_through_deletions": 26,
"schema_version": 1,
"status": "PASS_MASKED_E8_PUNCTURE_THRESHOLD",
"symmetry": {
"checked_root_images": 14400,
"reflections": 120,
"target_orbit": 120
},
"witness": {
"bad_neighbourhood_lines": 37,
"bad_neighbourhood_rank": 7,
"comparator_copy_ranks": [
9,
9,
9,
9,
9,
9,
9,
9
],
"copy_ranks": [
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9
],
"deleted_indices": [
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],
"diagonal_mutation_controls": 1,
"first_residual_three": {
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"source_doubled_root": [
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2,
0,
0,
0,
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],
"source_index": 118
},
"live_ports": 93,
"live_rank": 8,
"masked_error_entries": 0,
"matrix_entries_checked": 8649,
"normal": [
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],
"single_restoration_controls": 27,
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],
"target_index": 119,
"unmasked_error_entries": 56
}
}
222 changes: 222 additions & 0 deletions research/masked-e8-puncture-threshold/INDEPENDENT.json
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Original file line number Diff line number Diff line change
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{
"checker": "independent fundamental-normal Weyl orbits",
"e7": {
"completeness_premise": "standard conjugacy of maximal root-spanned flats to parabolic flats",
"flat_count": 8821,
"flat_sizes": {
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"13": 2016,
"16": 1008,
"21": 666,
"30": 63,
"36": 28
},
"max_flat_size": 36,
"method": "seven rational fundamental-normal Weyl orbits; Bareiss ranks",
"normal_incidence_transcript_sha256": "aa2a1dcf02346931e8f1d6df074c6b41df94ef23907d9cc7c0d8d0baeda1e422",
"orbits": [
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"normal_count": 1008,
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{
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{
"flat_size": 10,
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{
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{
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"seed": [
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},
{
"flat_size": 36,
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"seed": [
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]
},
{
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"rank6_supports_sha256": "33b3b5d35229e378c2e68c47a8e09cb0d9dce06484902b8b161abb288d0b3863"
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"e8_target_orbit_size": 120,
"first_failure_deletions": 27,
"rigidity_through_deletions": 26,
"root_order": "lexicographically sorted sign-positive doubled E8 roots",
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"scope": "finite geometry and explicit masked identity; no supplier or moment improvement",
"witness": {
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"bad_neighborhood_rank": 7,
"bad_neighborhood_size": 37,
"baseline_copy_ranks": [
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"normal": [
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],
"target_index": 119,
"twice_residual_census": {
"-2": 27,
"-6": 1,
"2": 27,
"6": 1
}
}
}
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