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Merged
Mister-Meeseeks merged 1 commit into from
Oct 15, 2026
Merged

Research: sharp fixed-port and two-root connector boundaries #2182

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133 changes: 133 additions & 0 deletions research/scalable-dirty-connectors/CENSUS.json
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{
"claim": "With all B and A child calls fixed at physical z0, six bidirectional root shears do not suffice for the universal five-source paired-readout connector; an explicit eight-shear fixed-port word covers all 31 nonzero masks.",
"model": {
"field": "F2",
"sources": 5,
"source_calls": 10,
"source_calls_per_label": 2,
"readout_labels": 31,
"readout_calls_per_label": 2,
"physical_B_port": "z0 for every call",
"physical_A_port": "z0 for every call",
"dirty_roots": 2,
"root_transfers": [
"S01: z0 += z1",
"S10: z1 += z0"
],
"readout_pair_condition": "The two A calls for one output must have the same current dirty-root covector; their source-coefficient difference is the XOR of projected source states at those boundaries."
},
"six_transfer_census": {
"transfers": 6,
"identity_direction_words": 22,
"transfer_placements_per_direction_word": 8008,
"canonical_source_pairings_per_frame": 945,
"full_schedules": 166486320,
"legal_fixed_port_schedules": 34977960,
"maximum_covered_masks_including_zero": 31,
"universal_schedule_found": false,
"coverage_histogram": {
"8": 3872,
"9": 6800,
"10": 96944,
"11": 147136,
"12": 188768,
"13": 519200,
"14": 680400,
"15": 1081536,
"16": 2488152,
"17": 1994240,
"18": 1653088,
"19": 4298968,
"20": 2104216,
"21": 4848184,
"22": 2417920,
"23": 2271608,
"24": 4468720,
"25": 879248,
"26": 2250328,
"27": 297016,
"28": 1960400,
"29": 71600,
"30": 19280,
"31": 230336
},
"best_schedule": {
"directions": [0, 0, 0, 0, 0, 0],
"transfer_slots_zero_based_among_16_events": [0, 1, 2, 3, 4, 5],
"canonical_source_word": [0, 1, 2, 0, 3, 1, 4, 2, 3, 4],
"normalized_source_axes": [1, 1, 1, 1, 1],
"covered_mask_bitset_hex": "ffdfffff",
"missing_mask_decimal": 21
}
},
"eight_transfer_positive_control": {
"transfers": 8,
"directions": [1, 1, 0, 0, 1, 1, 0, 0],
"transfer_slots_zero_based_among_18_events": [0, 2, 3, 5, 8, 10, 11, 13],
"event_word": [
"S10", "B0", "S10", "S01", "B1", "S01", "B2", "B3",
"S10", "B0", "S10", "S01", "B4", "S01", "B3", "B1",
"B4", "B2"
],
"canonical_source_word": [0, 1, 2, 3, 0, 4, 3, 1, 4, 2],
"normalized_source_axes": [3, 1, 1, 1, 1],
"root_product_identity": true,
"every_source_restored": true,
"readout_pair_count": 31,
"readout_call_count": 62,
"boundary_convention": "Boundary 0 is before the first event; boundary k+1 is after event k.",
"readout_pairs": [
{"mask": "00001", "boundaries": [0, 2], "row0": "01"},
{"mask": "00010", "boundaries": [2, 6], "row0": "01"},
{"mask": "00011", "boundaries": [0, 6], "row0": "01"},
{"mask": "00100", "boundaries": [0, 17], "row0": "01"},
{"mask": "00101", "boundaries": [2, 17], "row0": "01"},
{"mask": "00110", "boundaries": [2, 7], "row0": "01"},
{"mask": "00111", "boundaries": [0, 7], "row0": "01"},
{"mask": "01000", "boundaries": [7, 8], "row0": "01"},
{"mask": "01001", "boundaries": [7, 10], "row0": "01"},
{"mask": "01010", "boundaries": [10, 17], "row0": "01"},
{"mask": "01011", "boundaries": [8, 17], "row0": "01"},
{"mask": "01100", "boundaries": [5, 12], "row0": "11"},
{"mask": "01101", "boundaries": [6, 10], "row0": "01"},
{"mask": "01110", "boundaries": [0, 10], "row0": "01"},
{"mask": "01111", "boundaries": [0, 8], "row0": "01"},
{"mask": "10000", "boundaries": [10, 14], "row0": "01"},
{"mask": "10001", "boundaries": [7, 15], "row0": "01"},
{"mask": "10010", "boundaries": [15, 17], "row0": "01"},
{"mask": "10011", "boundaries": [7, 16], "row0": "01"},
{"mask": "10100", "boundaries": [0, 16], "row0": "01"},
{"mask": "10101", "boundaries": [2, 16], "row0": "01"},
{"mask": "10110", "boundaries": [0, 15], "row0": "01"},
{"mask": "10111", "boundaries": [2, 15], "row0": "01"},
{"mask": "11000", "boundaries": [10, 15], "row0": "01"},
{"mask": "11001", "boundaries": [7, 14], "row0": "01"},
{"mask": "11010", "boundaries": [10, 16], "row0": "01"},
{"mask": "11011", "boundaries": [8, 16], "row0": "01"},
{"mask": "11100", "boundaries": [5, 13], "row0": "11"},
{"mask": "11101", "boundaries": [6, 14], "row0": "01"},
{"mask": "11110", "boundaries": [0, 14], "row0": "01"},
{"mask": "11111", "boundaries": [2, 14], "row0": "01"}
],
"engine_control": {
"frame_patterns": 1,
"legal_pairings": 105,
"universal_pairings": 1,
"method": "visit_frame -> pair_calls_by_axis -> evaluate_pair_word -> difference_cover; same engine as six-transfer enumeration",
"exhaustive_eight_transfer_domain": false
},
"budget": {
"source_calls": 10,
"readout_calls": 62,
"total_child_calls": 72,
"paid_full_row_xors": 8,
"saving_vs_PR1887_pinned_schedule": 2,
"relative_transfer_count_reduction": "20%"
}
},
"validation": {
"six_transfer_histogram_source": "Completed exact local census with 22 identity direction words, 8,008 transfer placements, and 945 canonical pairings per frame.",
"eight_transfer_source": "Literal witness replay plus the bounded actual census-engine path on its frame; every source/root restores,all31 equal-covector output pairs validate, and the core engine detects1 universal among105 legal pairings.",
"limits": "The eight-transfer search is a positive control, not an exhaustive eight-transfer census. No upstream submission or remote post is included."
}
}
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