Skip to content

Scoped proof: two coordinate swaps need six paid coordinate-CNOT calls (no new kappa) #1414

New issue

Have a question about this project? Sign up for a free GitHub account to open an issue and contact its maintainers and the community.

Sign up for GitHub

By clicking “Sign up for GitHub”, you agree to our terms of service and privacy statement. We’ll occasionally send you account related emails.

Already on GitHub? Sign in to your account

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

Scoped proof: two coordinate swaps need six paid coordinate-CNOT calls (no new kappa) #1414

Show file tree
Hide file tree
Changes from all commits
Commits
Show all changes
1 commit
Select commit
File filter

Filter by extension

Filter by extension
Conversations
Failed to load comments.
Loading
Jump to
Jump to file
Failed to load files.
Loading
Diff view
Diff view
269 changes: 269 additions & 0 deletions research/coordinate-cnot-register-bound/EXPECTED.json
View file
Open in desktop
Original file line number Diff line number Diff line change
@@ -0,0 +1,269 @@
{
"censuses": [
{
"active_targets": 2,
"ball2_sha256": "28080106e83ff37e778fafd6566b5e0bfcbff830f0d7a25dcaff4a80405e03f9",
"ball2_size": 93,
"ball3_sha256": "2ff2b469b406a15c94c8e16c55a6a5a6d79b4199af25c2c48e353170e21f14ba",
"ball3_size": 559,
"direct_six_call_word": [
[
1,
1,
1
],
[
1,
1,
5
],
[
1,
1,
1
],
[
2,
2,
1
],
[
2,
2,
5
],
[
2,
2,
1
]
],
"exact_distance_layers_0_to_3": [
1,
12,
80,
466
],
"independent_dense": {
"directed_transition_attempts": 1116,
"exact_distance_layers_0_to_3": [
1,
12,
80,
466
],
"regular_dimension": 12
},
"intersections_through_five": 0,
"inverse_ball2_times_target_sha256": "3ae2db98c42806bbfa4c3b0b82016c363a4fed9f32fc11d51fb1650f7bd7cc8f",
"minimum_paid_calls": 6,
"paid_generators": 12,
"positive_identity_and_one_swap_minima": [
0,
3
],
"registers": 2,
"restored_dirty_registers": 0,
"scalar_rank_one_idempotents": 6
},
{
"active_targets": 2,
"ball2_sha256": "05521fd538449613da5686c55be67e9d5b1b1996699108ee6a36d4fe16c49f5b",
"ball2_size": 1807,
"ball3_sha256": "20636f0fc14cad71957ddfdbdeea96a9601c2b6db37b5e914788c75b23fabce9",
"ball3_size": 47203,
"direct_six_call_word": [
[
1,
1,
1
],
[
1,
1,
5
],
[
1,
1,
1
],
[
2,
2,
1
],
[
2,
2,
5
],
[
2,
2,
1
]
],
"exact_distance_layers_0_to_3": [
1,
56,
1750,
45396
],
"independent_dense": {
"directed_transition_attempts": 101192,
"exact_distance_layers_0_to_3": [
1,
56,
1750,
45396
],
"regular_dimension": 18
},
"intersections_through_five": 0,
"inverse_ball2_times_target_sha256": "20d752478e73028216184ca610ff5e901d07d7d48cd89b6989a9d3677abeb22f",
"minimum_paid_calls": 6,
"paid_generators": 56,
"positive_identity_and_one_swap_minima": [
0,
3
],
"registers": 3,
"restored_dirty_registers": 1,
"scalar_rank_one_idempotents": 28
}
],
"checked_context_inputs": [
"research/bit-three-register-lower-bound/README.md"
],
"controls": [
"omitted_call_0",
"omitted_call_1",
"omitted_call_2",
"omitted_call_3",
"omitted_call_4",
"omitted_call_5",
"wrong_address_label",
"unrestored_dirty_register",
"clean_only_dirty_leakage",
"nonidentity_scalar_augmentation",
"rank_two_projector_underpricing",
"uncharged_address_alphabet_expansion",
"nonfaithful_natural_representation",
"address_multiplication_order"
],
"format": "coordinate-cnot-register-bound-v1",
"group_permutations": [
[
0,
1,
2
],
[
0,
2,
1
],
[
1,
0,
2
],
[
1,
2,
0
],
[
2,
0,
1
],
[
2,
1,
0
]
],
"labels": {
"a": 1,
"b": 5,
"identity": 0,
"swap": 2
},
"scalar_normalization_checks": {
"conjugations": 4704,
"gl3_matrices": 168,
"rank_one_idempotents": 28
},
"symbolic_proof_checks": {
"four_call_patterns": [
{
"identity": "swap coefficient zero",
"word": "aaaa"
},
{
"identity": "swap coefficient zero",
"word": "aaab"
},
{
"identity": "swap coefficient has a common rank-one exterior factor",
"word": "aaba"
},
{
"identity": "swap coefficient zero",
"word": "aabb"
},
{
"identity": "swap coefficient has a common rank-one exterior factor",
"word": "abaa"
},
{
"identity": "swap plus reverse-pair coefficient is N1 N2",
"word": "abab"
},
{
"identity": "swap coefficient has a common rank-one exterior factor",
"word": "abba"
},
{
"identity": "swap coefficient zero",
"word": "abbb"
},
{
"identity": "swap coefficient zero",
"word": "baaa"
},
{
"identity": "swap coefficient has a common rank-one exterior factor",
"word": "baab"
},
{
"identity": "swap plus reverse-pair coefficient is N1 N2",
"word": "baba"
},
{
"identity": "swap coefficient has a common rank-one exterior factor",
"word": "babb"
},
{
"identity": "swap coefficient zero",
"word": "bbaa"
},
{
"identity": "swap coefficient has a common rank-one exterior factor",
"word": "bbab"
},
{
"identity": "swap coefficient zero",
"word": "bbba"
},
{
"identity": "swap coefficient zero",
"word": "bbbb"
}
],
"sign_homomorphism_products": 36,
"symbolic_label_patterns_through_four": 31
}
}
122 changes: 122 additions & 0 deletions research/coordinate-cnot-register-bound/OVERLAP.json
View file
Open in desktop
Original file line number Diff line number Diff line change
@@ -0,0 +1,122 @@
{
"checked_at": "2026-10-14T00:18:57.227036+00:00",
"mode": "offline complete-pagination snapshots; later changes can be missing",
"entry_coverage": {
"open_prs": {
"fetched_at": "2026-10-14T00:01:47.697042+00:00",
"complete_pagination": true,
"records": 861
},
"discussions": {
"fetched_at": "2026-10-14T00:02:09.289249+00:00",
"complete_pagination": true,
"records": 108
}
},
"final_coverage": {
"open_prs": {
"fetched_at": "2026-10-14T00:12:16.081794+00:00",
"complete_pagination": true,
"records": 864
},
"discussions": {
"fetched_at": "2026-10-14T00:12:33.355089+00:00",
"complete_pagination": true,
"records": 119
}
},
"queries": [
[
"--task",
"bit-new-register-model"
],
[
"--task",
"bit-helper-contract"
],
[
"coordinate CNOT",
"coordinate-CNOT",
"swap target",
"binary-affine-register"
],
[
"--task",
"bit-new-register-model"
],
[
"coordinate CNOT",
"coordinate-CNOT",
"two swaps",
"six-call",
"binary-affine-register"
]
],
"nearest": [
{
"number": 1333,
"title": "Research theorem: exact paid cost for binary affine register words",
"kind": "pr",
"url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1333",
"head": "7f25b6d0e1d7e995d4d2840f231d98b1a1a9fec2",
"updated_at": "2026-10-13T22:57:25Z"
},
{
"number": 1317,
"title": "Binary affine addresses: exact paid-call floor with arbitrary dirty registers",
"kind": "discussion",
"url": "https://github.com/CrocSwap/integer-mult-bounds/discussions/1317",
"updated_at": "2026-10-14T00:06:50Z"
},
{
"number": 720,
"title": "Research theorem: nine-call bound for arbitrary invertible three-register targets",
"kind": "pr",
"url": "https://github.com/CrocSwap/integer-mult-bounds/pull/720",
"head": "a942c0ae1b463710ca535c1fba1b07b6431b5a86",
"updated_at": "2026-10-13T04:45:45Z"
},
{
"number": 1317,
"title": "Binary affine addresses: exact paid-call floor with arbitrary dirty registers",
"kind": "discussion-comment",
"url": "https://github.com/CrocSwap/integer-mult-bounds/discussions/1317#discussioncomment-18911765",
"updated_at": "2026-10-14T00:06:50Z"
},
{
"number": 705,
"title": "Research: determinant obstruction for rank-homogeneous register paths (no kappa)",
"kind": "pr",
"url": "https://github.com/CrocSwap/integer-mult-bounds/pull/705",
"head": "eeb0cd605415a73b792915aaa9185000f293c84a",
"updated_at": "2026-10-13T04:33:58Z"
},
{
"number": 836,
"title": "Research: signed rank transport excludes unitary register mixers (no new kappa)",
"kind": "pr",
"url": "https://github.com/CrocSwap/integer-mult-bounds/pull/836",
"head": "7ae9124f59694bb1e5acf2ae99c65e63c115b2f4",
"updated_at": "2026-10-13T06:52:56Z"
},
{
"number": 800,
"title": "Research: weighted path valuations exclude a remaining eight-call Clifford word (no kappa)",
"kind": "pr",
"url": "https://github.com/CrocSwap/integer-mult-bounds/pull/800",
"head": "d7d83e0a9b98f95a4443d1060336be267ac3fd80",
"updated_at": "2026-10-13T05:53:19Z"
},
{
"number": 680,
"title": "Scoped negative result: certify 33 fixed Clifford register words (no kappa claim)",
"kind": "pr",
"url": "https://github.com/CrocSwap/integer-mult-bounds/pull/680",
"head": "c3a5b6b7afec35d259c29bc2d8bb8516e975ad31",
"updated_at": "2026-10-13T03:49:15Z"
}
],
"novelty_limit": "Titles/bodies, discussions, local top-level notes and ledger only; no exhaustive code-diff search or novelty certificate.",
"scope_difference": "PR1333 prices every affine homogeneous-rank-one address label as one unit, including the swap. This result restricts labels to the two coordinate CNOTs and proves exact cost six for two swaps with any finite number of restored dirty registers. Other listed register results concern rational abelian or Clifford/complex address alphabets.",
"claim_url": "https://github.com/CrocSwap/integer-mult-bounds/discussions/1317#discussioncomment-18911765"
}
Loading