Skip to content

Research exact Q8 three-role target minima #2248

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 15, 2026
Merged

Research exact Q8 three-role target minima #2248

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
368 changes: 368 additions & 0 deletions research/q8-r3-two-central-one-generator-seed809fc39d/CERTIFICATE.json
View file
Open in desktop
Original file line number Diff line number Diff line change
@@ -0,0 +1,368 @@
{
"cost": {
"candidate_gate_mixed": "at most 4 paid calls, saving at least 1/5 of this local word",
"candidate_gate_triple_central": "at most 5 paid calls, saving at least 1/6 of this local word; parity makes an odd saving length impossible, so a saving requires at most 4",
"direct_calls_mixed": 5,
"direct_calls_triple_central": 6,
"selected_kappa_change": false,
"setup_copy_hosting_precision_restoration_supplier_mapping": "zero in this optimistic formal-model screen; must be separately charged for physical adoption"
},
"model": {
"dirty_roles": 3,
"equality": "coefficientwise in full F2[Q8]",
"free_scalar_mixing": "normalized; all 168 GL3 conjugations preserve the 28 idempotents",
"group": "Q8={+/-1,+/-i,+/-j,+/-k}",
"paid_generators": 56,
"paid_labels": [
1,
2
],
"rank_one_idempotents": 28,
"registers": 3,
"x": 1,
"y": 2,
"z": 4
},
"parity_obstructions": {
"diag_z_z_x_or_y": "The x and y coefficient matrices in J/J^2 are E_kk for the one noncentral role and zero for the other label; trace forces odd count of that label and even count of the other, so every realizing word has odd length.",
"diag_z_z_z": "Both first-order coefficient matrices vanish; trace forces even counts of x and y calls, so every realizing word has even length."
},
"schema_version": 1,
"scope": "Six coordinate permutations of diag([z],[z],[x]) or diag([z],[z],[y]), plus diag([z],[z],[z]), in the stated three-register alphabet; no statement for other labels, groups, roles, or longer words.",
"search": {
"known_diag_z_z_e_depth": 4,
"layer_sha256_sorted_9_byte_states": [
"8c6a94754fb4364d433e02bca32367314b62f40c15aad5dd88748e5843715742",
"920b43f241039210191338537e0bd917afdd1d4c6ddbab3e31a16d15642b96cf",
"0403597968f6fb572c65e5da6a3edbd9afc2cec41b518afde02b8d6b78183b9c",
"e3f6671475c4ae9bb909dffea5cb05010c6aa8afbb0b3969d0ee471fbc0611b0",
"e4501b88905298a7098da79c9f11e9a1ed595bf41da4e1a3467a8d7addd9b2c0"
],
"max_depth": 4,
"new_states_by_depth": [
1,
56,
2324,
89574,
3286437
],
"raw_extensions_by_depth": [
0,
56,
3136,
130144,
5016144
],
"raw_words_lengths_0_to_4": 10013305,
"transition_crosschecks": 952
},
"status": "PASS_Q8_EXACT_MIXED_TARGET_FLOORS",
"targets": [
{
"candidate_word": null,
"deletion_controls": 5,
"diagonal": [
1,
4,
4
],
"direct_calls": 5,
"direct_word": [
[
1,
1,
1
],
[
1,
2,
2
],
[
1,
2,
2
],
[
1,
4,
4
],
[
1,
4,
4
]
],
"exact_minimum": 5,
"found_depth": null,
"linear_target_trace_x_mod2": 1,
"linear_target_trace_y_mod2": 0,
"minimum_through_four": true,
"realizing_word_length_mod2": 1
},
{
"candidate_word": null,
"deletion_controls": 5,
"diagonal": [
4,
1,
4
],
"direct_calls": 5,
"direct_word": [
[
1,
1,
1
],
[
1,
1,
1
],
[
1,
2,
2
],
[
1,
4,
4
],
[
1,
4,
4
]
],
"exact_minimum": 5,
"found_depth": null,
"linear_target_trace_x_mod2": 1,
"linear_target_trace_y_mod2": 0,
"minimum_through_four": true,
"realizing_word_length_mod2": 1
},
{
"candidate_word": null,
"deletion_controls": 5,
"diagonal": [
4,
4,
1
],
"direct_calls": 5,
"direct_word": [
[
1,
1,
1
],
[
1,
1,
1
],
[
1,
2,
2
],
[
1,
2,
2
],
[
1,
4,
4
]
],
"exact_minimum": 5,
"found_depth": null,
"linear_target_trace_x_mod2": 1,
"linear_target_trace_y_mod2": 0,
"minimum_through_four": true,
"realizing_word_length_mod2": 1
},
{
"candidate_word": null,
"deletion_controls": 5,
"diagonal": [
2,
4,
4
],
"direct_calls": 5,
"direct_word": [
[
2,
1,
1
],
[
1,
2,
2
],
[
1,
2,
2
],
[
1,
4,
4
],
[
1,
4,
4
]
],
"exact_minimum": 5,
"found_depth": null,
"linear_target_trace_x_mod2": 0,
"linear_target_trace_y_mod2": 1,
"minimum_through_four": true,
"realizing_word_length_mod2": 1
},
{
"candidate_word": null,
"deletion_controls": 5,
"diagonal": [
4,
2,
4
],
"direct_calls": 5,
"direct_word": [
[
1,
1,
1
],
[
1,
1,
1
],
[
2,
2,
2
],
[
1,
4,
4
],
[
1,
4,
4
]
],
"exact_minimum": 5,
"found_depth": null,
"linear_target_trace_x_mod2": 0,
"linear_target_trace_y_mod2": 1,
"minimum_through_four": true,
"realizing_word_length_mod2": 1
},
{
"candidate_word": null,
"deletion_controls": 5,
"diagonal": [
4,
4,
2
],
"direct_calls": 5,
"direct_word": [
[
1,
1,
1
],
[
1,
1,
1
],
[
1,
2,
2
],
[
1,
2,
2
],
[
2,
4,
4
]
],
"exact_minimum": 5,
"found_depth": null,
"linear_target_trace_x_mod2": 0,
"linear_target_trace_y_mod2": 1,
"minimum_through_four": true,
"realizing_word_length_mod2": 1
},
{
"candidate_word": null,
"deletion_controls": 6,
"diagonal": [
4,
4,
4
],
"direct_calls": 6,
"direct_word": [
[
1,
1,
1
],
[
1,
1,
1
],
[
1,
2,
2
],
[
1,
2,
2
],
[
1,
4,
4
],
[
1,
4,
4
]
],
"exact_minimum": 6,
"found_depth": null,
"linear_target_trace_x_mod2": 0,
"linear_target_trace_y_mod2": 0,
"minimum_through_four": true,
"realizing_word_length_mod2": 0
}
]
}
Loading
Loading