Skip to content

Research: sharp clean selector encoding width and volume screen #1924

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 3 commits into from
Oct 14, 2026
Merged

Research: sharp clean selector encoding width and volume screen #1924

Show file tree
Hide file tree
Changes from all commits
Commits
Show all changes
3 commits
Select commit Hold shift + click to select a range
7fb68fa
Research: characterize clean selector encoding widths and volume cost
ToikY Oct 14, 2026
16b57b5
Clarify literal host width and unchanged spectator scope
ToikY Oct 14, 2026
0a7c54d
Give the sharp closed residue formula for clean tensor encoding widths
ToikY Oct 14, 2026
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
387 changes: 387 additions & 0 deletions research/clean-selector-embedding/CERTIFICATE.json
View file
Open in desktop
Original file line number Diff line number Diff line change
@@ -0,0 +1,387 @@
{
"status": "PASS_CLEAN_SELECTOR_EMBEDDING",
"no_new_kappa": true,
"scope": "Exact invariant clean-subspace algebra; inherited full-volume tariff screen only",
"multiplicity_oracle_widths": 131,
"width_cases": 4096,
"width_table_sha256": "12873f0c677ad03b12084ccd8272ce8c006caa334c08c262c2512f633ee04637",
"closed_width_formula": {
"fixed_n1_extra1_s_mod8": [
0,
6,
7
],
"fixed_n2_extra1_s_mod8": [
0,
1,
5,
6,
7
],
"fixed_n_at_least3_extra": 1,
"fixed_other_small_cases_extra": 2,
"optional_fourth_root_phase_extra": 1
},
"fixed_width_counts": {
"1": 4032,
"2": 64
},
"optional_phase_width_counts": {
"1": 4096,
"2": 0
},
"fixtures": [
{
"n": 1,
"s": 1,
"d": 4,
"phase": 0,
"ambient_coordinates": 16,
"payload_coordinates": 4,
"volume_ratio": "4",
"mapping": [
0,
1,
15,
2
],
"intertwiner_entries": 64,
"gram_entries": 16
},
{
"n": 1,
"s": 1,
"d": 3,
"phase": 3,
"ambient_coordinates": 8,
"payload_coordinates": 4,
"volume_ratio": "2",
"mapping": [
1,
3,
2,
5
],
"intertwiner_entries": 32,
"gram_entries": 16
},
{
"n": 1,
"s": 2,
"d": 5,
"phase": 0,
"ambient_coordinates": 32,
"payload_coordinates": 8,
"volume_ratio": "4",
"mapping": [
0,
1,
15,
2,
23,
4,
27,
8
],
"intertwiner_entries": 256,
"gram_entries": 64
},
{
"n": 1,
"s": 2,
"d": 4,
"phase": 2,
"ambient_coordinates": 16,
"payload_coordinates": 8,
"volume_ratio": "2",
"mapping": [
3,
7,
5,
11,
6,
13,
9,
14
],
"intertwiner_entries": 128,
"gram_entries": 64
},
{
"n": 2,
"s": 1,
"d": 4,
"phase": 0,
"ambient_coordinates": 16,
"payload_coordinates": 8,
"volume_ratio": "2",
"mapping": [
0,
1,
2,
3,
15,
4,
8,
5
],
"intertwiner_entries": 128,
"gram_entries": 64
},
{
"n": 2,
"s": 1,
"d": 4,
"phase": 0,
"ambient_coordinates": 16,
"payload_coordinates": 8,
"volume_ratio": "2",
"mapping": [
0,
1,
2,
3,
15,
4,
8,
5
],
"intertwiner_entries": 128,
"gram_entries": 64
},
{
"n": 2,
"s": 2,
"d": 6,
"phase": 0,
"ambient_coordinates": 64,
"payload_coordinates": 16,
"volume_ratio": "4",
"mapping": [
0,
1,
2,
3,
15,
4,
8,
5,
23,
16,
31,
6,
27,
32,
47,
9
],
"intertwiner_entries": 1024,
"gram_entries": 256
},
{
"n": 2,
"s": 2,
"d": 5,
"phase": 2,
"ambient_coordinates": 32,
"payload_coordinates": 16,
"volume_ratio": "2",
"mapping": [
3,
7,
11,
0,
5,
13,
14,
15,
6,
19,
21,
23,
9,
22,
25,
27
],
"intertwiner_entries": 512,
"gram_entries": 256
},
{
"n": 3,
"s": 1,
"d": 5,
"phase": 0,
"ambient_coordinates": 32,
"payload_coordinates": 16,
"volume_ratio": "2",
"mapping": [
0,
1,
2,
3,
4,
5,
6,
7,
15,
8,
16,
9,
31,
10,
12,
11
],
"intertwiner_entries": 512,
"gram_entries": 256
},
{
"n": 3,
"s": 1,
"d": 5,
"phase": 0,
"ambient_coordinates": 32,
"payload_coordinates": 16,
"volume_ratio": "2",
"mapping": [
0,
1,
2,
3,
4,
5,
6,
7,
15,
8,
16,
9,
31,
10,
12,
11
],
"intertwiner_entries": 512,
"gram_entries": 256
},
{
"n": 1,
"s": 4,
"d": 7,
"phase": 0,
"ambient_coordinates": 128,
"payload_coordinates": 32,
"volume_ratio": "4",
"mapping": [
0,
1,
15,
2,
23,
4,
27,
8,
29,
16,
30,
31,
39,
32,
43,
47,
45,
55,
46,
59,
51,
61,
53,
62,
54,
64,
57,
79,
58,
87,
60,
91
],
"intertwiner_entries": 4096,
"gram_entries": 1024
},
{
"n": 1,
"s": 4,
"d": 6,
"phase": 2,
"ambient_coordinates": 64,
"payload_coordinates": 32,
"volume_ratio": "2",
"mapping": [
3,
7,
5,
11,
6,
13,
9,
14,
10,
19,
12,
21,
17,
22,
18,
25,
20,
26,
24,
28,
33,
35,
34,
37,
36,
38,
40,
41,
48,
42,
63,
44
],
"intertwiner_entries": 2048,
"gram_entries": 1024
}
],
"controls": [
"insufficient i eigenspace",
"duplicate eigenvector",
"unbilled phase",
"zero payload width",
"no batching",
"dirty complement not restored",
"constant-only smoke test insufficient"
],
"motivating_target_counts": [
16,
16,
0,
0
],
"native_d6_counts": [
16,
12,
16,
20
],
"native_d7_counts": [
36,
28,
28,
36
],
"tariff": "ambient/payload >= 2; B_native/B_lanes = 2^(d-n-s)*(d/n)^sigma > 2 for 0<sigma<1; all encoder costs waived"
}
Loading
Loading