Compute the 5A^4 braid-orbit route in public chunks.
The first implementation target is not a proof of M23 over Q. It is a deterministic public ledger for the smallest concrete Hafner-style unresolved braid-orbit search: fixed class vector (5A, 5A, 5A, 5A), pure braid group B4, and stop bound 30400.
Size of the first public search
- |M23|
- 10,200,960
- |5A|
- 680,064
- 5A centralizer
- 15
- raw (b,c) pairs
- 462,487,044,096
These counts are computed from GAP/CTblLib ATLAS data. The public search fixes the first branch cycle, so the first partition is over ordered pairs (b,c) in 5A x 5A.
What We Need To Compute
- 1Load M23 and the ATLAS conjugacy class 5A.
- 2Fix a representative a in 5A.
- 3Scan an assigned rectangle of ordered indices b,c in 5A.
- 4Set d = (a*b*c)^-1 and keep only d in 5A.
- 5Keep only tuples that generate M23.
- 6For selected generating tuples, compute the inner B4 braid orbit.
- 7Stop the orbit search when it closes or exceeds 30400 states.
- 8Emit hashes, counts, orbit status, logs hash, and scope caveat.
How The Public Work Is Split
The safest first partition is by rectangular chunks in the deterministic GAP ordering of Elements(5A). Each work unit owns a half-open rectangle [bStart,bEnd) x [cStart,cEnd). It can be run independently, reproduced independently, and merged by checking that chunk rectangles do not overlap and eventually cover the registered search domain.
| chunk width | pairs per chunk | chunks to cover 5A x 5A | best for |
|---|---|---|---|
| 100 | 10,000 | 46,248,705 | smoke testing |
| 500 | 250,000 | 1,849,949 | small laptops |
| 1000 | 1,000,000 | 462,488 | public default |
| 2000 | 4,000,000 | 115,622 | fast machines |
| 5000 | 25,000,000 | 18,500 | lab machines |
The default public chunk should be width 1000 only after the worker is benchmarked on ordinary machines. Until then, starter chunks can be much smaller and marked as calibration.
When A Task Is Complete
A chunk is complete when
- Every (b,c) pair in its rectangle is checked.
- Every candidate has d in 5A or is rejected with a deterministic reason.
- Every generating tuple selected for orbit search has status complete or exceeded.
- The packet includes task-card hash, input hash, output hash, script hash, logs hash, environment digest, and runtime.
- Another contributor reproduces the same output hash.
The route is not complete until
- The registered chunk ledger covers the target search domain without gaps or overlaps.
- Closed small orbits, if found, have full invariant tables and independent implementation checks.
- Genus and B4 cycle data are computed for every accepted closed orbit.
- Any proof-level claim passes later rationality, rational-point, rigidity, and descent gates.
- Conflicts and not_run/demo packets are excluded from progress.
What Counts And What Does Not
Counts
A reproduced complete/exceeded packet for an assigned chunk.
Useful but not progress
ChatGPT review notes, code suggestions, scope review, and failed setup reports.
Does not count
Sample packets, not_run packets, unredacted transcripts, unreproduced claims, or sampled-only coverage.