Research · Papers · The SHA-256 record and exact synthesis · ML-035
Fixed-interface factor-component contraction on the 22,215-row leader
Fixed-interface factor-component contraction is closed on 22,215-row leader: 20,525 full-rank paths (18,837×(1,1), 1,686×(2,2), 2×(3,3))
Published 2026-08-29
For everyone
Plain summary
We tested whether the 22,215-row leader can be shortened by compressing its individual factor components while leaving their boundary connections untouched. The screen partitioned the leader into 20,525 components. Every component proved to be an open path rather than a closed loop, and an independent crosscheck found each to be full-rank, meaning none contains redundant internal degrees of freedom. The screen cataloged 18,837 components of type (1,1), 1,686 of type (2,2), and 2 of type (3,3), yielding zero cycles and zero contraction candidates. This closes the local fixed-interface route on the leader. It does not rule out multi-component rewrites or strategies that shift interface boundaries. The register lists no prior art for this result.
Result
Fixed-interface factor-component contraction is PROVED closed on the 22,215-row leader. All 20,525 components are paths and full-rank: 18,837×(1,1), 1,686×(2,2), and 2×(3,3). The screen found zero cycles and zero contraction candidates.
Setting and definitions
A fixed interface preserves a component's affine boundary behavior under local contraction. Tuples (1,1), (2,2), and (3,3) specify component dimension classes returned by the factor screen. Full rank refers to the GF(2) linear independence verified during the crosscheck.
Method
The factor-component screen evaluated all 20,525 components across the leader, logging path topology and rank classes with zero cycles and zero contraction candidates. An independent GF(2) rank crosscheck verified the screen's output. Verification receipts are provided in the downloadable evidence pack.
Discussion
This rules out fixed-interface factor contraction on the leader. It establishes no bounds on rewrites that cross component boundaries, alter interface cuts, or operate on unrestricted XAG or multiplicative-complexity circuits. Curation notes show no corrections and no prior-art position. Page verdict: CAVEAT.
For everyone — the takeaway
What this means
This closes off one specific way to compress the leader. If we leave the inputs and outputs of each individual piece exactly as they are, none of the 20,525 pieces has any internal slack to trim. Every piece is an open path with full rank, so shrinking one in isolation won't work. It doesn't mean the leader cannot be shortened at all—only that any working shortcut will have to combine multiple pieces or change how their boundaries are drawn.
Register references
ML-035
Receipts: lens_l2_factor_component_screen_real.json; lens_l2_independent_rank_crosscheck.json.
Prior art: the register does not record this.
Every artifact named above is bundled in, or hashed by, this paper's evidence pack below.
Evidence pack
Everything needed to check this entry against its receipts: the register text, a manifest with a SHA-256 hash for every named receipt, and 2 of 2 receipt files bundled (28 KB). Anything not bundled is still hashed in the manifest and lives in the compute-box working trees.
Changelog
Last reviewed 2026-08-29
- 2026-08-29Published on this site.