Research · Papers · The quadratic hull and its defects · ML-034
Elimination of stationary additive carry/raw phases with terminal syndrome-only checks
491,040 candidates across 245,520 classes yield rank 74 with 40 independent directions; span indicator(c=s)*{1,u0,...,u9} is 88-dimensional
Published 2026-08-29
For everyone
Plain summary
This study tests a carry-repair method that assigns the same rule at every step and checks only the final total score (the syndrome). An exhaustive audit rules this entire class out. Ten flat c0*c2 phases leave the 24,576-point space of valid configurations completely unchanged. Variants that inspect semantic outputs, vary across positions, combine memory non-additively, use relational choices, or add separate constraints aren't tested here. No prior art is on record.
Result
The audit evaluates 491,040 nonzero candidates across 245,520 quotient classes, yielding rank 74 with 40 independent directions. Ten flat c0*c2 phases leave the 24,576-point quadratic hull unchanged. The direct 88-dimensional span indicator(c=s)*{1,u0,...,u9} covers every candidate increment and exhibits a three-column divergent carry return with zero relative moment. Stationary additive raw/state phases with syndrome-only terminal checking are dead; broader variants remain UNKNOWN.
Setting and definitions
The framework tests stationary additive raw-input/carry-state phases over the family indicator(c=s)*{1,u0,...,u9}, evaluated exclusively by terminal accumulated syndrome. Quadratic hull preservation and relative moment serve as exact rejection screens.
Method
Exhaustive span auditing and a three-column zero-moment holonomy replay prove the result. Raw audit logs and screening receipts are available in this paper's downloadable evidence pack.
Discussion
The elimination applies strictly to stationary additive carry/raw phases with terminal syndrome-only checks. The status of semantic-output-sensitive syndromes, position-dependent or non-additive automata, relational choices, and separate QCS constraints remains UNKNOWN. Corrections: NONE. No prior-art position is recorded.
For everyone — the takeaway
What this means
This closes off carry-repair strategies that track additive increments across steps but check only the final total. Even with an 88-direction span covering every candidate increment, a three-column carry divergence defeats the scheme. A working repair will need position dependence, non-additive tracking, output-aware syndromes, or relational constraints. Other carry constructions remain open.
Register references
- Entry: ML-034
- Receipts: CONT
fleet_a_independent_rank_and_holonomy_audit.json; CONTfleet_a_full_phase_span_holonomy_screen.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 0 of 0 receipt files bundled (1 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.