Research · Papers · The SHA-256 record and exact synthesis · ML-072
Universal screen refutation of the JSC one-catalyst class
For JSC-11, degree-3 evaluation hull accepts a non-honest point, killing all acyclic one-catalyst lifts k ≤ 1.
Published 2026-09-04
For everyone
Plain summary
When designing binary logic circuits, engineers sometimes compute an extra helper product alongside the main circuit to lower the total multiplication count. This technique is called a catalyst lift.
This entry tests whether adding a single helper product can fix a candidate design called the JSC-11 allocation. By running an exact algebraic test called a degree-3 evaluation hull, the check determines if any single-helper setup can tell real computation points apart from false ones. Every possible single-product setup accepts a known invalid point, regardless of the linear inputs chosen. Adding one catalyst multiplication cannot fix this design.
Result
For the JSC-11 allocation in the GF(2) XAG (XOR-free) cost model, the exact degree-3 evaluation hull of the honest computational graph contains a non-honest K00 evaluation point. Every acyclic one-catalyst lift q = A(z) * B(z) followed by graph-valid identity-C CSL rows accepts this false point for all affine forms A and B, refuting all acyclic lifts with k ≤ 1.
Setting and definitions
The target system is the JSC-11 allocation evaluated under the GF(2) XAG cost model. An acyclic one-catalyst lift augments the base variable vector z by appending an auxiliary product q = A(z) * B(z) for affine forms A and B over GF(2), followed by identity-C CSL constraint rows. The degree-3 evaluation hull is the linear span of all monomials of degree at most 3 evaluated across honest execution traces. A non-honest point satisfies local constraint rows while mapping to an incorrect global output.
Method
The algebraic certificate on the degree-3 evaluation hull proceeded as follows:
- Evaluated a linear system of 92,274,688 rows across 862 columns, yielding rank 837 and an exact 25-dimensional nullspace.
- Checked all 33,554,431 nonzero ideal elements per K pair.
- Established that no degree-3 relation separates the non-honest K00 point from the honest manifold, preventing any choice of A(z) and B(z) from eliminating the false point in the augmented CSL system.
Verification artifacts and logs are preserved in RECORD-JSC.md, RECORD-JSC-K2.md, and RECORD-JSC-K2-CLOSE-PROGRESS.log.
Discussion
The certificate establishes an obstruction for JSC-11 at catalyst parameter k ≤ 1: acyclic one-catalyst lifts cannot achieve soundness.
At k = 2, the allocation survives the degree-4 screen through an explicit replay-clean quartic separator. The augmented system still admits a distinct same-input false point per K pair. Over 13 or more refinement iterations, constraints showed zero shrinkage, reintroducing exactly 256 counterexamples at each step.
The conditional totals 17,841 / 16,881 / 15,921 recorded in the run logs are structural diagnostic tallies rather than optimization scores.
For everyone — the takeaway
What this means
A single helper multiplication cannot repair the JSC-11 circuit candidate. Every single-product configuration accepts false outputs as valid. Adding two helper multiplications bypasses the lowest-degree algebraic trap, but that design still generates persistent counterexamples under iterative testing. Making this structure work requires either higher catalyst counts or a different base allocation.
Register references
- ML-072
- RECORD-JSC.md
- RECORD-JSC-K2.md
- RECORD-JSC-K2-CLOSE-PROGRESS.log
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 3 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 2026-09-04
- 2026-09-04Published on this site.