Research · Papers · Direct sums, wedges and the p14 frontier · MF-038
On gate savings under repeated period doubling
Conditional on a verifier-legal p14 fusion, C(2r) ≤ 2 C(r) - Delta_r
Published 2026-08-29
For everyone
Plain summary
This entry proposes a rule for reusing circuit savings across repeated period doublings. Let C(r) be the cost of an r-period instance and Delta_r be the saving from combining two r-period copies. The proposed inequality sets the combined cost at C(2r) <= 2 C(r) - Delta_r. The conjecture is that Delta_r persists or grows through 2-, 4-, and 8-period doublings, opening an amortized path below the register's 20k target.
The claim depends on finding a period-two fusion accepted by the project verifier. The planned test takes two copies of that witness, runs three register checks (period-four hull, defect, and bounded completion screens), and measures Delta_2. The register lists this test protocol but contains no completed fusion, no measured Delta_2, and no proved recurrence. It states no prior-art position.
Result
Conditional on a verifier-legal p14 fusion, the cost satisfies:
C(2r) <= 2 C(r) - Delta_r
The conjecture asserts that Delta_r persists or grows under repeated doubling (r = 2, 4, 8) rather than vanishing, turning an isolated period-two reduction into an amortized descent toward sub-20k.
Setting and definitions
C(r) is the cost of an r-period instance in register notation. Delta_r is the gate saving achieved by fusing two r-period copies. A verifier-legal p14 fusion is a period-two fusion accepted by the verifier specified in the entry. Period doubling denotes the step from period-two to period-four and period-eight constructions.
Method
The protocol requires fully replaying a valid p14 witness, seeding period-four hull/defect and bounded completion screens with two copies of that witness, and measuring Delta_2. The register designates this as the minimal computational test of the conjecture. No period-four run has been completed.
Discussion
The claim rests entirely on the existence of a verifier-legal p14 fusion. It neither demonstrates that witness, supplies a value for Delta_r, nor proves that savings survive at higher periods. A validated recurrence would provide a systematic path to the sub-20k target. Decisive validation requires a replayed p14 witness, execution of the period-four screens, and an empirical measurement of Delta_2.
No correction, retraction, or restoration is recorded for MF-038. No prior-art position is recorded.
For everyone — the takeaway
What this means
The entry asks whether a single optimization trick can be repeated at larger scales. If a valid period-two shortcut exists, two copies can seed a period-four test. If the gate savings hold or increase at each doubling, costs drop predictably toward the sub-20k goal. If the savings collapse after one round, the recursive scaling strategy fails. The register specifies the screening pipeline and receipt but lacks the seed witness, the measured Delta_2, and a mathematical proof.
Register references
- Entry: MF-038
- Receipt:
ZKGOLF-PRO-STATUS-RETURN-2-2026-08-12.md - 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 1 of 1 receipt files bundled (3 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.