FPRD LabShare an approach

WFL residual-row capacity cycle

Date: 2026-07-29
Recovery status: exact source files were lost to automated scratch-workspace maintenance; the final report and deployment provenance survived in the research conversation.

Contents

Strongest result

For structural configuration cc, let Sx(c)S_x(c) count old-dependent effective fibers and Mx(c)M_x(c) count old-controlled sites. Then:

∣Ω∣≤∑c2min⁡{Sx(c),Mx(c)}, |\Omega|\le\sum_c2^{\min\{S_x(c),M_x(c)\}},

and:

H(R)≤H(C)+Emin⁡{Sx(C),Mx(C)}. H(R)\le H(C)+\mathbb E\min\{S_x(C),M_x(C)\}.

For the late-index cumulative-swap query, the response row reconstructs all LL layer bits:

H(C)+Emin⁡{Sx(C),Mx(C)}≥L. H(C)+\mathbb E\min\{S_x(C),M_x(C)\}\ge L.

Hostile-audit correction

The audit refuted the earlier bounded-head bridge. One midpoint fold and four sites compute x1⊕x2x_1\oplus x_2 across arbitrarily large blank padding. Consequently, global Look cannot be charged as one bounded local read. The appropriate charged resource is its old-dependent fiber/site incidence.

Literal-controlled specialization

Restricting the indexed query to parity yields:

S≥2L,M≥(L+1)2L,D≥L+1,F≥⌈log⁡2(L+1)⌉. S\ge2^L,\qquad M\ge(L+1)2^L,\qquad D\ge L+1,\qquad F\ge\left\lceil\log_2(L+1)\right\rceil.

The cycle reported successful checks of the arbitrary-padding XOR construction and the exact parity implicant census.

Comparator and remaining seam

The closest primary comparator identified in the cycle was the Fold-and-Cut/Look model of An, Demaine, Demaine, and Ku, where one Boolean Look evaluates many stack conjunctions in parallel. The answer-matrix viewpoint was compared with Gál and Miltersen.

The exact next attack was to quotient prefixes by equality of all legal future fiber-activation rows and determine whether the quotient is a computable finite right congruence enriched with legal head bonds.

Original filenames

  • fprd-wfl-residual-row-cycle-2026-07-29.md
  • wfl-global-look-charged-access-bridge-2026-07-29.md
  • fprd-wfl-charged-access-hostile-audit-2026-07-29.md
  • check_wfl_cumulative_parity.py
  • check_wfl_global_look_audit.py

Deployment provenance

  • FPRD Lab site version: 11
  • site source commit: ee1272b
  • deployed site: https://fprd-lab.joshgay.chatgpt.site/