RRLS: relations, rewrites & phase / Report

RRLS v0.18 — Algebraic Rank Wall

Superseded05 Sept 2026 · saved

The archived source is available to read.

01 / THE QUESTION

Editorial guide

Does an exact Boolean Nullstellensatz rank over GF(2) give a usable global emptiness test, and can coordinate rotations lower its degree?

02 / WHAT THE RECORD SAYS

Source passage

This is a significant correction to the earlier RRLS intuition. Linear coordinate rotation can reveal sparse formulas such as parity, but it cannot lower this particular algebraic proof-degree invariant.

03 / LIMITS & OPEN POINTS

Source passage

The last item is a resource-capped experiment, not a degree lower-bound proof.

04 / THE NEXT QUESTION

Source passage

The remaining challenge is to find a basis family that adapts as powerfully as RRLS wants without hiding exponential work in basis discovery or basis size.

05 / CHECKS IN THE RECORD

Source passage

The experiment is now directly in the territory of Polynomial Calculus, Nullstellensatz, Gröbner-basis algorithms and Ideal Proof System research.

Read this passage in context →

Previous connections

RRLS v0.17 — The Fiber Occupancy Wallseries order (mechanical)

Following connections

RRLS v0.19 — Adaptive Feature Algebraseries order (mechanical)

Source & provenance

Access: Public
Dates declared in the record: Not recorded
Project basis: Editorial topic association
Origin: d0re research collection (snapshot 1 October 2026)
Original path: /The Theory of Reality/RRLS_v18_ALGEBRAIC_RANK_REPORT.md
Authorship basis: Collection attribution; original record retains its own credits
Title basis: From the source
Date: 05 Sept 2026 · saved
Status basis: r-399db0176f55 replaces the monomial basis that capped here: "In v0.18, PHP 5->4 in the standard Boolean Macaulay hierarchy reached:"
Size: 11,522 bytes
Word count: 1,593 words
SHA-256 of indexed source: 11c0d538ba774a01d6ff002c4119ed0bacdc7cbaabc2516ec3fb121610442978

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RRLS v0.18 — Algebraic Rank Wall
Version 0.18
2026-09-05
d0re research record r-11c0d538ba77
https://www.d0re.com/library/records/r-11c0d538ba77.html
Authorship basis: Collection attribution; original record retains its own credits
Date basis: saved
Source SHA-256: 11c0d538ba774a01d6ff002c4119ed0bacdc7cbaabc2516ec3fb121610442978