READING PATH
RRLS: from a pattern compressor to a closed P versus NP proof gate
Can a lift–compile–collapse engine find compact exact relations in data, and later in SAT, so that apparent search collapses without hiding exponential work?
The founding note's idea: the right coordinates make a hidden relation short. RRLS tests it on compressors, then on SAT, where a universal collapse would mean P = NP.
Independently checked
Step 1
What was built. Notes of 23 August lift a generator and price bars into relational coordinates; a pasted note of 5 September turns hidden relations into an ANF and GF(2) basis search.
What was found. The PRNG note calls its ingredients established mathematics, with novelty awaiting a benchmark. In the pasted note a 5-term law looked like 595 terms in the wrong basis.
What it opens. The pasted note names the Relational Rotation-Lift Solver (RRLS) and carries its v0.1 code; no later record cites the August notes.
Independently checked
Step 2
What was built. RRLS Studio v0.7–v0.12 (5 September): a persistent relation vocabulary, a cross-domain corpus compiler, a Common Crawl mode, then leakage gates, support-gated predictors and an exact operator market.
What was found. Standard compressors won in v0.10–v0.11, and an earlier ~2x result was discarded as invalid. In v0.12 the transforms added only 0.421% beyond per-block coder selection, needing replication.
What it opens. A change of target: from compression ratio to whether lifting removes search, with a hard proof gate on SAT.
Independently checked
Step 3
What was built. v0.13–v0.14: a SAT engine with exact polynomial lifts (matching, GF(2), 2-SAT, Horn) and a proof gate that stays closed while any branching remains.
What was found. Pigeonhole and parity collapse to one node; random 3-SAT still branches. Local zeroing always works, but gluing frames is the original problem; pairwise projections lose joint structure.
What it opens. A separate audit of the v0.13 source, and the question of which representation could carry boundary relations cheaply.
Independently checked
Step 4
What was built. Alongside the releases: audits of an RRLS attachment and of v0.13's SAT module (a merge defect fixed), then checked CDCL/RUP learning and an exact-cover exclusivity lift.
What was found. A two-relation vocabulary is already NP-complete; the refinement's large speed-ups over v0.13 (about 75-fold on one case) came only from a constructed disguised-Horn family. RUP-only proofs meet Haken's bound, and an order-eight table defeats degree 2.
What it opens. A search for invariants that separate satisfiable from unsatisfiable formulas.
Independently checked
Step 5
What was built. A counterexample-guided invariant catalogue tested on a frozen fresh cohort, then the RE SAT structure laboratory: affine recovery from CNF, a learned route policy and verified relation reuse.
What was found. Opposite-label collisions fell from 290 to one, yet a fresh SAT/UNSAT pair shares the whole fingerprint. OR is no affine projection; solve-plus-check time fell 2.78-fold on one 34-case suite.
What it opens. Nonlinear residual constraints remain the deeper obstacle.
Independently checked
Step 6
What was built. v0.15–v0.20: knowledge-compilation targets, extension naming, reversible lifts, Nullstellensatz rank, feature bases synthesised from clause structure and a structure-by-algebra tractability map.
What was found. Four walls: compact is not tractable; naming relations is analogous to Extended Frege; straightened equations leave fibre emptiness; affine rotations cannot lower refutation degree. Random 3-SAT stays unresolved.
What it opens. Using the string and hair picture to design exact synchronisation operators; releases v0.21–v0.23 are not in the library.
Independently checked
Step 7
What was built. v0.24–v0.26: universal-cycle tomography, a ladder of exact synchronised-collision counters, then a self-audit called the exactness firewall.
What was found. Merging histories with identical futures led v0.25's ladder, but the audit found those counts syntactic: 10,302 residual CNFs collapse to 2 semantic futures. An export bug was fixed.
What it opens. Semantic rather than syntactic futures as the complexity observable.
Independently checked
Step 8
What was built. v0.27 (6 September), a dimensional future compiler that jumps to the next event, then an independent source audit and the v0.27.1 repair.
What was found. v0.27's 97-digit collision tick remains a historical, unreproduced claim. The audit repaired four defects and the impulse formula, and proved a finite prefix cannot certify generators outside a declared class.
What it opens. Adversarial testing of generator discovery; manuscript revision 1.15 records the audit.
Independently checked
Step 9
What was built. v0.28: an adversary forge, generator market, counterexample miner and a proof attacker that treats every branch as a proof failure; the minimised CNF is kept.
What was found. A hard n=40 snapshot had 38,191 residual syntaxes but one semantic future; on one explicit connected 3-CNF family, anchored polynomials need at least 3^m terms; the minimised failure was a budget limit, not a lower bound.
What it opens. Canonicalising residual futures without truth tables.
Independently checked
Step 10
What was built. v0.29–v0.30: direct CNF-to-ROBDD semantic canonicalisation with early FALSE checkpoints, then a dual-phase inversion and sign-gauge quotient.
What was found. ROBDDs recovered the exact semantic classes without truth tables, but compiling them still hit node caps; phase symmetry explained only a fraction of the redundancy.
What it opens. The open target: polynomial semantic canonicalisation, which no release achieves.
Connected questions
- The Theory of Reality: a projection idea that answers for its evidence →
The court audit's outcome frontier inherits RRLS's projection-collision discipline; revision 1.15 records the v0.27 audit, and 1.97 cites 'RRLS Studio 0.27 audited extension 2'. Journey relationship 'Coordinate language'.
Dimensional Reality: Court-Grade Mathematical and Physical Audit · RRLS v0.27 source audit and v0.27.1 repair · Theory of Reality - Reality Bit Engine: Millennium-problem routes with their scope stated →
The RE SAT laboratory and the attachment audit are companions to both lines; the engine's SAT prize lab rejects a false near-satisfaction stopping rule. Journey relationship 'Declared operators'.
Applying the RE engine to the structure inside SAT · RRLS: independent mathematical and computational audit · Reality Bit Engine - Dimensional Chess: what a lift is worth once it must carry a proof →
Both keep the proof gate closed until search is certified: RRLS counts any branching as open, and chess run R1 finds ordering is not the wallbreaker. Journey: 'Relations to bounded proof'.
RRLS v0.13 — P≟NP Proof Search · Dimensional Chess: Initial-Position Mate Frontier R1 - DRCT: when is an observation enough, and what must be added? →
Both synthesise descriptions with exact checks: RRLS lifts relations until residuals close, and DRCT invents morphism classes while stating the prior it still supplies. Journey: 'A language with a cost'.
Relational Rotation-Lift Solver: origin note · DRCT v21 — Morphism Ontology Induction
Where it stands
Editorial guide
v0.30 is the latest release and the P = NP gate stays closed. Edition 02 still lists no P = NP proof among its established results.
The next question. Can a canonical quotient of all live futures be kept current by polynomial local updates for arbitrary CNF, without truth tables, unrestricted branching or exponential order search?
Editorial guide