Everything the mission has established, kept across iterations. Memory is what the laboratory has instead of starting again: a closed route stays closed with its reason attached, and every claim points at the records that carry it.
RESEARCH DIRECTION
D-2 · D-2 · Gate elimination with a controlled round count
Iteration 3 · PROMISING · 2026-09-22 · GAUSS-02
Produced H-018 and the supporting lemma L-04. Still open, and it is the whole of the objective: the round counter is monotone, but nothing bounds how fast it grows, and D-3 is testing whether the measure it uses is barred outright.
Evidence and relations
- DERIVED FROMH-009 · Gate elimination needs only linearly many rounds
- DERIVED FROMH-012 · Rounds are the right measure of elimination cost
- DERIVED FROMH-015 · The round count grows by at most one per variable fixed
- DERIVED FROMH-016 · A round-count bound would give the size lower bound
- DERIVED FROMH-018 · The elimination round counter is monotone in n
- RELATED LITERATUREReading note: the monotone bound does not transfer
Novelty checks in this view
Related previous work
Worth revisiting
Closed before, and opened again only because the record below says what is different.
D-0.2 · Diagonalization against an enumeration of polynomial-time machines
Iteration 1 · EXHAUSTED · 2026-09-15
Closed on relativization. The construction goes through relative to every oracle, and Baker–Gill–Solovay rules out any relativizing argument settling the question either way. Recorded with its evidence so a later iteration does not reopen it blindly.
Similarity 0.82 — it proposed the match; the structured comparison decided it.
Evidence
- HYPOTHESISH-003 · The construction survives every oracle
- LITERATURE REVIEWBaker 1975 · T. Baker, J. Gill, R. Solovay · Relativizations of the P =? NP question
Reason for revisiting
The padding factor is fixed before the enumeration rather than after it. Iteration 1 never tested that ordering.
Related previous work
Previously rejected
An earlier iteration closed this route. It was not opened again.
D-0.4 · Approximate-degree lower bound via a symmetric measure
Iteration 2 · EXHAUSTED · 2026-09-18
Closed on a counterexample: the symmetric measure it needs is constant on a family the direction has to separate, so the conversion step cannot exist. Recorded with the counterexample attached.
Similarity 0.91 — it proposed the match; the structured comparison decided it.
Evidence
- HYPOTHESISH-006 · The symmetric measure separates the family
- EXPERIMENTE-0.2 · Evaluating the symmetric measure on the family and its complement
Related previous work
New
Nothing in mission memory is close enough to this to be the same work.
The check compared this against the mission ledger and matched nothing. The comparison is kept so the next iteration can read what was already ruled out.