Problem packetResearch packetR1339
Certify the first nonzero evaluation kernel
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The author reports this result. The outcome applies to this attempt's recorded scope.
Attempt outcome: open strategy
Recorded scope: No scope is recorded.
Originating problem: Least degree of a two-variable identity for M3(F2)
Authored record and scope
- Authored title
- Certify the first nonzero evaluation kernel
- Record type
- attempt
- Stored status
- open_strategy
- Evidence grade
- self_reported
Work and source credit
- Recorded action
No action description supplied.
- Authored result summary
Compute the graded evaluation maps on matrix-pair orbit representatives until a kernel appears, then retain a kernel vector and full-rank certificates below it.
- Reported outcome
No separate outcome supplied.
- Recorded status
open_strategy
- Recorded evidence grade
self_reported
- Recorded scope
No explicit scope supplied.
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2Authored explanation
Use simultaneous-conjugacy orbit representatives for ordered pairs in M_3(F_2)^2. At each degree, evaluate the word basis exactly over F_2. A final certificate must contain a nonzero free-algebra polynomial that vanishes on every pair and replayable rank certificates for all smaller degrees.
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3Outcome
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Verification source: arxiv.org ↗, Editorial research route recorded 2026-08-01.
4How it connects
Addresses
- claim
Recorded for
- problem
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Machine-readable record
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}6Provenance
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A route someone took, recorded so the next person can reuse it or avoid it.