Sparse Sylvester bounds for differential-contact elimination
- Model
- deepseek-v4-pro-0813
- Turns
- 115
- Duration
- 17 min
The attempt explored whether sparse Sylvester bounds could improve the lower-track proof enough to reach score 6816. The gate verified that this score requires radius 331404329/1073741824, corresponding to 80,909 MCA errors and agreement threshold 181,235; the existing proof instead hardcodes 80,899 errors and threshold 181,245 across many files. Those parameters cannot be transferred by monotonicity or domain restriction, and the changed threshold requires regenerated phase-1 coefficient-box and ledger certificates. Sparse Sylvester degree improvements leave those ledger parameters unchanged, so no candidate reached the gate and the attempt stopped before finishing.
Lesson for the next attempt. Before pursuing Sylvester degree reductions, establish that they change the coefficient-box or ledger parameters needed for the target; here the score increase required rebuilding those certificates for a different error and agreement threshold.
Ended because: gave up: Raising score past 6815 is infeasible in this session under the 10 GiB build cap. The only valid 6816 radius is 331404329/1073741824 (MCA errors 80909, agreement threshold 181235); every radius with errors 80899 scores at most 6815. The current proof is 153 files and hardcodes 80899/181245 throughout; the e=80909 theorem is not derivable by monotonicity or domain restriction, because NoLargeSelectedPencil depends only on polynomial identities in the seed set, while the agreement threshold weakens in the opposite direction. In universal_vanishing D=m*a: m=252 gives D=45673740 and m=166 gives D=30086670 for a=181245; for a=181235 the same m requires D'=45671220 and 30085010, so the phase-1 coefficient-box and ledger certificates must be regenerated. ArkLib's proved FRS capacity bound does not apply to this IRS code; the only scalar RS reduction lands outside Johnson, where the available bound is an axiom. Sparse Sylvester degree improvements leave a,D ledger parameters unchangedThought process
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started on "Sparse Sylvester bounds for differential-contact elimination" with DeepSeek V4 Pro (high effort)
+00:08 · 5.4s
turn 1: 2 tool calls, 192 output tokens
+00:08 · list_files
listed repo/ProximityPrize/SubmissionLower (155 entries)
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listed repo/ProximityPrize (168 entries)