Dihedral quotient pencil with exceptional half-sized fibres
- Model
- gpt-6.1-sol
- Turns
- 13
- Duration
- 5 min
The attempt analyzed dihedral quotient pencils with exceptional half-sized fibres, using exact searches for degrees 64, 128, 256, and 512. Even with square-valued endpoint keys, the best calculated agreement was 139519, below the incumbent of 139775; the gate verified no candidate. The attempt ended without Lean formalization or submission changes, and the result rules out only the modeled profiles.
Lesson for the next attempt. A next attempt on this strategy needs a stronger bound or a different way to reduce the cost of Laurent clearing, since the tested profiles remain below the incumbent even with square-valued endpoint keys.
Ended because: Stopped at its limit.Thought process
+00:00
started on "Dihedral quotient pencil with exceptional half-sized fibres" with GPT 6.1 Sol (medium effort)
+00:02 · 2.0s
turn 1: 1 tool call, 29 output tokens
+00:02 · list_files
listed repo/ProximityPrize/SubmissionUpper (7 entries)
+00:05 · 3.2s
turn 2: 2 tool calls, 88 output tokens
+00:05 · read_file
read repo/ProximityPrize/SubmissionUpper/OrbitPencil.lean lines 1-220
+00:05 · read_file
read repo/ProximityPrize/SubmissionUpper/Solution.lean lines 1-83
+00:12 · 6.8s
turn 3: 1 tool call, 39 output tokens
+00:12 · read_file
read repo/ProximityPrize/SubmissionUpper/OrbitPencil.lean lines 230-474
+00:42 · 29.6s
turn 4: 1 tool call, 1193 output tokens
+02:42 · run_python · 120.1s
run_python: timed out in 120s
+02:53 · 11.0s
turn 5: 1 tool call, 309 output tokens
+02:53 · run_python
run_python: exit 0 in 0s
+03:12 · 18.6s
turn 6: 1 tool call, 695 output tokens
+03:13 · run_python
run_python: exit 0 in 1s
+03:50 · 37.4s
turn 7: 1 tool call, 2118 output tokens
+03:50 · write_file
wrote scratch/dihedral_pencil.py (129 lines)
+03:55 · 4.6s
turn 8: 1 tool call, 154 output tokens
+03:55 · run_python
run_python: exit 1 in 0s
+04:03 · 7.8s
turn 9: 1 tool call, 114 output tokens
+04:03 · edit_file
edited scratch/dihedral_pencil.py
+04:08 · 4.8s
turn 10: 1 tool call, 43 output tokens
+04:09 · run_python · 1.4s
run_python: exit 0 in 1s
+04:52 · 42.7s
turn 11: 1 tool call, 2515 output tokens
+04:52 · write_file
wrote scratch/dihedral_degree_ledger.md (138 lines)
+04:58 · 6.4s
turn 12: 1 tool call, 266 output tokens
+04:58 · note
Dihedral quotient search (d=64,128,256,512), fully charging Laurent clearing, finds no improving profile. With minimal K=274980728111395088 and even square-valued endpoint keys p^r*((p-1)/2)^h, best agreement is 139519 (256 short of 139775). Ledger, exact count/bad-set bounds and Python fibre tests saved in scratch/dihedral_*; promoted files unchanged.
+05:04 · 5.5s
turn 13: 1 tool call, 274 output tokens
+05:04 · give_up
gave up: The specified dihedral pencil profiles do not beat the incumbent. After prescribing r top quotient coefficients and h branch evaluations, quotient degree is t=k-r-h-2; compulsory Laurent clearing X^(d