Schur-product composition with reciprocal challenge parameters
- Model
- deepseek-v4-pro-0813
- Turns
- 56
- Duration
- 17 min
The attempt explored Schur-product composition with reciprocal challenge parameters for the upper track. It confirmed the existing 512-fibre orbit pencil reaches agreement 139775, short of the 139782 needed to beat the best verified score; the natural routes to gain seven more agreements require an additional prescribed top coefficient, which the stated counting bound rules out. A reciprocal identity was verified in a scratch Lean file, but a degree analysis found that nontrivial paired orbit-pencil codewords produce a Schur product above the Reed–Solomon degree budget. No candidate reached the gate, and the attempt ended without a verified improvement.
Lesson for the next attempt. Before extending the 512-fibre pencil, check both the prescribed-coefficient counting bound and the Schur-product degree: the identified routes need an extra coefficient that the bound excludes, while nontrivial paired codewords exceed the degree budget.
Ended because: Stopped at its limit.Thought process
+00:00
started on "Schur-product composition with reciprocal challenge parameters" with DeepSeek V4 Pro (high effort)
+00:16 · 13.4s
turn 1: 4 tool calls, 641 output tokens
+00:16 · list_files
listed repo/ProximityPrize/SubmissionUpper (7 entries)
+00:16 · read_file
read repo/ProximityPrize/SubmissionUpper/Solution.lean lines 1-83
+00:16 · read_file
read repo/ProximityPrize/SubmissionUpper/score.txt lines 1-2
+00:16 · read_file
read repo/ProximityPrize/SubmissionUpper/unsafe-index.txt lines 1-2
+00:19 · 3.2s
turn 2: 4 tool calls, 376 output tokens
+00:19 · read_file
read repo/ProximityPrize/SubmissionUpper/OrbitPencil.lean lines 1-250
+00:19 · read_file
read repo/ProximityPrize/SubmissionUpper/PrescribedTop.lean lines 1-250
+00:19 · read_file
read repo/ProximityPrize/SubmissionUpper/IRSHalfRadius.lean lines 1-212
+00:19 · read_file
read repo/ProximityPrize/SubmissionUpper/HalfRadiusCollision.lean lines 1-250
+00:22 · 3.0s
turn 3: 1 tool call, 215 output tokens
+00:22 · read_file
read repo/ProximityPrize/SubmissionUpper/OrbitPencil.lean lines 250-649
+00:24 · 2.1s
turn 4: 1 tool call, 93 output tokens
+00:24 · read_file
read repo/ProximityPrize/SubmissionUpper/OrbitPencil.lean lines 650-819
+00:27 · 2.9s
turn 5: 4 tool calls, 307 output tokens
+00:27 · score_for_claim
score_for_claim 122368: 11613
+00:27 · score_for_claim
score_for_claim 122360: 11612
+00:27 · score_for_claim
score_for_claim 122350: 11611
+00:27 · score_for_claim
score_for_claim 122369: 11613
+00:32 · 5.0s
turn 6: 1 tool call, 376 output tokens
+00:32 · run_python
run_python: exit 0 in 0s
+00:36 · 3.7s
turn 7: 4 tool calls, 267 output tokens
+00:36 · score_for_claim
score_for_claim 122362: 11612
+00:36 · score_for_claim
score_for_claim 122363: 11613
+00:36 · score_for_claim
score_for_claim 122364: 11613
+00:36 · score_for_claim
score_for_claim 122365: 11613
+00:39 · 3.3s
turn 8: 1 tool call, 239 output tokens
+00:39 · read_file
read repo/ProximityPrize/SubmissionUpper/OrbitPencil.lean lines 1-250
+00:45 · 5.4s
turn 9: 1 tool call, 104 output tokens
+00:45 · read_file
read repo/ProximityPrize/SubmissionUpper/OrbitPencil.lean lines 259-658
+00:47 · 2.2s
turn 10: 1 tool call, 96 output tokens
+00:47 · read_file
read repo/ProximityPrize/SubmissionUpper/OrbitPencil.lean lines 659-819
+01:02 · 15.3s
turn 11: 1 tool call, 2133 output tokens
+01:02 · run_python
run_python: exit 0 in 0s
+01:05 · 2.3s
turn 12: 1 tool call, 192 output tokens
+01:05 · run_python
run_python: exit 1 in 0s
+01:08 · 2.9s
turn 13: 1 tool call, 270 output tokens
+01:08 · run_python
run_python: exit 0 in 0s
+01:25 · 17.7s
turn 14: 1 tool call, 2497 output tokens
+01:25 · read_file
read repo/ProximityPrize/SubmissionUpper/PrescribedTop.lean lines 250-592
+01:28 · 2.4s
turn 15: 1 tool call, 105 output tokens
+01:28 · read_file
read repo/ProximityPrize/SubmissionUpper/PrescribedTop.lean lines 1-250
+01:30 · 2.1s
turn 16: 1 tool call, 100 output tokens
+01:30 · read_file
read repo/ProximityPrize/SubmissionUpper/Solution.lean lines 1-83
+01:39 · 9.0s
turn 17: 1 tool call, 1642 output tokens
+01:39 · run_python
run_python: exit 0 in 0s
+01:57 · 18.6s
turn 18: 1 tool call, 2472 output tokens
+01:57 · run_python
run_python: exit 0 in 0s
+02:02 · 4.3s
turn 19: 1 tool call, 238 output tokens
+02:02 · read_file
read repo/ProximityPrize/SubmissionUpper/OrbitPencil.lean lines 80-259
+02:10 · 8.4s
turn 20: 1 tool call, 161 output tokens
+02:10 · run_python
run_python: exit 0 in 0s
+02:33 · 22.5s
turn 21: 1 tool call, 4452 output tokens
+02:33 · run_python
run_python: exit 0 in 0s
+02:40 · 7.1s
turn 22: 1 tool call, 998 output tokens
+02:40 · run_python
run_python: exit 0 in 0s
+03:26 · 46.1s
turn 23: 1 tool call, 2678 output tokens
+03:26 · run_python
run_python: exit 1 in 0s
+03:30 · 3.5s
turn 24: 1 tool call, 217 output tokens
+05:30 · run_python · 120.1s
run_python: timed out in 120s
+05:36 · 5.7s
turn 25: 1 tool call, 265 output tokens
+05:36 · run_python
run_python: exit 0 in 0s
+06:12 · 35.8s
turn 26: 1 tool call, 1916 output tokens
+06:12 · read_file
read repo/ProximityPrize/SubmissionUpper/PrescribedTop.lean lines 1-120
+06:19 · 7.3s
turn 27: 1 tool call, 278 output tokens
+06:22 · run_python · 3.3s
run_python: exit 0 in 3s
+07:14 · 51.6s
turn 28: 1 tool call, 2204 output tokens
+07:14 · search
search failed for /baseDimension/
+07:16 · 1.7s
turn 29: 1 tool call, 65 output tokens
+07:16 · list_files
listed repo/.lake/packages (21 entries)
+07:21 · 5.7s
turn 30: 1 tool call, 89 output tokens
+07:22 · search
searched repo/.lake/packages/Arklib/ArkLib for /baseDimension/: no matches
+07:23 · 1.5s
turn 31: 1 tool call, 82 output tokens
+07:23 · search
searched repo/.lake/packages for /baseDimension/: no matches
+07:24 · 1.4s
turn 32: 1 tool call, 87 output tokens
+07:24 · search
searched repo/.lake/packages for /IRSProfile/: no matches
+07:27 · 2.3s
turn 33: 1 tool call, 96 output tokens
+07:27 · search
searched repo/ProximityPrize for /IRSProfile/: 249 lines
+07:59 · 32.1s
turn 34: 3 tool calls, 1884 output tokens
+07:59 · score_for_claim
score_for_claim 122640: 11649
+07:59 · score_for_claim
score_for_claim 122639: 11649
+07:59 · score_for_claim
score_for_claim 122638: 11649
+08:06 · 6.7s
turn 35: 1 tool call, 442 output tokens
+08:06 · run_python
run_python: exit 0 in 0s
+10:21 · 135.1s
turn 36: 1 tool call, 7139 output tokens
+10:21 · search
searched repo for /winningSetDensity/: 17 lines
+10:23 · 1.8s
turn 37: 1 tool call, 116 output tokens
+10:23 · read_file
read repo/ProximityPrize/SubmissionUpper/HalfRadiusCollision.lean lines 290-549
+11:55 · 92.4s
turn 38: 1 tool call, 4308 output tokens
+11:55 · read_file
read repo/ProximityPrize/Benchmark/IRSProfile.lean lines 1-120
+12:16 · 20.6s
turn 39: 1 tool call, 1530 output tokens
+12:16 · read_file
read repo/ProximityPrize/SubmissionUpper/HalfRadiusCollision.lean lines 180-299
+12:49 · 32.7s
turn 40: 1 tool call, 1642 output tokens
+12:51 · run_python · 2.2s
run_python: exit 0 in 2s
+13:00 · 9.1s
turn 41: 1 tool call, 440 output tokens
+13:00 · run_python
run_python: exit 0 in 0s
+13:37 · 36.7s
turn 42: 1 tool call, 2113 output tokens
+13:37 · run_python
run_python: exit 0 in 0s
+14:15 · 38.3s
turn 43: 1 tool call, 2491 output tokens
+14:15 · write_file
wrote scratch/SchurDegreeSearch.py (77 lines)
+14:21 · 6.1s
turn 44: 1 tool call, 555 output tokens
+14:21 · write_file
wrote scratch/SchurPencil.lean (43 lines)
+14:23 · 2.1s
turn 45: 1 tool call, 78 output tokens
+14:40 · lean_check · 16.5s
lean_check scratch/SchurPencil.lean: 1 errors in 17s
+14:43 · 2.8s
turn 46: 1 tool call, 185 output tokens
+14:43 · edit_file
edited scratch/SchurPencil.lean
+14:45 · 2.5s
turn 47: 1 tool call, 53 output tokens
+14:50 · lean_check · 4.7s
lean_check scratch/SchurPencil.lean: 1 errors in 5s
+14:58 · 8.0s
turn 48: 1 tool call, 571 output tokens
+14:58 · edit_file
edited scratch/SchurPencil.lean
+15:01 · 3.1s
turn 49: 1 tool call, 53 output tokens
+15:06 · lean_check · 4.7s
lean_check scratch/SchurPencil.lean: 1 errors in 5s
+15:18 · 11.7s
turn 50: 1 tool call, 862 output tokens
+15:18 · edit_file
edited scratch/SchurPencil.lean
+15:19 · 1.2s
turn 51: 1 tool call, 53 output tokens
+15:24 · lean_check · 4.7s
lean_check scratch/SchurPencil.lean: 1 errors in 5s
+15:44 · 20.7s
turn 52: 1 tool call, 1515 output tokens
+15:44 · edit_file
edited scratch/SchurPencil.lean
+15:47 · 2.3s
turn 53: 1 tool call, 53 output tokens
+15:51 · lean_check · 4.7s
lean_check scratch/SchurPencil.lean: ok in 5s
+15:56 · 4.5s
turn 54: 1 tool call, 151 output tokens
+15:56 · note
Schur-product first stage: proved the unrestricted reciprocal identity in scratch/SchurPencil.lean over a Field. Python obstruction: for two nonzero orbit-pencil codewords c_A=R_A Q_A(X^512), c_B=R_B Q_B(X^512), Kγ has top X-degree dA+dB+512(qA+qB), never canceled by the affine parts; any nontrivial paired full pencils puts Kγ strictly above the RS budget.
+16:30 · 33.9s
turn 55: 1 tool call, 1976 output tokens
+16:30 · give_up
give_up: invalid arguments
+16:37 · 6.9s
turn 56: 1 tool call, 471 output tokens
+16:37 · give_up
gave up: No verified candidate below 11613 centibits within budget. 1. Beating the best needs unsafe index <= 122362 (agreement >= 139782), not 122363..122368: score_for_claim shows 122363 still gives 11613.