Joint-cell bounds with compact Bernstein certificates
- Model
- deepseek-v4-pro-0813
- Turns
- 20
- Duration
- 6 min
The attempt examined whether compact Bernstein certificates for joint-cell bounds could raise the lower-track score from 6815 to 6816 centibits. Exact checks showed that 6816 requires radius numerator 331404329, increasing the error count from 80899 to 80909 and reducing agreements from 181245 to 181235; the existing per-cell bounds therefore do not certify the larger received-list sets. The reducer budget is exactly saturated, and the supplied joint-Bernstein approach had already missed the binding cell at the proposed error count. No candidate reached the gate, and the attempt stopped without regenerating the reduction certificate.
Lesson for the next attempt. Before reusing these certificates for a higher score, identify a strictly stronger bound for the binding cell at the increased error count; the current saturated reducer leaves no slack to compensate elsewhere.
Ended because: Stopped at its limit.Thought process
+00:00
started on "Joint-cell bounds with compact Bernstein certificates" with DeepSeek V4 Pro (high effort)
+00:03 · 1.3s
turn 1: 2 tool calls, 140 output tokens
+00:03 · list_files
listed repo/ProximityPrize/SubmissionLower (155 entries)
+00:03 · list_files
listed repo/ProximityPrize/Benchmark (3 entries)
+00:07 · 3.2s
turn 2: 4 tool calls, 385 output tokens
+00:07 · read_file
read repo/ProximityPrize/SubmissionLower/Solution.lean lines 1-8
+00:07 · read_file
read repo/ProximityPrize/Benchmark/TargetLower.lean lines 1-60
+00:07 · read_file
read repo/ProximityPrize/Benchmark/IRSProfile.lean lines 1-178
+00:07 · list_files
listed scratch (0 entries)
+00:10 · 3.8s
turn 3: 4 tool calls, 364 output tokens
+00:10 · read_file
read [redacted].lean lines 1-7
+00:10 · read_file
read [redacted].lean lines 1-155
+00:10 · read_file
read repo/ProximityPrize/SubmissionLower/score.txt lines 1-2
+00:10 · read_file
read repo/ProximityPrize/SubmissionLower/radius.txt lines 1-2
+00:19 · 8.2s
turn 4: 2 tool calls, 780 output tokens
+00:19 · run_python
run_python: exit 0 in 0s
+00:19 · score_for_claim
score_for_claim 331366399/1073741824: 6815
+00:34 · 15.4s
turn 5: 1 tool call, 898 output tokens
+00:34 · run_python
run_python: exit 0 in 0s
+00:47 · 12.4s
turn 6: 3 tool calls, 1101 output tokens
+00:47 · search
searched repo/ProximityPrize/SubmissionLower for /331366399/: 6 lines
+00:47 · search
searched repo/ProximityPrize/SubmissionLower for /331404329/: no matches
+00:47 · list_files
listed repo/ProximityPrize/SubmissionLower (155 entries)
+00:52 · 4.9s
turn 7: 2 tool calls, 329 output tokens
+00:52 · read_file
read [redacted].lean lines 1-65
+00:52 · read_file
read [redacted]_12.lean lines 590-849
+01:51 · 59.3s
turn 8: 2 tool calls, 5173 output tokens
+01:51 · read_file
read [redacted].lean lines 1-117
+01:51 · read_file
read [redacted].lean lines 1-120
+01:59 · 7.5s
turn 9: 2 tool calls, 696 output tokens
+01:59 · search
searched repo/ProximityPrize/SubmissionLower for /181245/: 291 lines
+01:59 · search
searched repo/ProximityPrize/SubmissionLower for /80899/: 357 lines
+02:12 · 13.2s
turn 10: 1 tool call, 1058 output tokens
+02:12 · run_python
run_python: exit 0 in 0s
+02:39 · 26.8s
turn 11: 2 tool calls, 2022 output tokens
+02:39 · read_file
read repo/ProximityPrize/Benchmark/IRSProfile.lean lines 10-129
+02:39 · read_file
read repo/ProximityPrize/Benchmark/TargetLower.lean lines 1-60
+03:20 · 41.0s
turn 12: 2 tool calls, 3222 output tokens
+03:20 · read_file
read [redacted]_54.lean lines 1-120
+03:20 · read_file
read [redacted].lean lines 1-48
+03:55 · 35.7s
turn 13: 2 tool calls, 1922 output tokens
+03:55 · search
searched repo/ProximityPrize/SubmissionLower for /9659282057/: 2 lines
+03:55 · search
searched repo/ProximityPrize/SubmissionLower for /irs_scalar_finite_list_card_le/: 2 lines
+03:59 · 3.1s
turn 14: 1 tool call, 97 output tokens
+03:59 · read_file
read [redacted]_12.lean lines 480-659
+04:35 · 36.5s
turn 15: 1 tool call, 2616 output tokens
+04:35 · run_python
run_python: exit 0 in 0s
+05:22 · 47.2s
turn 16: 1 tool call, 3110 output tokens
+05:22 · write_file
wrote scratch/lower_6816_analysis.py (69 lines)
+05:26 · 3.3s
turn 17: 1 tool call, 149 output tokens
+05:26 · run_python
run_python: exit 1 in 0s
+05:32 · 6.2s
turn 18: 1 tool call, 503 output tokens
+05:32 · run_python
run_python: exit 0 in 0s
+05:37 · 5.0s
turn 19: 1 tool call, 371 output tokens
+05:37 · note
lower/irs-reduction: 6816 centibits is unreachable without redoing the whole certificate. Proven exactly: 6816 needs P>=331404329 -> errors=floor(P/4096)=80909 (current 80899, +10 errors -> agreements 181245->181235). Budget saturated: mcaBudget+listBudget==floor(|F|/2^128) exactly (zero capacity slack); Lambda term lst=9659282057 is the scalar RS list bound at 181245 agreements. Tree is hardwired to errors=80899 across ~155 files/14MB of generated receipts.
+05:45 · 8.1s
turn 20: 1 tool call, 466 output tokens
+05:45 · give_up
gave up: The 6815 -> 6816 jump requires re-generating the entire reduction certificate, and there is no slack to absorb it. Verified exactly: (1) score 6816 centibits needs radius P/Q >= 331404329/1073741824,