Padé slack factors instead of monic subset-polynomial collisions
- Model
- gpt-6.1-sol
- Turns
- 11
- Duration
- 3 min
The attempt replaced monic subset-polynomial collisions with degree-one and degree-two Padé slack factors. An exact count showed that the models still have 15 residual top constraints: even before endpoint and collision losses, the available count is short of the required challenges by about 18.315 bits. Newton and low-order complement identities did not yield a structural saving, and no candidate reached the gate. The agent saved a symbolic audit and a Lean-checked conditional quotient bound, IRS degree bound, selected-column agreement, and core agreement; submission files were unchanged.
Lesson for the next attempt. A follow-up needs to prove a family-wide rank identity that saves at least one base-field coordinate, or change the pencil; the checked generic bounds alone do not overcome the 15 residual constraints.
Ended because: gave up: No strictly improved attack was certified. The degree-one/two Padé models retain 15 residual top constraints: monic pairs number C(511,273)*p^d and the actual top key has p^(15+d) values. Even ignoring the endpoint and all collision losses, C(511,273)/p^15 has floor 843420585443, versus 274980728111395088 distinct challenges required; the exact pigeonhole comparison fails by about 18.315 bits. Newton and low-order complement identities supplied no structural saving; this does not exclude a special identity on the restricted root-of-unity family. Numerator multiplicities can further cost factors 274 or 37675. Saved scratch/pade_slack.py, scratch/pade_slack_results.md, and successfully kernel-checked scratch/PadeLocator.lean proving the conditional quotient bound, IRS degree bound, selected-column agreement, and core agreement. Submission files remain unchanged. Next attempt should establish a genuine family-wide rank identity saving a base-field coordinate, or change the pencilThought process
+00:00
started on "Padé slack factors instead of monic subset-polynomial collisions" with GPT 6.1 Sol (medium effort)
+00:03 · 3.0s
turn 1: 1 tool call, 39 output tokens
+00:03 · read_file
read repo/ProximityPrize/SubmissionUpper/OrbitPencil.lean lines 1-230
+00:11 · 8.1s
turn 2: 3 tool calls, 106 output tokens