# Atlas

- 2026-09-08 [Verified] mrlygame quests replay outside the engine: following the quest draw order through board, mask, rulebook, score and pivot options with a shift-and-add or FFT count reproduces `mrlygame::quest` cell for cell on seeds 1, 4, 7 and 9 under the default config, the four cheapest quests, each a single attempt at canvas climb 1 without the copy path; the other 60 quests, 37 of them re-attempts, rest on the same draw order and a stepper checked against `next_grid` on 24 random cases. Witness: lab/rs/still-hunt.
- 2026-09-08 [Verified] Over 64 default quests and 4626 frames, 609 pass the ring cut (peak-ring share at least three times a random field share at the same ring, wavelength at most twice the mask side, peak ring at or below half the field): 426 of 1043 basic-path frames, 76 of 92 copy-path frames, 107 of 3491 side-3 frames; 3 of the 64 settled stills pass, all on side-3 masks; the cut also admits envelope peaks, 149 of the 562 hits past generation 0 peaking at ring 1 or 2 of their field, 34 at a wavelength longer than the crop, among them 66 of the 73 copy-path hits, the copy path being one quest whose masks are its own 45-cell canvas on a 64 field; none of the 176 resolved drawn-mask hits sit at ring 1 or 2; the full-square peak leaves the ring cut for a Fourier corner in 376 of 4561 frames. Witness: lab/rs/still-hunt.
- 2026-09-08 [Verified] At canvas cap 512 and mask cap 128, seeds 65 to 68, the copy path yields 40 ring-cut frames of 51 and the one drawn-mask still, seed 66, a copy mask of side 75 on a board of 5 by 5 tiles, peaks at ring 10 of field 512, wavelength 51 cells or 0.68 mask sides, inside the lobe 8 to 13; seed 67 with a copy mask of side 121 on a board of 3 by 3 tiles peaks at the tile fundamental ring 4, one ring below its lobe 5 to 8, in 11 of its 27 hits, at ring 13 in 5 and elsewhere from 8 to 93 in the rest. Witness: lab/rs/still-hunt.
- 2026-09-08 [Proved] Sublattice closure: when every mask offset lies in `dZ^2` and zero is outside birth, every outer-totalistic rule carries a frame `A (x) B` on the `d side` torus to `A' (x) B`, with `A'` one step of the same rule on the `side` torus under the mask divided by `d`, because the count at a cell in position `p` of its tile is `B(p)` times the quotient count and a cell at an empty position reads count zero; verified frame by frame on 16 runs of the mini preset, all 16 rules, the carpet-tile seed at tessellation 3 under its copied-inverted mask of index 9. Witness: lab/rs/life-atlas.
- 2026-09-08 [Verified] On the mini preset, 848 runs on canvas 27 to 64 generations, 103 settled frames (34 distinct up to the dihedral group and torus translation) tested at every torus shift and both cuts 3 and 9: in place 72 are confined to one block of the cut, 4 are full tilings, 1 is the board footprint and the 3 proper cuts are the settled runs of the index-9 sublattice mask, no index-1 frame cutting properly; after a torus shift 6 index-1 frames cut properly, all at cut 9 and tessellation 3, the 16-cell still of the corner seed (four 2x2 blocks at spacing 3, shift `(1, 1)`, outer fill 4) on Moore under B357/S357, B3/S3 and B3/S23 and on the two-bar and cross masks under B3/S23, and the 36-cell still of the two-bar seed on the cross mask under B3/S23 (shift `(1, 0)`, outer fill 6); index-2 and index-3 masks cut properly nowhere. Witness: lab/rs/life-atlas.
- 2026-09-08 [Verified] Mini fate table (dead, still, loop, timeout): number rules 106, 24, 56, 132; design rules 448, 2, 0, 27, the rolls off leaving at most one count of the nine design sequences inside budget 8, the budget of 45 of the 53 mask cells, the other 8 being tessellation-3 copy masks of budgets 26 to 80; B3/S23 31, 17, 4, 1; the 160 timeouts hold no mover, a timeout being a lower bound on the period and never a class. Witness: lab/rs/life-atlas.
- 2026-09-08 [Verified] The median level set of the visit counts cuts properly in 9 of 848 runs in place and 10 after every torus shift, eight of them sublattice-lemma runs and the others the cross-tile heat frame of one index-1 run and the two-bar seed under the cross mask and B3/S23; on the 103 settled runs the proper heat sets coincide with the proper frames, so the heatmap is a design no more often than the frame it summarises. Witness: lab/rs/life-atlas.
- 2026-09-08 [Refuted] The lobe law on the sequence rules of mrlygame: the peak ring sits in the mask first negative lobe in 52 of 176 resolved drawn-mask frames (crop at least four mask sides, generation above 0, 15 chapters of 13 quests, correlated frames); witness seed 3, chapter 1, generation 1, mask side 23, peak ring 11 against lobe 13 to 22; the lobe centre reads 0.64 mask sides at the median while the hits wavelength over mask side fills every quarter bin from 0 to 2, the cut itself; the copy path 35 of 73 is one quest whose lobes sit at rings 2 to 4 of a 64 field, the envelope scale of its 45-cell crop. Witness: lab/rs/still-hunt.
- 2026-09-08 [Refuted] The seed-comb product law: on the 176 resolved frames (15 chapters, comb spacing 1.08 to 5.69 rings, median 5.22, 22 rows on one-tile boards) the peak ring is within half a ring of a comb multiple in 77 against 52.9 by chance, the chance confirmed by a uniform-ring null at 52 and a permutation null at 53, and on both comb and lobe in 22; the 77 counts correlated frames, not independent trials; witness seed 3, chapter 1, generation 1, peak ring 11 against the multiple 10.04 of comb 5.02 and outside lobe 13 to 22. Witness: lab/rs/still-hunt.
- 2026-09-08 [Refuted] That a tessellated seed still peaks on the seed comb: of 21 stills from tessellation 3 on canvas 27 (comb 9), the 5 comb hits are two lattice-mask runs of index 3 and 9 and three four-cell frames of peak share 0.06 on the index-2 corner mask, while every Moore still peaks at ring 1, 4 or 6; the witness is the two-bar seed at tessellation 3 under Moore and B3/S23, still at generation 53, ring 4 against comb 9 and lobe 9. Witness: lab/rs/life-atlas.