From the twin-multi prototype (af742b889, d197507c7), rebased onto twin-gate rule B and cleaned up.
The twin arm takes a list of laws: RefinementReflections::mates per law and mates_from (the converse,
which the GPU gathers the gradient by, as a three-fold is not an involution), one fraction per law,
the twinned amplitude k sqrt(a0 |U(h)|^2 + sum_d a_d |U(T_d h)|^2) on the CPU and the GPU, and the
fraction fit as the same intercept regression with one column per law (a law whose coefficient comes
out negative taken out). RefinementTwinDomains: every coset of find_twin_laws, of any order.
DecideTwin keeps the single-law rung as it was (null at 3 SE, or 2 with the L-test). Where that law
is taken and the lattice has more domains, all of them are refined at once and taken where the added
domains beat their own null (their mates unrelated, the adopted law's kept) by 3 SE, summed per twin
group, each at a fraction of 0.05 or more (domains under it dropped and the rest refined again).
TwinNull generalised from pairs to twin groups: kept adjacent, partners (Laws+1)(k+1) apart; for one
law it is the null it was.
CloseFreeSet, in RefineModel before both arms: every orbit under the domain operators in one set.
An unsplit orbit stays; a split one goes free with the probability of its own free share (a salted
hash of the orbit), so the free fraction is kept - the prototype's majority took a C-centred
pseudo-hexagonal merge's free set from 4020 to 891, an unsalted hash inflated free sets by 60%.
Open arm, against twin-grid on 23 twin/pseudo-symmetric sets (runs twinfix-grid2 / twinfix-multi /
twinfix-multi2): the second rung ran on 9 sets and was taken on one, 9hnc (P2 on a tetragonal metric,
deposited four domains at 0.06 each): domains 0.058/0.058/0.055, z 13.1, R-free 0.2174 -> 0.2063. On
the other 8 the added domains refine to 0.000-0.016 and the single law stands. The closure moves
reflections on 5ebi and the two C222 pseudo-hexagonal sets 6fvz/6fwc (their law, FREE_SET_SPLIT
before, is now tested and refused); 5ebi's R-free 0.347 -> 0.377 on the closed free set. Single-law
sets move by up to 0.003 (the regression and GPU gather round differently), all others <= 0.0002.
Wall time +10-50% on the sets that reach the second rung. 5ebi deposited data (--mode refine): the
closure moves 1 reflection and its strongest law is tested: R-free 0.390 -> 0.364.
Report: REFINE_TWIN_MULTI*, REFINE_TWIN_FREE_CLOSED. Tests: RefinementTwin_domains_gradient,
RefinementTwin_free_set_closed. Docs: §15.12, RUGNUX_REPORT.md, ACKNOWLEDGEMENT.md.
Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01UqXYdL4qBGYRiSXSGXfCLu
leonarski_fandClaude Opus 5.5
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