Established within the stated premises
Native equivariant classes and complete forgetful images
finding:native-reflection-rotation-lift-classes-and-forgetful-images
Exact original field relations give binary ranks20,20,24,30 on40,40,40,48 variables for reflections s=0,1, rotation and joint s=0 marking. Character gauge rank4 gives65536,65536,4096,16384 marked classes. Complete forgetful images in original Gamma moduli have2176,2560,256,64 classes. All168 columns independently checked in original cocycle field action and ranks with SymPy GF2; all forgetful image orbits separately enumerated.
Scope: Complete only in the explicitly fixed native projection and morphism classes. Not all normalizer reflections or primitive physical source/state selection.
Required premises and original source excerpts
- Active purely mathematical marked-seam program
Within the stated mathematical scope, marked pairs, lattice transport systems, reflections, clocks and cohomology are independent mathematical objects. Earlier origin/completion tasks are historical, not active. Distinguish new definitions, derived theorems and optional markings.
premise:marked-seam-pure-mathematical-program - Existing even E8 lattice, Gaussian J and sign lifts
Given existing even unimodular E8 with actual J(x0,x1,...)=(-x1,x0,...) and J²=-I, and the original ordered sign lattice cocycle. Sign automorphisms have kernel Hom(L,F2). Retain original integral ordered basis and generator phases; no enlargement to U1 characters except explicitly defined scalar pushouts.
premise:native-even-e8-gaussian-clock-and-sign-extension - Four ordered punctures with fixed quarter-clock projection
X is CP1 minus ordered(1,i,-1,-i), positive meridians product1, fixed rho(gamma_i)=J. Classify all sign lifts into full preimage Gamma of<J>, modulo simultaneous Gamma conjugation with optional prescribed peripheral conjugacy classes. No mapping-class, puncture permutation or additional spatial reflection-equivariance quotient.
premise:ordered-four-punctures-fixed-quarter-projection - Fixed native spatial reflection and rotation markings
In the original E8 sign lift stratum M_i=D_ci j, additionally mark T=D_t j^s t0 for s=0,1 and/or R=D_r j. T0 is the existing alternating sign isometry. Impose the stated peripheral equivariances and dihedral relation at s=0. Marked morphisms are simultaneous character conjugations with fixed projected operators. Forgetful images use full Gamma conjugacy. No arbitrary normalizer isometries or physical selection.
premise:fixed-native-reflection-rotation-character-markings
- experiments/theory-contracts/seam-equivariant-active-search-20261024/THEOREMS.md, lines 5–104
Source SHA256: 666123fe4881001a342ec762bbe42595033b74a015282f774ef17d05903c5f49
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- experiments/theory-contracts/seam-equivariant-active-search-20261024/results/independent-check.json, lines 1–35
Source SHA256: 6839380a7739725582aa2ad495215717428680150c07292297fe7012e5be84c4
bounded-excerpt · current-at-snapshot