Established in scope
Complete pure mapping class quotient with157696 normal forms
In the question: Active mathematical program: marked seam monodromies and lattice lifts
Ordered four J sign lift stratum and pure mapping classes. No puncture permutations, silently frozen reflection marking quotient, or physical origin theorem.
Read the exact result, assumptions and evidence
Result
For N=I+A, N²=0, b_i² adds N(ci+c_(i+1)) to both adjacent characters. The pure mapping class action on original Gamma classes factors faithfully through C2×C2. Burnside and independent enumeration of all2^20 character gauge classes give157696 orbits with original Gamma class size census1:4096,2:46080,4:107520, weighted total526336. Every normal form is saved.
Required assumptions
- 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.
- 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.
- 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.
- Pure Hurwitz quotient of the ordered quarter clock stratum
In addition to original Gamma conjugacy identify ordered four J tuples by pure mapping classes generated by adjacent squared Hurwitz moves b0²,b1², with b_i(x,y)=(xyx^-1,x). No puncture permutations or silently frozen extra reflection marking.
Original evidence
- THEOREMS.md lines 106–151
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/seam-equivariant-active-search-20261024/THEOREMS.md
666123fe4881001a342ec762bbe42595033b74a015282f774ef17d05903c5f49
- pure-mapping-class.json lines 1–33
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/seam-equivariant-active-search-20261024/results/pure-mapping-class.json
7f9d6a0a4e49a359a62bf8bb3557188eed70061ab0fe659db4ac636c7b783f9d
finding:quarter-clock-pure-mapping-class-complete-quotient