Established in scope
Circle-fixing base reflection does not fix entire cubic cable seam pointwise
In the question: Automated construction of operator maps and sources
Only literal pointwise fixed-locus identification on actual C and specified circle map excluded. Sheet-permuting reflection,different original cut or reflected-source transport remain possible. Retain valid q/p point map,spin formula and previous open-source reflection. No global P1 impossibility or ban of geometric doubles. Choosingπ*|dz|² is not forced by canonical spin-line identity. the reviewed source global G calibration question now solved by explicit G,not another gap. Orbit fact doesnot introduce artificialnew physicalchoice:iforiginalQuarterisSeedmorphism,thetwo representativescanbeequivalent. Must checkactualsidemarks. For explicitpointmapσk fiberisU^k;oppositeU^-kframeidentity remainsvalidunderpropercontravariantconvention.
Read the exact result, assumptions and evidence
Result
Actual lift τ_C(w,η)=(−barw,barη) of z→1/barz is antiinvolution,sendingq_a→p_-a,but does not fix wholeπ^-1(|z|=1). Exact regular fiber:z=e^(iπ/4),η=√2,w=(√3+i)/2,(−√3+i)/2,−i. First two are exchanged,only third fixed. Each other global cubic deck liftc^kτ_C likewise fixes only one of three. Literal identification Fixτ_C=entire cable seam fails away from every vertex. Valid half-form relationJτ√dz=±iz^-1√dz determines spin transition in specified reflected inner/outer frame,not original physical Γ± normal-frame identification. Complete marked-circle class:16Mobius/antiMobius sphere mapsi^kz,i^k/z,i^kbarz,i^k/barz give8D4circle actions. Amongq-compatibleanti-cuts,σ1=ibarz ANDσ3=−ibarz avoidmarks and areQ-conjugate. Data giveone mark-freeorbit,not absolute representative. Spinξanti-frame phase is not a newlinearΓ±clutch proof.
Required assumptions
- Recovered genus2 cover with retained coefficients
Retain exactly the older three-sheet cover C:w³=(z²-1)/(z²+1), eta=z(1-w³), eta²=1-w⁶, six Weierstrass points p_a=omega^a,q_a=-omega^a, given z base and clock markings. Seek actual flat coefficient lines for existing v117 monodromy, not mere permutation equivalence or an assumed field intertwiner.
- Do not identify source types
Observable algebra, OS reflection, state, collar operator, time evolution, carrier connection, family holonomy, and readout are distinct data until an original map relates them.
Original evidence
- CLAUDE27-DECK-FIRST-TEST.txt lines 1–64
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/tfpt-unified-source-derivation-20261029/aps_source_review/CLAUDE27-DECK-FIRST-TEST.txt
1b0866e9de6957e97e2598086bb897af312da0b3f5fb772a17e2c0f6abdd99f9
- 004-subsection-auch-die-skalen-besitzen-einen-gemeinsamen-va.tex lines 276–290
Source checked at this snapshot
Original location and fingerprint
documents/tfpt_explorer--docs--session-2026-09-28--TFPT_Gesamtsynthese_2026-09-28/sections/004-subsection-auch-die-skalen-besitzen-einen-gemeinsamen-va.tex
574058876ebe23d693a9fce061f68da6fdec63419af78243ac9d457d7858f74b
- CLAUDE28-CUT-FIRST-REVIEW.txt lines 1–138
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/tfpt-unified-source-derivation-20261029/aps_source_review/CLAUDE28-CUT-FIRST-REVIEW.txt
e7a8c9f509bfc5d57e4d3bf57cc8f9cb5c6e694f58988281f039cc26d43340f3
finding:double-circle-reflection-does-not-fix-entire-cubic-cable-seam