Established in scope
Existing source spin is the canonical ramified sphere-spin pullback
In the question: Automated construction of operator maps and sources
Exact spin-line origin and square/lift map on already reconstructed original π source. Common spin sign is ordinary frame sign,not new relative quarter fit. Meromorphic coefficients at poles are not nonvanishing fiber values. No identification of physical BΣ with freely selected pullback operator:actual metric,connection,weighted Sobolev/trace domain at four ramification vertices,whole coefficient system and Γ± face assignment must transport. Spin Real map is not CAR C0 or OS reflection. Triple coefficient pullback is not physical generation count. Preserve old once norm and Kummer/fiber-lift corrections.
Read the exact result, assumptions and evidence
Result
For actual original triple map π:C→P1_z,w³=(z²−1)/(z²+1),all four ramification indices are3. With Rhalf=Rπ/2 and K=Iplus+Iminus,Rhalf∼2K and2Dq∼3K. Canonical ramified pullback of unique sphere spin is S_can=π*O(-1)⊗O(Rhalf)≃O(Dq−K)=S0. Explicit square-compatible map is e_can=√3·w/(w³+1)·Φ0 for Φ0²=μ0=(w³+1)dw/η,with e_can²=π*(dz/z²) and √dz=√3·w/η·Φ0. Actual old lifts satisfy c e_can=e_can,Q e_can=ξ e_can,Q√dz=barξ√dz. Contravariant E0=Qτ0 anti-pullback has J_E√dz=ξ√dz,J_E²=1. S0 is not an additional spin choice on this source.
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.
- Unchanged A0* Fuchsian equation and actual C4 clock
Fix exactly v115 A0*, U=diag(1,i,-i), residues U^k A0* U^-k at i^k and regular base point z=0. Retain base rotation, positive meridian on t=z⁴ and simultaneous fiber basis change. No new Riemann Hilbert solution or D4 reflection lift is assumed.
- 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
- CANONICAL-BRANCHED-SPIN-PULLBACK.txt lines 1–87
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/tfpt-unified-source-derivation-20261029/aps_source_review/CANONICAL-BRANCHED-SPIN-PULLBACK.txt
c61a15753a64da286cef464067e221860cda9495f6efa61082bd39398606d5c3
- 004-subsection-auch-die-skalen-besitzen-einen-gemeinsamen-va.tex lines 203–290
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
- SOURCE-SELECTED-THETA-SPIN.txt lines 28–145
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/elliptic-moebius-source-bridge-20261026/SOURCE-SELECTED-THETA-SPIN.txt
cf4478191ccd75d62a2f049a54193541009bed24877df9cbe0ed9f942d07d717
- CLOCK-Q-PACKET-COMPATIBILITY.txt lines 22–54
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/elliptic-moebius-source-bridge-20261026/CLOCK-Q-PACKET-COMPATIBILITY.txt
fe37f20bbb2d959dfe678ca1bf435a69067cfcb859a3d36769294bbe9bf61c32
- SOURCE-SPIN-ZERO-SECTIONS.txt lines 9–49
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/tfpt-unified-source-derivation-20261029/aps_source_review/SOURCE-SPIN-ZERO-SECTIONS.txt
8ace4e928bf950e97d3010d53001a904b03ddedea1f51933e8bea7434938c333
finding:source-spin-is-canonical-ramified-base-spin-pullback