Established in scope
Existing C2 real forms yield the concrete annulus and Moebius quotient
In the question: Common clock sectors, quartic geometry and operational reconstruction
Exact theorem only in the named h,Q,kappa subgroup and its eight-member anti coset. There the unordered OS annulus pair is canonical. Full already marked D4 lift has16 antiholomorphic members and an additional equatorial dividing pair;earlier unqualified full canonicity is narrowed by finding:full-marked-c2-lifts-distinguish-equatorial-and-os-real-slots. No square-modulus derivation or physical P1 cover identity. Free-deck uniqueness only among h,Q²,hQ².
Read the exact result, assumptions and evidence
Result
The complete affine census of eight h^a Q^b kappa has precisely two dividing members:hQkappa and hQ³kappa. With O=(0,i),T=(1+i)/2,Qz=iz,hz=−z+T,kappaz=−i bar z+T. Their halves have width1/2,circumference1 and Q exchanges them. Delta=hQ² is the unique free involution among h,Q²,hQ²;on the annulus it acts(t,s)->(1/2−t,s+1/2),with Moebius quotient. The earlier kappa-only nondividing statement is correctly scoped. v507 half-period origin,v510 free-deck/Fock class and v519 free RP are reused results.
Required assumptions
- Existing C2 group with untwisted raw flat spin pullbacks
On the existing marked parity curve E:y²=x⁴−1,study h=(x,−y),Q=(ix,y),kappa=(bar x,bar y) and flat square-lattice spin characters. The explicit raw one-particle calculation uses the untwisted line alpha with chi(A)=chi(B)=−1. Complex-linear pullbacks U and anti-linear Real structures j are distinct;no fitted U1 phase. This is not the normal twist alpha tensor p*O1 with its two-dimensional kernel. An original P1 Spin/Pin or Calderon transport is not presumed.
- Existing marked cyclic cover tower and compact elliptic images
Use only existing C_n:u_n^n=x^4-1 with fixed x base,deck Delta_n and already forced compiler clock R12=Q12 Delta12^4=(ix,omega s),Q12=(ix,s). Compare compact algebraic curves over C and pullback function fields. A comparison of punctured local systems must retain its removed points,peripheral loops,spin and field transports.
- 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
- THEOREMS.txt lines 1–100
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/elliptic-moebius-source-bridge-20261026/THEOREMS.txt
648dc0af6af2ad7f31ca6249af644512b829cdd9241deac0250512928a410290
- GEOMETRY.txt lines 1–190
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/elliptic-moebius-source-bridge-20261026/GEOMETRY.txt
be6dca12fe366f6aeba7953dd7ba1c100ddfe40d5faca43d8ea1a883fe85c4ce
- GEOMETRY.txt lines 191–380
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/elliptic-moebius-source-bridge-20261026/GEOMETRY.txt
be6dca12fe366f6aeba7953dd7ba1c100ddfe40d5faca43d8ea1a883fe85c4ce
- ORIGINAL-RELEVANCE.txt lines 191–380
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/elliptic-moebius-source-bridge-20261026/ORIGINAL-RELEVANCE.txt
516d23005f6b55e0471279ab7b1ab85d4f7f8b56282423c0aae4fabf51ef4362
- ORIGINAL-RELEVANCE.txt lines 381–523
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/elliptic-moebius-source-bridge-20261026/ORIGINAL-RELEVANCE.txt
516d23005f6b55e0471279ab7b1ab85d4f7f8b56282423c0aae4fabf51ef4362
- UPDATE-REAL-SLOTS-AND-SOURCE.txt lines 1–115
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/elliptic-moebius-source-bridge-20261026/UPDATE-REAL-SLOTS-AND-SOURCE.txt
c2d8461181fdd54a61cfcd68617a1905964e76b50cb5737e404a75b42717fc9e
finding:existing-c2-dividing-real-forms-realize-moebius-annulus-tower