Scoped exclusion
Elliptic normal spin pullback doubles index and deck-quarter lifts anticommute
In the question: Common clock sectors, quartic geometry and operational reconstruction
Excludes only index-one and quarter-compatible single-line pullback in this normal spin factor. Actual normal-base identity and original field transport are absent;an actually existing further tensor factor may compensate the projective cocycle. Does not exclude original bosonic doublet count or whole TFPT. Does not identify Calderon projector with deck projector.
Read the exact result, assumptions and evidence
Result
On old E:y²=x⁴-1,the spin Dirac twisted by p*O1 has ordinary complex index2 for every spin. In q-fixed even spin alpha=O(T-O),u=(y+i)/x²,kernel is span(1,u). Genuine deck and quarter lifts have D=[[0,-1],[1,0]],Q=a diag(1,-1),so D²=-I and QD=-DQ independently of scalar phases. Quarter exchanges the two deck eigenlines;no common rank1 kernel sector.
Required assumptions
- Existing elliptic curve with a specified normal spin factor
On the actually existing E:y²=x⁴-1 with p=x,delta:(x,y)->(x,-y),q:(x,y)->(ix,y),compare normal spin Dirac operators twisted by p*O1. In the q-fixed nontrivial spin alpha=O(T-O),O=(0,i),T=(0,-i),transport the two-dimensional holomorphic kernel with genuine spin lifts. No identity of this curve base with the original normal base or of delta with the Calderon reflector is assumed.
- 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
- ORIGINAL-BASES-AND-ELLIPTIC-SPIN.txt lines 37–120
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/original-admissible-source-closure-20261025/ORIGINAL-BASES-AND-ELLIPTIC-SPIN.txt
bf6b2336e24a39aef26b9907c24f033a47a8a1318f8f19ae561e4c477680ce67
finding:elliptic-normal-spin-pullback-doubles-index-and-deck-quarter-lifts-anticommute