Conditional result
Actual genus-two sign family closes common parallel K connection on cover
In the question: Automated construction of operator maps and sources
Constructive new combination of two solved source components,not new cover or repeated monodromy proof. Data and alignment remain explicit. Clock is adapted representative of whole native class; unchanged originally marked clock needs actual mark/connection map. No automatic descent of local matrix between unequal D powers. Triplet equality is necessary fixed-mark condition; coarse descent across branches also needs actual linearization/isotropy. Whole D/Phi/domain action,charged CAR products,original state,OS and physical time do not follow from connection identity alone. Full existing operational Seed retains its state/time. Old bare μ12 cover does not automatically contain q lines by existing ramification proof; no identity with original Fermat source.
Read the exact result, assumptions and evidence
Result
Already proved v117 splittingπ*F=L0⊕L1⊕L2 onC plus trivial line gives genuine flat SU4 sign bundle. Transitionsdiag(l0,l1,l2,1),product1,commute with existing natural Spin/family lift. For mA=(0,0,−1,−1)this gives global K=(Spin10×SU4)/Z4 cocycle with(16,4) branchW=ΛevenE⊗[L0⊕L1⊕D^-1L2⊕D^-1]. Half-determinant signs cancel in quotient. Whole associated E8 algebra and Lie products are global. Actual combined connection isA_W=ρ(A_E)⊗I+I⊗(Ma+A_L). Diagonal flatA_L commutes withM and nativeR=diag(ω,ω²,ω²,ω). Along with color center,κ,σ0 andκσ0 are thus global parallel automorphisms on all E8 branches. Irreducible lower A4 holonomy becomes abelianV4 upstairs; lower Schur/mF conclusion cannot be applied unchanged onC. Original ternary deck instead cycles three distinct lines. Unchanged parallelM andR marks require equal triplet values/phases. mA andR2+2 fail this fixed-mark condition and each has three-element transported-mark orbit.
Required assumptions
- Supplied split carrier with actual q sign lines on genus-two cover
Given existing split carrier E3⊕E2 with unitary split connection onX and actual unitary flat q linesL0,L1,L2 on old coverC:w³=(z²−1)/(z²+1),η²=1−w⁶,product1 andπ*Fv117=L0⊕L1⊕L2. Pull these data toX×C and combine with declared alignment to mA slots. This does not selectX,E,mA or alignment as original P1 quantum source.
- 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
- C3-COVER-JOINT-CONNECTION-REVIEW.txt lines 1–88
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/tfpt-unified-source-derivation-20261029/aps_source_review/C3-COVER-JOINT-CONNECTION-REVIEW.txt
c14eecf0ae67e49227c7626b851e7801275721c543ef3c832007add1ce3bb550
- SIGN-LINE-COVER-DICTIONARY.txt lines 1–180
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/elliptic-moebius-source-bridge-20261026/SIGN-LINE-COVER-DICTIONARY.txt
555f75a2d3c67347fa5f8e3c4f7f46e79d94cb4172176c84010224585dc842e7
- SIGN-LINE-COVER-DICTIONARY.txt lines 181–250
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/elliptic-moebius-source-bridge-20261026/SIGN-LINE-COVER-DICTIONARY.txt
555f75a2d3c67347fa5f8e3c4f7f46e79d94cb4172176c84010224585dc842e7
- PROOF.md lines 36–78
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/source-joint-spin-family-lift-20260922/PROOF.md
d3ae02543e90d840879808554816f923cc36cab52268a032d1ce29c2569f5bd2
- JOINT-LIFT-NATIVE-CLOCK-CONNECTION.txt lines 37–175
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/original-admissible-source-closure-20261025/JOINT-LIFT-NATIVE-CLOCK-CONNECTION.txt
edd2cdaea4c4debd337b4850d48da95de68e9367d780b9e3f0a96755588a45c8
finding:actual-genus-two-sign-family-closes-common-parallel-k-connection