Established in scope
Existing elliptic Gaussian source determines full quarter current functional
In the question: Common clock sectors, quartic geometry and operational reconstruction
Complete free current source on existing elliptic midpoint annulus under expressly given Gaussian quantization. b4pi belongs toHalpha,2pi to2Halpha,32pi toKalpha=Halpha/8;the same density operator. No physical temperature,primitive P1 measure,marked equator-graph/collar intertwiner,or interacting Wick theorem. Native unbounded limits retain old domains/smearing/normal-order hypotheses.
Read the exact result, assumptions and evidence
Result
The actual labelled Calderon/Szego covariance gives C_r=(1+exp(4pi(r+alpha)))^-1 and rho=Z^-1 exp(-4pi Halpha),Halpha=N+Q²/2+(alpha-1/2)Q per quarter. The full current functional is omega(Wf)=Theta_alpha(f0)/Theta_alpha(0) exp[-1/2 sum_m m coth(2pi m)|fm|²],with exact original BCH phase for every finite ordered Weyl word. Theta retains all charges. The explicit normal representation is left action on the rho^(1/2) cyclic space;its subspace for currents alone,the full HS space for full CAR. Previously reconstructed neutral vertex products give the same Wick field correlations in this state. Finite fermion determinants and grouped1/2/4/8 pair comparisons independently check the analytic derivation;normal and-OO are byte-identical.
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.
- Free chiral Cauchy quantization of the canonical elliptic annulus
Treat the dividing half of the given square curve in its canonical flat conformal representative as a product collar. Compute the Cauchy graph of Dplus=partial_t+B_Sigma,B_Sigma=−i partial_s with NS boundary,then interpret it using the expressly free chiral CAR construction as a quasifree two-boundary state. The labelled second-face compression is the covariance;the other is complementary. This Gaussian interpretation does not derive the original relative spectral-action measure,P1 time or EM/Quillen response.
- Original quarter CAR source with fixed fold and current dictionary
The already supplied single-channel CAR source with actual quarter domains alpha=1/4,3/4, negative-D sea, positive original excitation time, unitary eightfold F and actual channel diagonalization is fixed. M,O,U+ and the conformal NS point-splitting reference are the same original dictionary data; the single delta counterterm follows from the kernel difference. Even CAR current composites retain full arc correlations, charges, domains, all modes, original time and the existing subtraction prescription including finite derivative counterterms. No E8 root/spinor extension is assumed for this neutral current subalgebra. Identity with the original P1 net, Theta, collar and reference sector is not supplied. Real profiles and pulse strengths are intervention data.
- 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
- ELLIPTIC-CURRENT-SOURCE.txt lines 1–178
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/native-arc-charge-source-interface-20261026/ELLIPTIC-CURRENT-SOURCE.txt
657b2ace6d7152c53dbb29c76d8e0daca6e6b1ce747c535da7dffb0ff38d9b48
- check_elliptic_current_source.py lines 1–134
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/native-arc-charge-source-interface-20261026/check_elliptic_current_source.py
f754d9f025e4a7823734d3ca617de762fd874b29bd1264e9d7976da786442412
- elliptic_current_source_results.json lines 1–114
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/native-arc-charge-source-interface-20261026/elliptic_current_source_results.json
7b8c4003ffac61f99f420af8e5a9808714c6378586e6a891973733b349ca534c
- ELLIPTIC-CURRENT-REVIEW.txt lines 1–8
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/native-arc-charge-source-interface-20261026/ELLIPTIC-CURRENT-REVIEW.txt
0bcbfe2267bd39ff1ed008c0d0883f64cc77b514990138f9f92e08e9fc86b9ed
finding:actual-elliptic-gaussian-source-determines-full-quarter-current-functional