Established in scope
Elliptic current state differs locally from Hardy even at Q0
In the question: Common clock sectors, quartic geometry and operational reconstruction
Exact state witness whose positivity is not inferred from finite regulators. No exclusion of other originally derived P1 states,admissible subalgebras,or properly transported current/time maps. Q0 conditioning is a mathematical comparison,not claimed physical selection. Purification leaves these marginal expectations unchanged.
Read the exact result, assumptions and evidence
Result
Exact telescoping of the actual Fermi covariance gives omega(J_-m J_m)=m/(exp(4pi m)-1),hence omega_Q0(J_-1 J_1)=0.00000348735451780811656...>0 versus0 in the old Hardy state. Q0 conditioning removes only the theta factor. Every nonzero real smooth mean-zero profile supported in a proper interval obeys omega_ell(Wf)/omega_Hardy(Wf)=exp[-sum_m m|fm|²/(exp(4pi m)-1)]<1. States thus differ already on every such local neutral current net under the unchanged original current dictionary.
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 65–160
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-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:elliptic-current-state-differs-from-hardy-on-every-proper-current-interval