Scoped exclusion
The given quarter energy is not a Borchers translation
In the question: Common clock sectors, quartic geometry and operational reconstruction
Only identification of this same source energy with the Borchers translation generator. Other gapless generators, correctly constructed local standard pairs and HSMI remain possible. Lean formalizes the elementary spectral-set statement, not Stone, spectral theory or the actual P1 source. Other KMS/spectral-profile identifications still require their actual operator dictionaries.
Read the exact result, assumptions and evidence
Result
Using this same gapped quarter energy as a modularly scaled translation fails already at the full spectral gap: the group law and Stone uniqueness imply unitary equivalence of H and H/2. The least positive spectral point would have to be both1/4 and1/8. Lean grind proves the elementary spectral-set lemma with only the three standard axioms. Independent review confirms the analytic connection and scope. The source remains a conditionally supplied model; neither original-P1 source derivation nor its universal refutation follows.
Required assumptions
- 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.
- The same given quarter energy as Borchers translation
Use exactly the already given full chiral quarter source H_alpha, alpha1/4 or3/4, with spectrum containing0 and least positive spectral point1/4. The proposed standard-pair bridge identifies U(s)=exp(is H_alpha) as its strongly continuous translation group and requires unitary modular conjugation V_t U(s) V_t*=U(exp(-2pi t)s) for all real s,t. This is an additional proposed identification to be tested, not an original P1 consequence.
Original evidence
- PROOF.txt lines 1–143
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/elliptic-moebius-source-bridge-20261026/source_origin_derivation_20261029/PROOF.txt
db1151d97d3901948564a4dbc8da10a6bd794c60c6b3b2bd096b6db9f9e3111b
- GapObstruction.lean lines 1–16
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/elliptic-moebius-source-bridge-20261026/source_origin_derivation_20261029/GapObstruction.lean
69ed2727ded694d9275cef1a5047c04eaaa16c74eef8cf2cbeb505a37af5bfc0
- LEAN-RESULT.txt lines 1–15
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/elliptic-moebius-source-bridge-20261026/source_origin_derivation_20261029/LEAN-RESULT.txt
fec7f3725f3a8b0e0720301f4eca3116bbc87eef52834a683554306b579ad97a
- INDEPENDENT-REVIEW.txt lines 1–25
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/elliptic-moebius-source-bridge-20261026/source_origin_derivation_20261029/INDEPENDENT-REVIEW.txt
6fec4a3ad092c6703c3231a3e956ab95f70559ae73d0116d63ac4e63dd3e475f
finding:gapped-quarter-energy-cannot-be-same-borchers-translation