Manuscript I-B-VP-2@1 · I-B-VP-2-v1.tex · section · f4bd2b11
Ledger update and conclusion
Ledger update and conclusion · lines 1825–1937
{}1.12
| Object | Status here | Exact boundary |
|---|---|---|
| Object | Status here | Exact boundary |
| Massless Friedrichs spectral covariance on | Retained and globally analyzed | The kernel and state prescription are (eq:W); compact-test infrared control is retained. |
| Local Hadamard form | Constructed | Lemma lem:local; each regular developing neighbourhood. |
| Global ordinary two-point wavefront set | Exactly determined | Theorem thm:main, including all angular transitions. This is the V2 result for the specified state. |
| Strict diffraction | Classified | Absent exactly for ; otherwise the complete joint relation occurs. |
| Positive frequency and causal-kernel orientation | Constructed | Theorem thm:main and Corollary cor:EWF, with the charged ordering (eq:chargedCCR). |
| Selected products and restrictions | Constructed | Same-orientation kernel products, equal-time pullback, and timelike-curve pullback; not arbitrary interacting products. |
| Global hyperbolicity or state uniqueness | Not established | Non-global-hyperbolicity remains. No uniqueness among all algebraic ground states is claimed. |
| Quantum state or field algebra across | Open here | Neither the present wavefront theorem nor the one-point finite parts of I-B-VP-1 construct it. |
| Massive, non-Friedrichs, thermal, spinor, constrained, interacting cases | Open here | No transfer from the present exact massless covariance is asserted. |
precise V2 update. For the fixed massless Friedrichs spectral ground state, V2 is resolved at the level of the exact ordinary wavefront set of the global two-point covariance on the regular host. This is stronger than a generic-pair containment and includes transition angles and exceptional quotient sectors. It is not a classification of every state or every extension.
V1 retains the prescribed-completion qualifications of I-B-VP-1 CheungIBVPOne. The other V-items retain their own extension, mass, thermal, apex-curvature, spinor, and interacting scopes. Here “Open” means not resolved in the declared companion scope, not unknown throughout the literature.
sourcing or programme-wide status change. The cone, character, Friedrichs condition, and spectral state are prescribed inputs. The theorem does not derive the metric, impose Einstein or Maxwell dynamics, solve backreaction, or establish spacetime emergence CheungIB,CheungXAST. No OpenAI catalogue claim is a mathematical premise.