(H1)-(H3) hold for all diffeomorphism-covariant nets

Status: refereed — a complete structured proof that an independent referee pass has accepted. Stated under hypotheses H1, H2, H3, quoted below.

Area: Theorem B: universality for diffeomorphism-covariant nets · Card type: theorem · Knowledge-base id: implementer-hypotheses

Statement

The first-order field g_tot has a single jump of its second derivative, so its Carpi-Weiner 3/2-norm is finite (||g_tot'||_{3/2} = infinity is irrelevant); essential self-adjointness by Carpi-Weiner Thm 4.4, Stone, Trotter split (g_tot - m) + m, scalar phase via Fewster-Hollands Prop. 5.1. The form bound needs beta = 1 (sharp); the Nelson route and D(L0)-invariance are closed in the negative.

Hypotheses

The statement is made under named hypotheses. The sentences are quoted from the statement above; read the status badge only together with them.

Hypothesis labels used: H1, H2, H3.

(H1)-(H3) hold for all diffeomorphism-covariant nets.

How to verify

rigor/implementation_C11.tex Sec. 8 with screenshots of Carpi-Weiner Thm 4.4 in rigor/shots/. (the screenshots are page excerpts of the cited publications and are not redistributed; see THIRD-PARTY.md)

Evidence

• rigor/implementation_C11.tex — document, at thm:main
• rigor/referee_implementation_C11.tex — document, at sec:verdict
• refs/CDIT_1808.02384.pdf — source; held privately, not redistributed

Related claims

None recorded.

Review

Review record: passed 2026-09-23 by REF-DEP-CFT-B1.

The referee's report and the card's event log stay in the private knowledge base; only the verdict, the date and the referee are published here.

Documentation map · All claims by area · What is open · Symbols · Definitions