Manuscript Hawk02-A@1 · Hawk02-A.tex · section · 7fbae745
Separate interfaces remain separate
Stage 4: renormalization and characteristic admission › Separate interfaces remain separate · lines 1218–1262
The proposed renormalization interface must not conflate:
The crossed arrows mean that no automatic implication is supplied, not that every possible bridge is obstructed.
The supplied records have the following boundaries:
XVI-L constructs the complete-source contribution of a stated two-edge graph under imported root hypotheses; its EFT bridge is recorded as matching questions, not a complete loop or Wilson match CheungXVIL.
XVI-M records graph-specific counterterm and scale specializations. A graph-specific curvature-ledger obstruction is not a universal gravitational beta function or ultraviolet completion CheungXVIM.
XVI-N's stated massless obstruction concerns a regular, seed-preserving, antifield-linear completion in a specified class. Even accepting the supplied summary of an unprepared classical complex through order , closure of the separately prepared insertion does not follow CheungXVIN ({
thm:massless-obstruction}).XVI-O restores a kernel two-point subsector under a stated prescription; it expressly distinguishes this from the functional Slavnov–Taylor identity and bulk restoration. Gate 3 remains partial and O.1 remains
NOT_CLOSEDCheungXVIO.
A physical effective-field calculation needs a new source ledger: graph inventory, operator domain, regulator, local normalization freedom, relevant Ward/BV identities, state, observable, and remainder. Inheriting one two-edge agreement does not inherit a full nonlinear one-loop identity, higher-point coverage, two-loop subdivergences, or all-order control.
Displayed formulas in this passage
unlabeled · line 1221