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

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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_CLOSED CheungXVIO.

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

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