Manuscript XI-D@1 · XI-D.tex · section · 994a5c1b
Decision table and qualified handoff
Decision table and qualified handoff · lines 1091–1148
| Gate or statement | Status |
|---|---|
| XI-C classical tree and physical sign | Retained: |
| Compact microcausal source symbols | Retained; not quantum admission |
| Exact off-shell shadow of all XI-B generators | Proved incompatible with its equation quotient |
| On-shell admission interface | Explicitly formulated |
| Quantum extension, product, and admission map | Unresolved; no general nonexistence claim |
| Ghost number of | Zero |
| Free variation of | Explicit; generally nonzero |
| Free-shell closure witness | Evaluated in (eq:witness) |
| Bare closure under a compatible prospective admission | Conditionally obstructed for the witness tests |
| Antibracket and its Jacobi identity | Not constructed |
| Interacting differential and nilpotence | Not constructed |
| Held-fixed-metric forward defect | |
| Inherited positive witness pairing | Retained in (eq:backgroundwitness) |
| Mixed loop, state, sharp limit | Not opened |
| Empty fixed-input Einstein jet | Unchanged |
The overall ending is Unresolved, because D2 has not been constructed or excluded in its consistent on-shell formulation. The paper does not promote a classical symbol to a quantum class.
At the same time, the bare-closure request has a concrete lower-order problem: for the diagnostic tests, an admission with the correct free classical action cannot make closed by positive-order coupling corrections. This conclusion is independent of a chosen state and precedes a loop calculation.
A successor therefore receives three distinct tasks:
construct a quantum admission with an explicit distinction between off-shell representatives and on-shell symbols;
define the antibracket, antifield-dependent interaction, and differential on a named domain;
identify the complete observable whose coefficient closure is intended, instead of requiring closure of its bare dressing alone.
It also receives both evaluated witnesses. Neither may be erased by relabelling a background pullback as the free ghost rule.