Manuscript XXII-A@1 · XXII-A.tex · section · 9e4e9f66
Continuum and comparison ledger
Continuum and comparison ledger · lines 652–738
XIX-C supplies two specific cautions for any later continuum step
CheungXIXC (prop:two-limits, prop:interpolation):
two refinement families can share one coarse complete channel, obey one-site scheduled locality, and converge to different semigroups;
finite sampling constraints can leave interpolation ambiguity.
The first counterexample chooses different missing refinement data; it does not assume an additional projective-consistency condition. Such consistency would itself be an extra hypothesis. These warnings do not exclude a unique continuum limit after suitable additional data and assumptions are supplied.
The documentary roles of the other named components are fixed below. None substitutes for Research target target:selection.
{}1.16
| Component | Role in XXII-A | Boundary |
|---|---|---|
| En08-A | Obstruction and conditional representation record | Scheduler consistency does not select the cone; faithful affine representation and cone structure are additional CheungEn08A. |
| VII-J | Three-relation discipline | Scheduled support and operational influence are distinguished; physical containment needs a causal embedding CheungVIIJ. |
| XIX-C | Continuum warning | One finite channel or finite sampling record does not select the missing refinement and continuum evolution CheungXIXC. |
| En08-B | Possible later approximation layer | Finite SWAP protocols approximate a prescribed null boundary. The metric and speed are inputs; endpoint approximation is not cone selection or a global continuum evolution CheungEn08B (thm:main, cor:operational-limit). |
| VIII-A/B/C | Documentary geometric comparison | Declared conical families and fixed-deficit packets are not an operational derivation of their cone or deficit CheungVIII. |
| Em02-E | Documentary clock comparison | The reported relational lapse uses an installed classical background; its quantum audit is not supplied here CheungEm02E. |
| XIX-A–E; XX-A–F | Clock and admission boundaries | Finite registers, scheduled support, and classical lapse prescriptions are not silently promoted to native continuum evolution or a derived metric CheungXIXA,CheungXIXE. |
| OpenAI catalogue | Negative-control record | Area laws, random-tree limits, VOA-net claims, and local Ward records do not supply the missing operational cone-selection argument CatalogueRecord. |
This ledger records scopes, not proof-transfer paths. In particular, null-boundary approximation in En08-B cannot be used to derive the metric or speed with which its targets were defined. Similarly, an independent geometric construction does not become an operational extraction by changing the name of its input.