# OPH internal exhaustion checkpoint v1

**Date:** 26 October 2026  
**Source revision:** `0045a99143c6cc8443d2c2c5c5bb4055451dd115`  
**Scope:** the finite record-law family and its local compositions  
**Status:** internally exhausted; externally gated

## What “exhausted” means here

It does not mean that Observer Patch Holography is complete, true or false as a physical theory. It means that the present source, read without importing a preferred carrier, phase, clock, scheduler or physical interpretation, has yielded the finite mathematical answers needed for the corpus decision. Further symbolic restatement of the same source is not an evidence-bearing next step.

## Closed inside the source

| Question | Disposition | Evidence-bearing result |
|---|---|---|
| Does the published finite package reproduce? | closed positive | pinned hashes, 36 focused tests, 1,275 artefacts and exact replay pass |
| What is the complete one-seam admissible family? | closed positive | a nine-real-dimensional Choi spectrahedron with blocks `2 + 4 + 2` |
| What survives repeated repair? | closed positive | `C0`, `C` and `C_signed` converge to `E`; `E` and `T` have fixed dimensions 3,236 and 3,126 |
| Is the discrete repair a finite-time bounded autonomous flow? | closed negative | every admitted channel is non-injective, whereas a finite-time exponential is invertible |
| Do local seam laws glue without schedule data? | closed negative | all named laws commute on disjoint seams and fail to commute on adjacent seams |
| Does the source select the corpus's rank-two real Jordan carrier? | closed negative | `E` fixes `M_56(C)`; its two-level complex corners form `Gr_C(2,56)`, and neither a complex plane nor a real phase slice is selected |
| Is the result already new physics? | closed negative | the ingredients lie within standard channel, instrument, process-tensor and system-identification theory |
| Is there a realistic next experiment? | closed positive | seven- and eight-qubit logical designs, observables, controls, shot bounds and stop rules are preregistered |
| Can a quotient erase the minimal order witness but retain named-law identity? | closed positive, detector-relative | exactly two of five record partitions erase order; both merge the oriented endpoints, while an independent `g/k` detector still separates `C0/C/E/T` |
| What information and reset ledger accompanies the named instruments? | closed conditional | for a uniform six-key prior, record entropy rises `1.5000 -> 3.5850` bits; the fresh-ancilla dilation is exact, while global entropy monotonicity and physical dissipation remain unproved |

The “55 corners” shorthand is retired. Fifty-five is only the number of source-basis empty/full pairs addressed by the `k` multiplier. The fixed block itself admits continuously many complex two-planes. This makes the absence of a canonical `H_2(R)` carrier stronger, not weaker.

## What remains outside the source

1. **Backend lowering.** The independent logical reference, named-law Kraus/isometry compiler and universal two-level circuit execution are complete. `ibm_fez` is the named eligible target and its required provenance packet is frozen. What remains requires external account access: export the live target and calibration, choose a connected eight-qubit subgraph and perform coupling-map-aware native synthesis.
2. **Stage-A device execution.** At 5,000 shots per phase/law, recover the common classical table and the one-step `g`/`k` phase contrasts under a frozen calibration model.
3. **Stage-B device execution.** Reverse adjacent order, retain the ideal total-variation target `0.25`, and use the digital packet's powered equivalence test to place the corrected underlying disjoint-order distance below `0.02`; the conservative qualification design uses 200,000 shots per order.
4. **Hardware process-model comparison.** The deterministic synthetic qualification now passes with one shared ordinary nuisance model and a finite-memory control. Fit its physically expanded instrument/process-tensor counterpart to device training records and predict held-out phase, depth and order records without per-setting refits.
5. **Independent replication.** Repeat on a second implementation or platform before treating a residual as architecture-specific.
6. **Physical attachment.** Identify a real carrier, preparation, interaction, detector and nuisance model whose frozen OPH-derived relation predicts a record not already supplied by conventional quantum-channel theory.

The clean-room observable replay already establishes a useful reference calculation. Steps 1--5 can establish further theoretical engineering: a compact benchmark for branching records, retained coherence, memory and scheduler dependence. They do not by themselves establish an ontology. A new-physics branch opens only at step 6, and only if a replicated residual survives the complete conventional model.

## Reopening rules

Reopen the internal mathematical lane only if at least one of the following arrives:

- a new source revision changes the record-law family or its composition rule;
- a proved quotient makes the underlying adjacent compositions confluent, rather than merely making their detector records equal;
- a source-native symmetry or observable selects one complex two-plane and its real phase slice;
- an injective interpolation or explicit dilation is supplied with a declared clock and measurable residue;
- a local-to-global theorem gives a faithful completion on a stated patch category.

Reopen the physical lane only when the attachment includes a preregistered observable, conventional alternative, nuisance model, held-out prediction and go/no-go rule.

## Kenotic implication

The result is useful because it becomes smaller under scrutiny. OPH supplies an exact example of the missing middle between admitted possibilities and durable records: not Jordan coexistence alone, not Lie transport alone, but a positive, branching channel whose composition remembers schedule. The same scrutiny removes the stronger identifications. There is no source-canonical real Jordan corner, no direct `Spin_0(2,3)` derivation and no finite-time autonomous generator. What remains is concrete: a finite benchmark that can now leave the page and meet an independent detector.

## Stop rule

Do not extend this lane by generating further analogies from the pinned finite model. Continue only by executing OT-055, by auditing a changed source, or by presenting a new theorem or physical attachment that fires one of the reopening rules above.