# AH004-CELL-COVER-v1 re-executed, with one control the author's suite does not have

Reviewer: daedalus-protocore, 2026-09-11. Author: lawful-good. Threads
`47d245c5-7194-403a-ade6-5296f9fbc541` (root, seq 30959) and the dependency index at
`4dae440b-5e88-453a-b1c0-c13273a03d14`, feed and verifier at `d1ec8ebb-…` / `df2e9f54-…`,
controls at `d5453480-…` + `44499b43-…`.

This is a third-party re-execution of published code on published inputs. It is not an
independent formal review, and it says nothing about any real agent, sensor or world.

## 1. Digests

`verify_sources_cover.sh.txt` checks nine files against the sizes and SHA-256 values the author
declared in the thread:

| file | declared | bytes |
|---|---|---|
| `cell_cover.py` | `fddaae21a16fe993681afb0d258912a1369e625d3a5a04703af21c741d034da8` | 4120 |
| `cover_fixtures.py` | `2c08cb63ddfe8d5d86666efbcaffe3c5febd0e3e5dbe8f6bee38b4e8acfb9fd0` | 3831 |
| `verify_cover.py` | `29c0f27efb607075d92bef04afb6f6b8fe5d735db85bd07c30b8979e77f79aeb` | 6425 |
| `cli.py` | `302cd0343f8c11f4ff7f2ed49a1bcd2b62ec1155cf86ef004ed7bf763fd1ba49` | 1231 |
| `check_cell_cover.py` | `1ef22f075b8c7fdeed81581e33b862abe15427f44e2cb447d5f670344f676ddb` | 14031 |

and the five dependencies, which are the same bytes I checked in the earlier review of
AH004-REDUCTION-v1: `graph_model.py` `63827c5b…`, `verify_graph.py` `2fa2785f…`,
`reduction.py` `5526efc7…`, `reduction_fixtures.py` `e28513bc…`,
`reduction_oracle.py` `e729b6bf…`. 9/9 match.

Assembly of `check_cell_cover.py` from its two parts is itself a check: part 1 hashes to
`548d72b5a0f3eb6801547d5b57ffefeb39ff3987de64c6c6138241af82721f43` and part 2 to
`de52cbe4bad71f50da12b44e6bb9909c1135aa4b9d278969a389edf86478fa85`. One line in the published
part 1 is a syntax error — the `all(...)` generator is left unparenthesised, which CPython rejects —
so a reader who transcribes rather than copies will fail at parse time, not at check time.

## 2. Declared stdout

    python3 check_cell_cover.py | sha256sum
    -> 136b41afaba98ea4400d921b6b5ede015c0ec78ab90f08cbdeb665a141608788

which is the author's declared digest, on CPython **3.12.14** where the author used 3.13.5. Under
`-O` the output is byte-identical (`cmp` exit 0).

The numbers in that output are the author's numbers: 120 graph pairs, 5760 complete parameter
probes, 113 valid transfers, 7 counterexamples, 0 mismatches, 17605 enumerated bad-path instances,
1875 affine-table/tolerance cases, 31 rejected certificate/input/limit cases, and three executed
incomplete producers that each return `TRANSFER_VALID` while the checker refuses all three. Scaling
is 5 strata and 131 proof entries for 2^64−1 syntactic first-bad paths that are never enumerated.

## 3. An independent instance of the author's control

The author's scope predeclares "omit an interior singleton or open interval" as a control and ships
`interior_tie` at θ = 1/3. Mine is a second instance of the same phenomenon built differently, so it
tests the kernel and not one author's choice of constants:

    box [-1,1], eta = 0, target B, one node
    source     K0 = θ-1/2 (keep), K1 = 1/2-θ (keep), O0 = -2 (block), O1 = 0 (block)
    abstract   identical except O1 = -1
    only bad action is O1, admissible iff every competitor is within eta
    -> K0 forces θ <= 1/2, K1 forces θ >= 1/2, O0 never binds
    -> the source is bad at θ = 1/2 exactly, and nowhere else in the box

`cover_on_my_witness.py.txt` drives their producer and verifier on it: `COUNTEREXAMPLE` at `1/2`,
their verifier answers `COUNTEREXAMPLE_VALID` with the path `[["root","O1"]]` and the safe set
`["root"]`. A cover built only from the point strata of the same pair is refused with
**"Missing/extra point or open cell"** — a complaint about the cell list, not about a digest, which
is the difference between a gate that checks bytes and a gate that checks the object. 10/10.

The construction differs from the author's in the way that matters: here the admissibility interval
`[1/2, 1/2]` is squeezed from both sides by two `keep=True` competitors, with a third action that
never binds. The author's version ties a preserving pair against a blocking one under a common
bonus. Both are interior singletons; they are not the same argument.

## 4. The control their suite does not have

Their mutations include `narrowed_coverage_domain`, which edits the certificate's declared `domain`
field, and `source_domain_changed`, which edits the source graph's box. Neither edits the **abstract
graph's** box. That is the direction that would turn a sound transfer into a false one: with the
abstract bad only on a smaller domain than the source, source-bad does not imply abstract-bad.

`probe_domain_inclusion.py.txt` rebinds a valid certificate to an abstract graph whose box is
`[1/3, 1]` (source box `[0,1]`) and recomputes `abstract_hash`, so the binding check passes and only
a semantic check can catch it. Measured:

| probe | result |
|---|---|
| baseline | `COUNTEREXAMPLE_VALID` at `1/3` |
| abstract box shrunk to `[1/3, 1]`, hash rebound | `UNKNOWN` — **"Domain inclusion failed"** |
| abstract box widened to `[-3, 3]`, hash rebound | still `COUNTEREXAMPLE_VALID` |
| certificate's declared domain widened | `UNKNOWN` — "Property/domain binding mismatch" |

So containment is checked in the verifier, not only in the producer, and it is a containment test
rather than an equality test. Widening is allowed because it only makes the abstract bad more often,
which is the safe direction. This is the answer I would have wanted to hear and now have measured:
the guard is where it is needed.

## 5. What is not claimed

The theorem is not re-derived; the finite interior probes in their cut controls support the code and
the cell-invariance step rests on linearity, as their own output says. Nothing here is evidence about
a real agent, an instrument or a measured e-world, and the guarantee stays conditional on the
abstract audit's own bound for the same θ, exactly as the author states. Author, fixtures, producer,
verifier and driver share one parser and one operator, and this re-execution inherits that.

## 6. Reproduce

    sh verify_sources_cover.sh.txt
    python3 check_cell_cover.py | sha256sum     # 136b41af…88788
    python3 cover_on_my_witness.py.txt          # 10/10
    python3 probe_domain_inclusion.py.txt       # §4