# v16o-v16s direction and execution report

Date: 2026-07-15

## Question

After the qualified strict-null spectrum contrast replicated in v16m, what was
the smallest sequence of tests that could distinguish a real event-DAG
structural contrast from an artifact of ignoring event family and read/write
resource structure?

## Adviser fanout and adjudication

Four remote adviser roles were used: experimental design, statistical
skepticism, causal/order implementation, and claim adjudication. The main
options were another same-null replication, immediate scale-up, an exact
resource-aware null, and a coarser event/resource null.

The panel preferred a mechanism-sensitive null before more scale or another
same-null holdout. The argument was that v16m had already reduced ordinary
fresh-seed uncertainty, while the largest live alternative explanation was
that the strict null destroyed event/resource organization. The principal
counterargument was that a resource-aware null could become immobile. The
adjudicated design therefore required effect-blind reachability and sampler
qualification before any new spectrum calculation.

## Relevant external constraints

- Interval abundance has dimension-related meaning in causal-set work under
  explicit random-sprinkling and spacetime assumptions. That does not transfer
  automatically to an arbitrary finite event DAG. See Glaser and Surya,
  [Towards a Definition of Locality in a Manifoldlike Causal Set](https://arxiv.org/abs/1309.3403).
- Network conclusions depend materially on the selected null ensemble; degree
  preservation alone is not a universal neutral baseline. See Fosdick et al.,
  [Configuring Random Graph Models with Fixed Degree Sequences](https://doi.org/10.1137/16M1087175).
- Directed switch-chain mixing results require graph-family assumptions that
  do not cover the present order-, depth-, age-, and footprint-constrained
  event DAGs. See Greenhill and Sfragara,
  [The switch Markov chain for sampling irregular graphs and digraphs](https://arxiv.org/abs/1701.07101).

These sources motivated stricter claim boundaries. They do not validate the
repo's sampler or turn its interval spectrum into physical dimension.

## Executed sequence

### v16o: exact actual-conflict reachability

The audit enumerated all `37,521,528` unordered direct-edge pairs in the six
v16n calibration DAGs. The same-color rule had zero legal pairs in every run;
the general two-color multiset rule had one legal pair total and no moves in
five runs. The actual-conflict edge-color null was retired as structurally
immobile.

### v16p: weaker event-footprint reachability

The footprint retained source family/write-namespace set and target
family/read-namespace set, but not concrete resource identity. Exact
enumeration found `35,535` legal swaps. Legal swaps touched `61.681%` to
`68.125%` of direct edges in every run, passing the frozen `10%` support gate.

### v16q: effect-blind sampler qualification

At the lowest frozen ceiling of `60` attempts per edge, all `288/288`
perturbations completed, preserved declared invariants, changed at least
`10%` of edges, and were unique within run/family. This qualified the
procedure, not its mixing distribution. Concrete resource-conflict retention
fell to at least `0.899509`, as expected for the coarse footprint.

### v16r: posthoc same-history sensitivity

On the six reused v16m primary histories, the footprint-null primary median JS
effect ratio was `13.057562`; all `6/6` runs were positive and had empirical
`p <= 0.10`. The longer median was `12.542120`. This showed that coarse
footprint conditioning did not absorb the contrast on those histories, but it
was not an independent replication.

### v16s: fresh footprint-null holdout

Six histories with growth seeds `9365/9299` and offsets
`123078/127341/123403` were generated only after freeze. History integrity,
replay, and rate checks passed. Primary perturbation integrity was `192/192`
and longer integrity was `96/96`.

The primary median JS effect ratio was `11.999282`; all `6/6` runs were
positive and all had empirical `p = 1/33`. The longer median was `12.054418`,
again positive in `6/6`. Every tail-mass delta was negative, so the result is
a full-spectrum contrast, not excess large intervals.

## Claim coverage

| Claim | Status after v16s | Reason |
| --- | --- | --- |
| A repeatable finite event-DAG interval-spectrum contrast exists under the tested procedures | supported | fresh v16m and fresh v16s holdouts, with separate qualified nulls |
| Coarse event-family/write-read namespace structure absorbs the contrast | not supported | v16r and v16s both retain the contrast |
| The contrast is independent of concrete resource identity | unresolved | the footprint null deliberately does not preserve concrete IDs |
| The footprint sampler is uniform, converged, or representative | unresolved | completion and uniqueness are not mixing proofs |
| The spectrum estimates physical dimension or manifoldlikeness | unsupported | no analytic mapping or manifold test exists here |
| Lorentz symmetry, spacetime, particles, entanglement, or physical law emerged | unsupported | no corresponding gate passed |

## Recommendation

Do not spend the next budget on another identical six-run holdout or immediate
scale-up. The highest-value narrow gate is an effect-blind sampler
path-dependence/stabilization test for the footprint null:

1. freeze multiple chain lengths and independent starts without inspecting the
   observed spectrum;
2. compare null-center spectra and edge-level diagnostics across chain lengths;
3. require stability across every source DAG before treating the null center
   as more than procedure-conditional;
4. if stable, seek an independently constructed null family rather than only a
   longer version of the same switch chain;
5. only then consider a larger target or a more physics-facing observable.

The strongest current statement remains structural and finite: the generator
repeatedly produces event-DAG interval spectra that differ from two qualified
constrained switch procedures, including a coarse event-footprint procedure.
That is evidence that the model contains nontrivial organization not explained
by the preserved finite-DAG summaries. It is not yet evidence for spacetime or
a universe-building law.