# v16u interpretation and next direction

Date: 2026-07-15

## What v16u resolved

V16u implemented the repair required by the v16t realized-effort audit. The
existing `10%` changed-edge rule was used only to create a shared burn-in state.
Every branch then advanced by exact accepted-swap increments with
`K = ceil(0.100 * source edge count)`.

Across six frozen v16s source DAGs and sixteen replicates per source:

- all `384/384` null outputs passed structural and uniqueness checks;
- all `96/96` branches realized exact `+K` and `+2K` increments;
- direct `+2K` and staged `+K+K` differed by zero accepted swaps in `96/96`;
- staged paths branched from the exact direct `+K` prefix in `96/96`;
- direct and staged endpoints were different graphs in `96/96`, so the path
  comparison was not an identity comparison;
- realized-length center stability passed `18/18`, maximum ratio `0.666516`;
- matched-effort path stability passed `6/6`, maximum ratio `0.180595`;
- the frozen limit remained `2.0`.

This closes the specific v16t design gap. Within the tested finite effort range,
the event-footprint null center is not visibly driven by the changed-edge stop
rule, exact post-burn-in chain length, or one RNG reset after a shared prefix.

## Current evidential position

The leading effect result remains v16s: a finite event-DAG full-spectrum
contrast on six fresh histories under the qualified event-footprint null. V16u
does not recompute that effect. It strengthens only the procedure-level basis
for using the local event-footprint switch family as a reference distribution.

V16u does not prove irreducibility, mixing time, convergence, stationarity,
independence, representativeness, or uniform sampling. It also does not show
that the v16s contrast survives a null generated by a different construction.
No dimension, Lorentz symmetry, spacetime, particle, entanglement, invariant,
or physical-law claim is advanced.

## Recommended next gate: v16v

Run an effect-blind feasibility audit for an independently constructed
event-DAG null family. It must not call `v16q.footprint_rewire` or obtain its
samples by continuing the current local switch chain.

The narrow candidate is a global constrained edge-slot reconstruction:

1. treat source out-degree slots and child in-degree slots as a bipartite
   assignment problem;
2. allow only parent-child assignments that preserve scheduler order, exact
   causal depth compatibility, dyadic age bin, and event-footprint class;
3. forbid duplicate edges and preserve exact in/out-degree sequences;
4. seek multiple distinct complete assignments from independently randomized
   global matching objectives;
5. compute no interval spectrum or observed-effect statistic in the feasibility
   gate.

The first gate is feasibility and diversity, not effect existence. It should
report whether all six source DAGs admit multiple globally reconstructed DAGs,
which constraints cause infeasibility, and whether the construction is truly
independent of the local switch path.

## Decision rule

- If all sources support multiple structurally valid global reconstructions,
  freeze and qualify that independent null family before one new effect test.
- If only some sources are feasible, do not silently relax constraints. Report
  the exact blocking constraint and test the smallest predeclared relaxation
  effect-blind.
- If the joint constraints uniquely or nearly uniquely determine the DAG,
  retire this independent-null route and state that the current v16s result is
  conditional on the local switch family.

Do not increase graph target, fit a dimension, or rerun the v16s effect before
this independent-construction question is resolved.