The design
A network of units, each with a local state. The units are coupled physically, or simulated as such. Each edge carries a correspondence map saying which pairs of local states count as agreeing. An apparatus measures the units and may be allowed to revise the maps. Three things are varied independently:
- Physical coupling:
- weak or strong;
- dissipative or conservative;
- with or without a common external drive.
- Correspondence maps:
- compatible around every cycle, or frustrated (nonzero holonomy);
- scalar or of higher-dimensional stalk, so that reduction can need higher-order relations (THEORY-1090).
- Apparatus revision:
- none;
- by consistency alone, as in discourse sheaves (THEORY-1088);
- by consistency checked against held-out interventions the apparatus did not choose (CLAIM-342).
Regimes from A22 §10, extended by the owner’s review:
| regime | isolates |
|---|---|
| compatible maps, weak coupling | coherence without integration |
| compatible maps, strong dissipative coupling that enforces those maps | attraction to the specified compatibility space, and whether the gap in relaxation rates is large enough to separate time scales usefully (CLAIM-481) |
| compatible maps, strong dissipative coupling that enforces other relations | strong coupling without attraction to the specified compatibility space |
| compatible maps, conservative coupling | coherent oscillation without relaxation |
| frustrated maps | persistent incompatibility and compromise organization |
| common drive, no reciprocal coupling | apparent synchrony without mutual integration (QUESTION-063) |
| higher-dimensional stalks with interior units | boundary constraints the parts’ relations cannot state (QUESTION-283) |
| revision by consistency alone | coherence without knowledge |
| revision checked against held-out interventions | revision that can improve prediction |
Coupling assumptions
The experiment is informative because coupling and correspondence can be set independently. So the regimes must not assume that one delivers the other.
- Strong coupling alone does not attract to the specified compatibility space. Dissipative coupling drives the states toward the kernel of whatever operator it actually realizes. That is the specified space only when the coupling enforces the specified correspondence maps: in the linear case, when its Laplacian is δ*δ for the apparatus’s own coboundary δ. A strongly dissipative coupling that enforces other relations attracts to a different space. That is why it is a regime of its own above.
- A positive gap is not a useful separation. For a connected, enforcing Laplacian flow, every incompatible mode decays, so there is always some gap above the kernel. A separation of time scales that supports a reduced description needs a gap large relative to the slower dynamics and to the observation horizon (CLAIM-481’s window, 1/(κK) ≪ t ≪ 1/(κε)). The readout is the size of the gap against those scales, not whether it is positive.
Readouts
For each regime:
- whether an exact or approximate global section exists;
- whether the dynamics reach it, and at what rates;
- which normal modes emerge;
- what effective boundary law an observer confined to some units can fit, and whether it is pairwise, higher-order or history-dependent (CLAIM-480);
- whether the organization survives localized interventions;
- how much communication and computation it takes to recover the correspondences from measurements.
In the revising regimes, the key readout is whether revision improves predictions on interventions the apparatus did not choose. A22 §10: this tests “the difference between becoming more coherent and becoming more knowledgeable.”
What it would show
The transitions CLAIM-474 says are distinct can be made to come apart on purpose. Where they come apart in the study, the claim gains a constructed case. Where they never come apart across the regimes, the claim’s defeater is in view. The revising regimes also bear on QUESTION-282. They do so only as adaptation of an apparatus, unless the revised maps feed back into the physical coupling. A variant in which they do would be the study’s closest approach to interaction changing the operative correspondence structure.
Standing
Stipulated, since nothing has been run. It is set out from A22 §10, A23 §XIII and the owner’s review of the pull request, 2026-10-27: “The key experimental proposal should compare systems in which physical coupling, correspondence maps, and apparatus revision are independently manipulated.”
Note of 2026-11-03: the arms the design lacks
U27 to U33 of the exchange “Assess SDT Coverage” (2026-11-02) proposed most of this study again (A28 §8, A29 §10, A32’s “Case B”). What they add are arms it does not have:
- Declared tolerances on the overlaps, so that compatibility is CLAIM-538’s frontier and not exact agreement.
- Own against outside channels on the same modes (CLAIM-542).
- Observer-limited policies, which can use only what the revising apparatus can read (CLAIM-537, CLAIM-535).
- A captured-correspondence arm, in which the evaluator’s comparison omits one overlap of a witnessing cycle while it still operates, so that evaluation reports a compatibility that does not hold (CLAIM-538’s omission clause; THEORY-1088, CLAIM-404, CLAIM-251). The cover, the declared scenario and the evaluator’s effective observations must be kept separate.
- Maintenance-provenance knockouts (CLAIM-522, CASE-161).
- A positive arm (A33): correspondence changes generated inside the system, judged by held-out control and viability against requirements fixed independently of it (TERM-097), as CLAIM-532’s test asks.
The study is still proposed.