# CCT Coordination-Order Challenge — Phase-0 Report

**Original working title:** CCT Nonseparable Programmability / Correlation-Order Challenge  
**Status:** Completed developmental prospective holdout.  
**Scope:** Standard-equation synthetic methods benchmark; not novel physics, a universal invariant, material evidence, or hardware performance.

## Frozen question

Can a common intervention ladder predict the minimum organization required by
a control program before full policy search, while every evaluated policy has
the same horizon, amplitude alphabet, per-channel energy (`4.0`) and total
energy (`12.0`)?

The descriptor used eight static factorial interventions, six directed
sequence interventions, and one candidate/ablation pair on four calibration
seeds. Predictions were checksum-frozen before the 16 pilot seeds were opened.

## Prospective results

| Holdout system | Frozen CCT handle | Empirical minimum handle | Predicted effect | Decision | Order | Relabeling |
|---|---|---|---|---:|---:|---:|
| linear_relaxation | static:0:+1 | static:0:+1 | no_structured_advantage | PASS | PASS | PASS |
| quadratic_mixer | static:0*1:+1 | static:0*1:+1 | access | PASS | PASS | PASS |
| cubic_mixer | static:0*1*2:+1 | static:0*1*2:+1 | access | PASS | PASS | PASS |
| path_dependent_gate | temporal:0>1:+1 | temporal:0>1:+1 | access | PASS | PASS | PASS |
| null_response | none | none | no_structured_advantage | PASS | PASS | PASS |

Aggregate:

- Correct prospective effect decisions: **5/5**.
- Correct minimum-order decisions: **5/5**.
- Correct destructive-ablation directions: **5/5**.
- Representation checks: **5/5**.
- Prospective-decision gate: **PASS**.
- Cross-class transfer gate: **PASS**.
- Numerical gate: **PASS**.

## Incumbent closure

The sector-native composite—full static factorial/Volterra-style interaction
analysis plus an ordered-sequence commutator—made
**5/5** correct decisions using
the same 16 intervention types per calibration seed. The CCT distinctiveness
gate therefore **did not pass**.

This is not a defective negative result. It shows that:

1. a coordination-order ladder can prospectively distinguish when correlation
   structure is useful, what order is required, and which matched ablation
   should destroy the effect;
2. total energy and individual channel energy are insufficient to specify
   programmability in the higher-order and path-dependent cases;
3. this first descriptor is presently an integrated restatement of established
   factorial interaction and switched-system response analysis, not yet a
   uniquely CCT quantity.

## What is earned

Inside these declared models, the Phase-0 challenge establishes a functioning,
representation-checked benchmark for **coordination-dependent
programmability**. It separates:

- no structural advantage in a first-order system;
- pair-correlation-dependent access;
- third-order-correlation-dependent access;
- temporal-order-dependent access; and
- a null case where no available program reaches the target.

It does not establish that `k*` is basis-independent in general, that the
descriptor beats the strongest established workflow, or that the result
transfers to real hardware. The next phase should freeze the same reporting
contract on a genuinely different, externally specified model or dataset and
seek either lower intervention cost, a better prospective decision, or a
resource/observer effect that the incumbent composite omits.

## Integrity

- Frozen manifest: `d9b6ee3d2249e5958097a64989fab4851e85fd0c3cfd54f660d3e3d24f4bf426`.
- Evaluation records: `1600` expected policy/ablation rows.
- Energy match: **PASS**.
- Numerical comparisons: `40`; label disagreements:
  `0`; maximum score change:
  `0.002771`.
