Cluster Pairing and Geometric Frustration in CCA Sticking#

experiments.md established that no search-strategy modification to CCA sticking — rotation modes, candidate scoring, pair prefilters, Γ-expansion, FFT docking, soft relaxation — produces a measurable difference in hard-regime success rates. All of these operate within a fixed, already-chosen pair of clusters at a fixed, scaling-law-derived contact distance γ. This page examines a variable none of them touch: which clusters are paired in the first place.

Motivation#

pyfracval/cca/pairing.py::_generate_pairs chooses merge partners by greedy first-fit: for each cluster, the first later cluster (in arbitrary index order) that passes a loose feasibility gate is taken, and the search stops. pyfracval/cca/aggregator.py::_run_iteration then attempts to stick each chosen pair; if any single pair fails, the entire round is aborted and the PCA/CCA attempt restarts from scratch with a fresh shuffle, discarding every other pair that stuck successfully in that round.

This leaves open a question the earlier retrospective did not address: when a hard-regime run fails, is it because no collision-free configuration exists for that cluster pool (frustration is fundamental, as concluded for search strategy), or because greedy first-fit selected a poor partner for one cluster while a different pairing of the same pool would have succeeded?

Method#

benchmarks/pairing_frustration_probe.py runs single-shot PCA/CCA trials (no internal retry, so each seed maps to exactly one outcome). Whenever a trial fails, a census is run on the exact cluster pool at the failing round:

  1. For every pair (i, j) in the pool, the production sticking path (_perform_cca_sticking) is attempted, with three independent retries per pair to rule out chance, and the outcome recorded, producing a feasibility graph.

  2. The graph is tested for a perfect matching (every cluster paired, or exactly one left over as the pass-through “odd one out” CCA already supports) via brute-force matching with memoization. Round pool sizes are small (bounded by roughly 1 / n_subcl_percentage, ~11 for the default, independent of N), so this is exact and cheap; the Blossom algorithm is not needed at this scale.

  3. The exact pair the real run attempted is re-tested, to distinguish “this pair required a genuinely different partner” from “this pair would have worked on retry, with no repartnering needed.”

The census consumes additional draws from the shared RNG. Its bit-generator state is saved and restored around the census so the outcome of the real run downstream is not perturbed.

Results#

40 single-shot trials per regime, N=128:

Regime

Params

Success rate

CCA failures

Rescuable by pairing

Universally frustrated

Hard

Df=2.25, kf=0.95, σ=1.9

2.5%

39

38 (97.4%)

1 (2.6%)

Easy control

Df=1.8, kf=1.0, σ=1.5

100%

0

-

-

The 2.5% single-shot rate is lower than the 16.7% figure reported in experiments.md for the same nominal regime because that figure includes the internal 20-attempt retry loop each real CLI/run_simulation call uses; this probe bypasses that loop to obtain a clean seed-to-outcome mapping. The two are different metrics, not a contradiction.

Characteristics of the failing rounds:

  • Every failure occurs at the first CCA round — the initial ~11 PCA subclusters merging down to ~6 — rather than at later rounds with a handful of large clusters.

  • The feasibility graphs are dense, not sparse: edge density ranges 40–95% of all possible pairs (median ~70%). Most pairings of the pool succeed; greedy first-fit selects one that does not and the round is discarded.

  • The killing pair’s degree in the feasibility graph is almost always well above zero (e.g. [9,8], [7,10], [10,10]): the cluster that caused the round to fail typically had other viable partners that greedy first-fit never considered.

  • Of the 38 rescuable failures, 20 (53%) require a genuinely different partner: re-testing the exact pair the real run attempted also failed on census. These cases are not explained by retrying with a different rotation; a different pairing choice is required.

Raw data: benchmark_results/pairing_frustration_probe.json.

Discussion#

The earlier conclusion that frustration is fundamental and no search strategy helps is correct for everything that was tested, but pairing choice was outside its scope, and the present data identify it as the relevant lever. Round pools are small (~11 clusters), failures concentrate almost entirely at round 1, and the feasibility graph is dense enough that a different pairing strategy — a true matching in place of greedy first-fit, or backtracking to a different partner on merge failure instead of aborting the whole attempt — has substantial, low-cost leverage on hard-regime success rates.

hard_regime_boundary_sweep.md maps the Df/kf/σ/N boundary around the hard regime on the unmodified implementation, forming the baseline against which a pairing-choice fix is evaluated.

Status#

This page documents a diagnosis, not a fix. The follow-up implementations and their outcomes are reported in matching_pairing.md (negative result) and backtracking_pairing.md (adopted).