CAMS Protocol R (CAMS-R-2026-001): preregistration, single-run results, and rubric erratum final
Repairing the Instrument Strengthened the Signal: Protocol R2, a Preregistered Replication of CAMS Relational Structure with Co-Primary Detrended Endpoints Study ID: CAMS-R2-2026-001 (CAMS-TEST-1.0 §8, co-primary endpoints) Authors: K. McKern (ComplexityWorkz, Sydney) Date: 2026-09-20 Status: Preregistered, single holdout run, STRONG_PASS on all gates Predecessor: CAMS-R-2026-001 (doi:10.5281/zenodo.22852600) Archive: Zenodo concept 10.5281/zenodo.22852374 (v3 pre-run: 10.5281/zenodo.22853455) Abstract CAMS-R-2026-001 established that the 28-edge node co-movement vector of societal dynamics generalises across independent rosters (raw ρ = 0.7417, all gates passed), but with two registered qualifications: only 9 of 12 holdout societies were eligible — three panels carried flat-anchored node-metrics from a scoring-rubric defect — and a report-only common-trend control collapsed the correlation to 0.2447, leaving the edge-specific relational component unresolved. Protocol R2 was registered before any new data existed to close both qualifications. The four casualty panels had only their flagged flat series re-scored under an anti-saturation rubric amendment by scorers operating under a disclosed blindness limitation; the detrended endpoint was promoted to co-primary with its gate (ρ ≥ 0.25) and a four-outcome verdict mapping fixed in advance. On the sealed 13-society vintage — the original twelve holdout societies plus the United Kingdom admitted under a registered mechanical rule — eligibility was 13/13. The raw endpoint replicated at ρ = 0.7537 (gate ≥ 0.50; permutation p = 0.000843; temporal p = 0.0001). The detrended endpoint passed at ρ = 0.7783 (gate ≥ 0.25; permutation p = 0.000025; temporal p = 0.0001) — exceeding the raw endpoint, the reverse of the R1 pattern. Leave-one-out ranges were tight on both endpoints (raw [0.725, 0.779]; detrended [0.773, 0.808]). The R1 common-trend caveat does not replicate on the repaired vintage: the relational structure of institutional dynamics generalises including its edge-specific component, and the R1 detrended collapse was likely driven in part by the measurement defect itself. Verdict per the registered mapping: STRONG_PASS. 1. Introduction The first preregistered test of the CAMS relational claim (CAMS-R-2026-001) passed every gate and still left its authors uneasy. Two qualifications were registered alongside the verdict. First, four of the twenty-six audited national panels — the United Kingdom, New Zealand, Sweden and Latvia — contained node-metrics held at a single value for decades to over a century (United Kingdom Helm Capacity = 8 for 126 years; Sweden with all eight nodes at Abstraction 10 for thirty years). This defect, filed as rubric erratum E-2026-001 (flat-anchoring), cost the study four societies. Second, and more substantively, the registered report-only common-trend control reduced the headline correlation from 0.7417 to 0.2447: most of the raw agreement between rosters was whole-of-society co-movement, and the edge-specific component — the part that distinguishes one institutional linkage from another — appeared modest. Protocol R2 was designed to close both qualifications under registration. Its design principle was that the rules must exist before the numbers: the preregistration was completed, hashed and archived before any re-scoring began, and the verdict language was fixed in advance with all four outcomes declared publishable. 2. Methods 2.1 Design R2 retains the R1 development roster and its frozen raw development vector (reused by reference; assert-verified at R2 freeze to reproduce the R1 vector exactly). The holdout roster comprises the twelve R1 holdout societies, with the three R1-ineligible panels (New Zealand, Sweden, Latvia) re-scored, plus the United Kingdom as a conditional thirteenth society, admitted if and only if its re-scored panel passed the §8 constant-series rule at sealing — a mechanical rule registered in advance. 2.2 Re-scoring under the anti-saturation amendment Only the series flagged in erratum E-2026-001 were re-scored (United Kingdom Helm K, 1900–2025; New Zealand Shield A and Archive A, 1964–2014; Sweden all-node A and Archive C, 1969–1998; Latvia Stewards C/K/S/A, 1929–1958); all other node-metrics retain R1 values byte-identically. Re-scoring used the cams-ensemble protocol (three independent passes, ensemble means) under a binding anti-saturation amendment: no node-metric may hold an identical extreme value (1 or 10) for more than five consecutive years without year-specific written justification, with a mandatory per-series constant-difference scan at scoring time. All sixteen re-scored series passed the scan with zero violations. Blindness limitation, disclosed at registration. The re-scoring agent had discovered the flat values during the R1 audit and had computed the R1 results; full blindness was impossible. The vintage was therefore registered as a draft, with an independent blind re-score registered as a desirable robustness check and any repeat run requiring a logged amendment before any R2 result was seen. 2.3 Co-primary endpoints and gates Two endpoints were registered. Raw: Spearman(dev, holdout) on the 28-edge vectors from first annual differences, gate ρ ≥ 0.50 (carried from R1). Detrended: the same computation after subtracting the cross-node mean within society/year/metric before differencing, gate ρ ≥ 0.25 — fixed at registration to demand at least the R1 observed detrended value (0.2447), chosen before any R2 holdout data existed. Each endpoint carries the R1 null models applied separately: the exact 8! = 40,320 node-relabelling permutation null and the 9,999-replicate circular-shift temporal null (seed 20261001), both gated at p ≤ 0.05. The detrended development vector was derived from the frozen R1 development panels by the registered deterministic transformation (mean −0.0874, sd 0.0876, nonconstant). 2.4 Verdict mapping (registered in advance) STRONG_PASS: both endpoints pass all gates. SYSTEMIC_PASS: raw passes; detrended fails the ρ gate but passes both nulls, or passes ρ with a null failure. WEAKENED: raw passes; detrended fails both nulls. FAIL: raw fails any gate. The mapping may not be renegotiated post-hoc. 2.5 Custodianship and execution The R2 vintage was sealed (13/13 panels passing the sealing constant-series scan, including the United Kingdom, which was thereby admitted), custody re-declared, and the pre-run state archived (Zenodo 10.5281/zenodo.22853455). The holdout side executed once. One infrastructure deviation was logged: a 300-second execution cap terminated the run during the final (detrended temporal) null; the null, verdict and sensitivity were completed in a deterministic continuation with identical seed and draw order, upstream values verified numerically identical. No new randomness, no selection, no re-computation of upstream quantities. 3. Results Eligibility: 13/13, log clean. The full roster was restored; no society required exclusion. Raw endpoint: ρ = 0.7537 (gate ≥ 0.50, PASS); exact permutation p = 0.000843 (34 of 40,320); temporal p = 0.0001 (0 of 9,999). PASS. Detrended endpoint: ρ = 0.7783 (gate ≥ 0.25, PASS); exact permutation p = 0.000025 (1 of 40,320); temporal p = 0.0001. PASS. Sensitivity (report-only): leave-one-out raw ρ ∈ [0.7247, 0.7789]; detrended ρ ∈ [0.7729, 0.8084]. No society — including the four re-scored panels or the admitted United Kingdom — moves either endpoint by more than ≈ 0.03. Verdict: STRONG_PASS (both co-primary endpoints pass all gates, per the registered mapping). Comparison with R1: raw ρ replicates almost exactly (0.7417 → 0.7537). The detrended endpoint reverses the R1 pattern: 0.2447 (report-only, 9 societies) → 0.7783 (co-primary, 13 societies), exceeding the raw endpoint. 4. Discussion Three findings matter, in ascending order of surprise. First, the R1 raw result replicates on a restored and enlarged roster at essentially the same value. The relational claim was not fragile to the roster repairs. Second, the instrument repair worked as an instrument repair should. The anti-saturation amendment, designed against the flat-anchoring failure mode, restored four panels to full eligibility with zero violations, and the corpus scan accompanying erratum E-2026-001 found the defect concentrated in the older scoring generations. The re-scored series behave like measurements: they vary, they respond to events (the United Kingdom's executive capacity dips through the IMF crisis, the ERM ejection, Brexit paralysis and the 2022 gilt crisis; Latvia's stewardship collapses in 1940 and bottoms at collectivisation), and they survive leave-one-out. Third — the finding that rewrites the R1 interpretation — the detrended endpoint did not merely clear its gate; it exceeded the raw endpoint. In R1 we warned that anyone quoting 0.74 without 0.24 was overclaiming. That warning is now withdrawn on evidence: with the flat series repaired, the edge-specific relational structure is stronger than the raw co-movement that contains it. The most plausible reading, stated as inference rather than established fact, is that the R1 detrended collapse was substantially an artefact of the defect itself: flat series inject zero-variance edges into the vectors, and the demeaning transformation amplifies their distorting effect. Repairing the rubric repaired the measurement, and the measurement shows that which-institutions-move-together is a robust, generalisable property of societal dynamics — not a by-product of shared national fortunes. The blindness limitation stands on the record. It is mitigated, not eliminated, by the leave-one-out insensitivity of both endpoints and by the mechanical nature of the sealing rules. The registered offer of an independent blind re-score remains open; on these results we judge it unlikely to alter the verdict, and we say so knowing that this judgement itself is registered. Scope discipline is