CAMS Temporal Inelasticity

Pilot study · Cuba (1990–2026) · Iceland (2000–2026) · ASPI (2003–2026) · 2026-08-15

1. The Problem: JUNO Bonds Are Rank-1

The JUNO v1.2 bond formula factors completely into a product of node-level weights:

Bij = √(qi · qj) × 2−(Si+Sj)/10 = [√qi · 2−Si/10] × [√qj · 2−Sj/10] = wi · wj

The bond matrix B = w⊗w is the outer product of a single vector with itself. It is rank-1. Every row is proportional to every other row. There is no pair-specific information anywhere in the matrix — only node-level weights. lam2 (Laplacian algebraic connectivity) computed from this matrix is therefore also algebraically constrained rather than empirically discovered.

Consequence: the current JUNO framework can identify which nodes are strong or weak, but cannot detect whether Helm–Archive is more or less tightly coupled than Helm–Lore. Both bonds are entirely determined by the node weights. The graph structure is not discovered from data; it is imposed by the formula.

2. Temporal Inelasticity: A Pair-Specific Coupling Measure

If history becomes structure (the path-dependence thesis), coupling should leave a measurable trace in how nodes move relative to each other over time. A strongly coupled pair should show a stable relative configuration — it can move through node-score space together while resisting being pulled apart.

Rij(t) = xi(t) − xj(t) ← relative configuration (Node Value difference) ΔRij(t) = Rij(t+1) − Rij(t) ← year-on-year change in relative position Iij = 1 − Var(ΔRij) / [Var(Δxi) + Var(Δxj)]

Interpretation: Iij near 1 → the pair's relative position is extremely stable despite individual node movement (rigid coupling). Iij near 0 → relative position varies as much as the nodes themselves (no coupling beyond coincidental co-movement). Negative → movements amplify divergence.

Coupling classification

ClassConditionMeaning
RigidIij > 0.7Relative configuration resistant to displacement
Loosely associated0.3 – 0.7Some tendency to co-move, separable under pressure
Directionally constrained0.3 – 0.7 and |asymmetry| > 1.0One node consistently drives the other
Weakly coupledIij < 0.3Nodes move largely independently

Directional asymmetry (conditional response)

CRj←i = mean Δxj(t+1) over years where |Δxi(t)| > 1σ Asymmetry = |CRj←i| − |CRi←j| (positive = i drives j)

3. Universal Findings

Consistent across Cuba, Iceland, and ASPI — three radically different system types.

Most universally rigid pairs (cross-society means)

PairMean IStdLoop
Stewards–Flow0.8220.101Cross
Hands–Flow0.7400.176Fast–Fast
Stewards–Hands0.7300.176Cross
Helm–Archive0.6500.172Slow–Slow
Hands–Archive0.6290.053Cross

The economic triad is the universal structural core. Stewards–Flow–Hands forms the most rigid cluster in all three societies. Finance, commerce, and labour stay tightly coupled regardless of political system, size, or entity type. This suggests economic coordination is the load-bearing architecture of institutional systems.

Shield is universally elastic. Shield is the most weakly coupled node in Cuba, Iceland, AND ASPI — three completely different system types. Cuba Shield–Stewards I=0.102; Iceland Shield–Hands I=0.099, Shield–Flow I=0.101; ASPI Shield–Craft I=0.225. Security/coercive functions move independently of institutional coordination in all three cases. Shield either leads discontinuously at crisis moments or is insulated from normal institutional flux. It does not stay in lockstep with anything.

Slow–Slow pairs are more inelastic than Cross-loop pairs. The hypothesis that cross-loop pairs would be most rigid (as the stability mechanism) was incorrect. Slow nodes co-move because they share longer institutional timescales — not because cross-loop coupling is stronger. Cross-loop stability may only manifest during crisis intervals, not across full-trajectory averages.

4. Society-Specific Signatures

Cuba
Craft–Hands I=0.911 ★
Stewards–Hands I=0.804
Craft–Flow I=0.778
Most rigid in dataset. Command economy: production and labour structurally locked. Flow receives asymmetric pull from Craft, Hands, Helm, Lore — everything drives commerce, commerce drives nothing.
Iceland
Stewards–Flow I=0.939 ★
Hands–Flow I=0.900
Helm–Archive I=0.847
Small open economy: finance and commerce are most tightly coupled. Helm–Archive rigid — strategic direction and memory stay aligned. Shield is directionally dominant when it moves (drives Stewards, Flow, Archive) but decoupled in normal times.
ASPI
Stewards–Flow I=0.771
Helm–Flow I=0.680
Shield–Archive I=0.672
Most elastic of the three — only 1 rigid pair. Relationships between functions reorganise readily. Stewards dominates Flow asymmetrically (asym=+0.825). Craft–Hands are loosely coupled — unusual for an organisation.

5. Theoretical Implications

Elasticity structure as the deeper invariant

If a society can traverse large regions of node-score space while its Iij matrix remains stable, then the elasticity structure is more characteristic of the society than its current node scores. "What kind of system this is" may be better described by the 28-element inelasticity vector than by the 32-element contemporaneous CAMS profile. This would make coupling structure the deeper invariant — closer to what we mean by "institutional character."

Path dependence as measurable inelasticity

Path-dependent constraint predicts that historically embedded couplings should be more inelastic than recently formed ones — even when absolute node scores are similar. Ancient Forest societies should show higher mean Iij than Greenhouse Garden or Ruptured societies, particularly in Slow–Slow and Archive-involving pairs. This is a testable consequence that extends the Robson Gauge into a trajectory-based prediction.

The Shield anomaly needs theory

The universal Shield finding is not predicted by any current CAMS theory. Three possible explanations deserve testing: (1) coercive functions respond to a different threat signal than the rest of the system, so they move asynchronously; (2) Shield is subject to political insulation that decouples it from economic and cultural dynamics; (3) Shield scores are inherently noisier to assess, and the elasticity is partly a measurement artefact. The fact that Shield becomes directionally dominant in Iceland during stress (when it moves, it drives Archive, Stewards, Flow) suggests explanation (1) or (2) rather than (3).

6. Next Steps

Add societies Run on USA, Germany, China, Sweden, Thailand (telescope_2 dataset) to increase cross-society n to 8+.
Crisis windows Recompute Iij separately for crisis intervals and normal intervals to test whether cross-loop rigidity appears under stress.
Robson link Correlate η_soil with mean Iij across Archive/Lore pairs — tests whether Robson Gauge is already capturing inelasticity implicitly.
Shield theory Design a targeted test: does Shield elasticity predict praetorian basin transitions better than Shield node value alone?
cams-calc v1.3 Add Iij computation to cams-calc for societies with ≥10 years of data. Output as Block 3.


CAMS Temporal Inelasticity Pilot · cams_inelasticity.py · wintermute repo · 2026-08-15