Definition
| symbol | meaning | where it is used |
|---|---|---|
| δ (spectral) | the gap separating a cluster of singular values, or a block of strong couplings, from the rest | CLAIM-164; Simon’s near-decomposability, LIT-905 |
| ε (spectral) | the size of couplings across a block’s edge, or of a perturbation | CLAIM-164 (Davis–Kahan bound ‖δT‖/δ) |
| δ (Bayesian) | the posterior effect μ of a candidate direction | CLAIM-154 |
| ε (Bayesian) | the posterior standard deviation σ of that direction | CLAIM-154 |
| d′ | δ/ε in the Bayesian sense, μ/σ | CLAIM-154 |
| Occam | ln(s²/σ²): prior-to-posterior variance ratio, the information the data added | CLAIM-154 |
| τ | the threshold, τ² = Occam; reify when d′ > τ | CLAIM-154, CLAIM-157 |
| D | downward causation: a macro-variable’s unique power to predict individual parts’ futures (ΦID) | TERM-051, CLAIM-158, LIT-025 |
| G | causal decoupling: a macro-variable’s unique power to predict its own future (ΦID) | same |
| Φ | monodromy around a cycle of contexts, α₁₂ + α₂₃ + α₃₁ | CLAIM-153 |
| γ | a coherence measure whose conservation along the system’s own dynamics is persistence | CLAIM-161 |
| V, X | macro-variable and its micro-parts | TERM-051 |
The two senses of δ/ε. The threshold criterion (CLAIM-157) joins them. It uses the spectral sense to find a block, and the Bayesian sense to price it. MOM-CLM-160 identifies the two: ε as the posterior standard deviation of a direction is its Cramér–Rao floor, and δ as the posterior effect is the gap. That identification holds when the candidate direction is a parameter of a fitted model, so the spectral gap of a coupling matrix must first be expressed as an estimated parameter with a posterior. It is an assumption of the criterion, stated here, and it is not shown in general.
What it is not
- Not new mathematics. It fixes symbols the claims already use. A claim that needs a symbol in a new sense adds a row here, or supersedes this term, rather than redefining the symbol in its own text.