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Created page with "== Esoteric Maneuverability Score (Equations and variables) == This article compiles equations and variables from Esoteric Maneuverability Score and linked concepts: Methodological Foundations for Probabilistic Geo-Temporal Timelines, Network Gravity in Intellectual History, Argument from Silence in Bayesian Historiography, Peripatetic Esotericism. Equations are listed with source; variables include derivation/calculation subsections. No new formalism..."

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== Esoteric Maneuverability Score (Equations and variables) ==
This article compiles equations and variables from [[Esoteric Maneuverability Score]] and linked concepts: [[Methodological Foundations for Probabilistic Geo-Temporal Timelines]], [[Network Gravity in Intellectual History]], [[Argument from Silence in Bayesian Historiography]], [[Peripatetic Esotericism]]. Equations are listed with source; variables include derivation/calculation subsections. No new formalisms introduced; focus on extraction and explication.

=== Equations ===
From [[Esoteric Maneuverability Score]]:

EMS := \int_{t=0}^{T} P(m_t | e_t, r_t, n_t) , dt / T (normalized Bayesian posterior over lifespan)
r_t = 1 - \exp(-\lambda d_t) (risk multiplier)

From [[Methodological Foundations for Probabilistic Geo-Temporal Timelines]]:

P(H|E) = \frac{P(E|H) P(H)}{P(E)} (Bayes' theorem for location hypothesis)

From [[Network Gravity in Intellectual History]]:

G_{ij} = \frac{m_i m_j}{d_{ij}^2} (gravity between nodes)
P(location_i | associates) \propto \sum G_{ij} (proportional posterior for position inference)

From [[Argument from Silence in Bayesian Historiography]]:

L = \frac{P(E|H)}{P(E|\neg H)} (likelihood ratio; posterior adjustment P(H|E) \downarrow if L << 1 and E absent)

From [[Peripatetic Esotericism]]:

No explicit equations.

=== Variables ===
Comprehensive list: d_{ij}, d_t, e_t, E, G_{ij}, H, L, m_i, m_j, m_t, n_t, P(E), P(E|H), P(E|\neg H), P(H), P(H|E), P(location_i | associates), P(m_t | e_t, r_t, n_t), r_t, t, T, \lambda, \neg H.

==== d_{ij} ====
Inter-node distance in [[Network Gravity in Intellectual History]] (km or affiliation divergence). Derived from gazetteers ([[World Historical Gazetteer]]) or confessional metrics (e.g., 0 for same faith, 1 for adversarial). Calculated via geodesic formulas (Haversine) or categorical scaling; input to G_{ij}.

==== d_t ====
Distance to threat loci at time t in [[Esoteric Maneuverability Score]] (km). Derived from geo-temporal timelines; priors from inquisitorial centers (e.g., Rome=0). Calculated as min Euclidean distance to known persecution sites, overlaid in QGIS.

==== e_t ====
Archival evidence density at t in [[Esoteric Maneuverability Score]] (count/km^2 or normalized 0-1). Derived from source hierarchies (autographs=1.0). Calculated by aggregating weighted evidence within t-window, using Nodegoat ingestion.

==== E ====
Evidence in Bayesian contexts ([[Methodological Foundations for Probabilistic Geo-Temporal Timelines]], [[Argument from Silence in Bayesian Historiography]]). Derived from archival triangulation. Calculated as binary (present/absent) or weighted sum per hierarchy.

==== G_{ij} ====
Gravity between i,j in [[Network Gravity in Intellectual History]]. Derived from masses and d_{ij}. Calculated directly as (m_i m_j)/d_{ij}^2; summed for inference.

==== H ====
Hypothesis (e.g., location) in Bayesian equations. Derived from geo-temporal priors. Calculated contextually (e.g., binary true/false); input to P(H|E).

==== L ====
Likelihood ratio in [[Argument from Silence in Bayesian Historiography]]. Derived from P(E|H)/P(E|\neg H). Calculated numerically; thresholds L<0.1 flag uncertain.

==== m_i, m_j ====
Node masses in [[Network Gravity in Intellectual History]] (publication count, centrality). Derived from prosopographies (e.g., PageRank in EMLO). Calculated via graph algorithms in NetworkX.

==== m_t ====
Maneuver probability at t in [[Esoteric Maneuverability Score]] (>50km relocation). Derived from timeline P(m_t | ...). Calculated via conditional Bayesian update.

==== n_t ====
Network gravity at t in [[Esoteric Maneuverability Score]] (weighted associates). Derived from subgraphs. Calculated as \sum G_{ij} over cohort, per [[Network Gravity in Intellectual History]].

==== P(E) ====
Marginal evidence probability. Derived as P(E|H)P(H) + P(E|\neg H)P(\neg H). Calculated via law of total probability.

==== P(E|H) ====
Likelihood of E given H. Derived from source scope (e.g., 0.7 mention rate). Calculated empirically from cohorts.

==== P(E|\neg H) ====
Likelihood of E given not H. Derived inversely from P(E|H). Calculated similarly, often near 0 for strong silence.

==== P(H) ====
Prior probability of H. Derived from baselines (e.g., 0.3 mobility). Calculated from historical cohorts.

==== P(H|E) ====
Posterior probability. Derived via Bayes' theorem. Calculated numerically in PyMC.

==== P(location_i | associates) ====
Posterior location given associates. Derived proportionally from \sum G_{ij}. Calculated via normalization.

==== P(m_t | e_t, r_t, n_t) ====
Conditional maneuver posterior. Derived via Bayesian network. Calculated by updating priors with e_t, modulated by r_t, n_t.

==== r_t ====
Risk prior at t. Derived from proximity to threats. Calculated as 1 - exp(-\lambda d_t).

==== t ====
Time index (years) in integrals. Derived from lifespan segmentation. Calculated discretely (e.g., annual bins).

==== T ====
Total lifespan (years). Derived from biographical data. Calculated as death - birth year.

==== \lambda ====
Persecution intensity scalar in r_t (events/km). Derived from historical rates (e.g., 0.01 for Inquisition zones). Calculated from archival event densities.

==== \neg H ====
Negation of H. Derived logically. Used in likelihood ratios.

Esoteric Maneuverability Score (Equations and variables) - Revision history