Esoteric Maneuverability Score (Equations and variables)

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.