Loopy Belief Propagation

No LBP moves yet. Run LBP_APPLY_BELIEFS=true inference/.venv/bin/python scripts/ops/run_loopy_belief_propagation.py on the droplet.

Per-iteration update for each non-fixed node c with parent edges (p_i → c):
  α_i = edge.p_dst_given_src       # P(c=T | p_i=T)
  β_i = edge.p_dst_given_not_src   # P(c=T | p_i=F)
  edge_implied_prob = belief[p_i] × α_i + (1 − belief[p_i]) × β_i
  edge_logit = logit(edge_implied_prob)

  # Pool incoming edge implications: geometric mean of odds
  mean_edge_logit = mean(edge_logit_i)

  # Mix with intrinsic prior (current_prob from Part 2 blend)
  mixed_logit = w_intrinsic × logit(intrinsic[c]) + (1 − w_intrinsic) × mean_edge_logit

  # Damp to prevent oscillation in cycles
  new_logit[c] = α_damp × mixed_logit + (1 − α_damp) × old_logit[c]
  new_belief[c] = sigmoid(new_logit[c])

Convergence: max |Δbelief| < ε across all nodes.

Parameters (defaults):
  damping       α_damp      = 0.5
  intrinsic mix w_intrinsic = 0.5
  max_iters                 = 50
  ε convergence             = 0.01

Edge conditional defaults (if NULL):
  prereq:  P(c|s=T) = clamp(c.prior, 0.05, 0.95)   P(c|s=F) = 0.05
  killer:  P(c|s=T) = 0.05                          P(c|s=F) = clamp(c.prior, 0.05, 0.95)

Fixed inputs (belief never updates):
  thesis_killer nodes (TK01..TK15) — root exogenous risks set by analyst.

NOT pure Pearl LBP — approximate damped log-opinion-pool with intrinsic
anchoring. Documented in futurepredictiontool.md Phase 4 Part 4.