feat: stochastic-process discrimination + process→regime→option→archetype crosswalk

[mdheller]

Follow-on to #50. Builds on the merged MemoryRegimeCharacterization and reuses its estimators — scripts/memory_regime_estimators.py is unchanged (pure reuse of Hurst / Lyapunov / kurtosis / receipt). Adds stochastic-process discrimination and a total process↔regime↔option-family↔archetype crosswalk.

OU vs traditional Markov

New Ornstein-Uhlenbeck estimator: dX=θ(μ−X)dt+σdW → estimate θ, long-run μ, and half-life = ln2/θ. OU autocorrelation decays exponentially (e^{−θτ}) with a finite timescale, so OU is the canonical short_decaying / mean-reverting regime and is anti-persistent — its variance-time (aggregated-variance) Hurst is < 0.5 because k-step-move variance saturates instead of growing like a random walk. Distinguished from discrete-state Markov regime-switching (Hamilton): both are "Markov", but OU is a continuous mean-reverting diffusion with a timescale; regime-switching is memoryless jumps between discrete states (regime memoryless/state-only). Fractional-OU (OU driven by fBm) is provided as the hybrid = mean-reversion + long memory.

Process-family discriminator

Classifies a process path/observable among {brownian_gbm, markov_regime_switching, ornstein_uhlenbeck, fractional_brownian_motion, hawkes, jump_levy}, reusing the Hurst/Lyapunov estimators and adding the OU fit, a variance-time diffusion Hurst, and a jump/heavy-tail test.

VERIFIES (seeded, deterministic, robust across seeds): OU(θ∈{0.7,0.3,1.0}) → ornstein_uhlenbeck/short_decaying with θ̂>0, finite half-life (θ=0.7 → θ̂≈0.74, half-life≈0.93), anti-persistent variance-time H≈0.05 (<0.5); fBm(H=0.7) → fractional_brownian_motion/long_memory; GBM/Hawkes/jump-Lévy paths → their families. REJECTS: OU mislabeled long_memory; θ≤0 called mean_reverting; fBm mislabeled memoryless; OU missing ou_params.

The crosswalk (reference doc + typed mapping with teeth)

process family	memory regime	kernel	option-model family (anchor)	archetype
brownian_gbm	memoryless	delta	Black-Scholes	efficient-market / no-edge
markov_regime_switching	memoryless (state)	delta	regime-switching models	greed/fear & bull/bear shift
ornstein_uhlenbeck	short_decaying	exponential	Vasicek/Hull-White/CIR/Heston/Stein-Stein	contrarian / value / market-maker (fade extremes)
fractional_brownian_motion	long_memory	power_law	rough volatility (GJR) / rBergomi / MMAR	trend-follower / momentum / Elliott
hawkes	short_decaying (self-exciting)	exponential	Hawkes / jump-clustering / contagion	herd / FOMO / reflexive
jump_levy	memoryless (fat-tail jumps)	delta	Merton-jump / variance-gamma / CGMY / smile-tail	shock / crash / tail-hunter

Crosswalk teeth: the mapping is asserted total (every process family present) and coherent (each entry's regime matches the canonical process→regime map); the anchor option families are checked (OU→Vasicek/Heston, fBm→rough-vol). REJECTS a crosswalk mapping OU↔long_memory or fBm↔memoryless, and a non-total crosswalk (a family missing).

Rough-vol → vol surface

The fractional_brownian_motion ↔ rough volatility tie makes the Hurst axis govern volatility itself (Gatheral-Jaisson-Rosenbaum, vol is fractional H≈0.1), unifying the long-memory work with the vol surface (economic-prophet #44) by reference; the fBm risk_distribution_F carries the Hurst H a rough-vol calibration / the RAROC risk(F, reference, kernel, horizon) interface consumes.

Files

scripts/process_family_estimators.py, schemas/process-family-characterization.schema.json, schemas/process-regime-crosswalk.schema.json, examples/process-family/ (5 valid + 4 invalid), examples/process-regime-crosswalk/ (1 valid + 3 invalid), scripts/validate_process_family_crosswalk.py, docs/architecture/process-regime-crosswalk.md, workflow + Makefile + README.

Local: make validate-process-family-crosswalk → VERIFIES (9 seeded paths) + REJECTS (7 fixtures) + crosswalk totality/coherence + receipt teeth all green. Deterministic, stdlib-only. Records carry proof-artifact-spine SHA-256 receipts (FIPS-180-4 algorithm; not a FIPS-140 module).