Per-Stage Probability Mechanisms — Cross-Domain Reference

Status: Reference doc. Per-stage mechanism tables for the X-genesis family — abiogenesis, ontogenesis, phylogenesis, technogenesis, sociogenesis. Each table maps stages to recommended probability models (per probability-model-architecture.md) so analysts can populate population_context.v1.transitions[].probability_model correctly for whichever domain they're analyzing.

Pairs with: probability-model-architecture.md (the registry design + ProbabilityResult interface), framework-synthesis-cross-domain-and-population.md (the cross-domain manifestation framing), summary-abiogenesis-complete.md §2-3 (the corpus's three-layer model + proto-SSA hardening framework).

TL;DR: Different stages of any developmental trajectory have different probability mechanisms — chemistry rules at R0, autocatalytic threshold at R1.3, vesicle group selection at R1.7, frozen accident at R1.9→R2, Darwinian post-R2. The same pattern recurs in ontogenesis (canalized developmental gates), software adoption (network-effect cascades), cultural development (transmission with drift). The framework's job is to declare which mechanism applies at each stage; this doc is the cross-domain menu.

1. Abiogenesis (biology, R0 → R2-LUCA)

The canonical reference. All stage characterizations drawn from summary-abiogenesis-complete.md §2.3 + exploration-genesis-transition-molecular-resolution.md §3 + exploration-code-structure-and-pre-R2-feedback.md §2.

Mechanism notes

• chemistry_kinetic dominates the early stages (R0 → R1) where molecular dynamics governs reaction rates. ΔG-driven Boltzmann factor + catalyst enhancement + Bernoulli population sampling.
• autocatalytic_threshold is THE distinctive transition at R1 → R1.3. Below threshold, fidelity improvement is linear; above, exponential. The bootstrap loop is the canonical autocatalytic instance.
• vesicle_group_selection at R1.7 captures Eigen 1971's error-threshold solution: open-pool genomes get swamped by parasites; vesicle compartmentalization + group selection on vesicles eliminates parasites and stabilizes the genome. Population genetics, not Bernoulli.
• frozen_accident is the singularity. The genetic code crystallizes once, in one lineage; competitive exclusion locks it. First-success Bernoulli with code-dependency scaling.
• darwinian is the post-R2 regime where heritable variation × differential reproduction takes over. All subsequent biology lives in this regime.

Distribution shape (probability funnel)

Per summary-abiogenesis-complete.md §2.3, the funnel narrows and broadens at different stages:

Pre-R0  R0→R0.5  R0.5→R1  R1→R1.7  R1.9→R2  R2→LUCA  LUCA→eukaryogenesis
 ████   ███      ██       █         ▎        ████       █
 wide   narrowing narrow  narrowing narrow   broadening narrowing

The autocatalytic narrowing at R1→R1.7 and the singularity at R1.9→R2 are where the funnel is tightest. The framework's job is to model these mechanisms specifically rather than treating them all as Bernoulli.

2. Ontogenesis (biology, fertilization → mature organism)

A SINGLE organism's development. N=1 globally, but each cell is a sub-instance with its own developmental gates.

Mechanism notes

• developmental_canalization (NEW model class — author when ontogenesis analysis warrants it) — Waddington's epigenetic landscape. Each gate has a specific morphogen-gradient threshold; either canalized (deterministic) or chreodic (probabilistic but constrained). Per-trial probability is HIGH (near 1) because development is reliable.
• N=1 changes the framework usage: instead of "many parallel experiments," it's "many canalized cells in one organism." The Bernoulli model with N=1 is degenerate; what matters is whether the development reaches each gate at all.
• The probability funnel for ontogenesis is QUITE NARROW throughout — developmental robustness is the defining property. Failure modes are at boundary conditions (gastrulation defects, etc.) where canalization breaks down.

3. Phylogenesis (biology, species evolution)

Multi-organism, multi-generation. N = species population × generations. Standard population genetics applies.

Mechanism notes

• darwinian is the steady-state model for phylogenesis.
• Major transitions (endosymbiosis, multicellularity, eukaryogenesis) are frozen_accident analogs — one-shot, irreversible. The Margulis-style endosymbiosis events fit here.
• bottleneck / genetic_drift capture stochastic narrowing during pop crashes.
• The framework supports analyzing phylogenetic trajectories at the species level (manifestation = species snapshot) with population genetics models.

4. Technogenesis (entity arrangement, software adoption)

Multi-organization, multi-release-cycle. N = adopters or organizations.

Mechanism notes

• network_effects (NEW model class) — value scales with users (Metcalfe's law, weak Reed's law variants). Per-trial probability of adoption rises with current adopter count. Below threshold, adoption is rare; above, it tips.
• autocatalytic_threshold at the Rogers tipping point (~16%) is structurally identical to the abiogenesis bootstrap. Different domain, same mechanism.
• frozen_accident at standardization: once a wire format / protocol crystallizes (HTTP, TCP/IP, JSON), competing alternatives can't displace easily because of dependency depth. The Git format crystallization is a clean example.
• competitive_displacement (NEW) — when a new technology offers strict superiority in some dimension, adoption can flip rapidly (pager → cellphone → smartphone).

The Git evolution trajectory (data/trajectories/git-evolution.v1.json) is an existing instance of technogenesis at the entity-system level. Per-stage mechanism declarations could refine it.

5. Sociogenesis (cultural development)

Multi-person, multi-generation. N = practitioners × generations.

Mechanism notes

• transmission_with_drift (NEW) — like genetic drift but for cultural variants. Per-transmission fidelity < 1 means variants accumulate; high fidelity preserves orthodoxy.
• The mechanism table maps directly onto Henrich-style cultural evolutionary theory.
• autocatalytic_threshold for cultural epidemics: ideas spread when adoption density crosses a critical fraction of the network.

6. Cross-domain mechanism abstraction

Many of these models are the SAME structure with domain-specific parameters:

The framework should support each abstract mechanism as a registered model class. Domain-specific implementations specialize via parameters. The user's directional ask — "drop in whatever model we need" — is exactly this: same registry pattern, parameters per scope.

7. Framework usage guidelines

When authoring a population_context.v1 for a new stage:

1. Identify the dominant mechanism for the transition out of this stage (use the tables above as a menu).
2. Declare it in transitions[].probability_model.
3. Provide parameters in transitions[].model_parameters.
4. If the model isn't implemented yet — declare it anyway. The fallback chain transparently uses population_sampled until you author the model. The fallback is recorded in the output's fallback_chain.
5. Cite corpus or literature in transitions[].notes and population_context's source_documents.

When implementing a new model:

1. Read the design doc §2.1-2.5 (probability-model-architecture.md).
2. Implement the function in compute/lib/probability_models.py (or a domain-specific file like probability_models_chemistry.py).
3. Decorate with @register_model("name").
4. Return None for missing data — let the fallback chain catch it.
5. Set provenance and notes so analysts can trace where values come from.

8. Status of model implementations

As of

Future model classes (named for completeness; implement when warranted):

• developmental_canalization (ontogenesis)
• network_effects (technogenesis)
• competitive_displacement (technogenesis, sociogenesis)
• transmission_with_drift (sociogenesis)
• genetic_drift (phylogenesis)
• bottleneck (phylogenesis)
• combinatorial_search (any rare-event search-space transition)

9. Open questions / known limitations

1. Multi-domain transitions. When a transition involves multiple primitives (e.g., abiogenesis R≥1.7 ∧ Cmp≥1 ∧ P≥0.5), should the model apply to the joint move or be decomposed? Currently the model receives the joint transition and decides; per-primitive decomposition is a future refinement.

2. Continuous time vs discrete trials. population_sampled uses discrete N trials. chemistry_kinetic and darwinian are continuous-time. The model interface accepts both via the elapsed_time field on ModelContext. Mixing them in one analysis requires consistent time semantics — flag this in analysis script if needed.

3. Distributions vs point estimates. Baseline models return point values. More sophisticated models might return distributions; the ProbabilityResult.distribution field accommodates this. Downstream compute either uses point estimate or samples the distribution.

4. Reverse-walk direction. The forward+Bayesian-backward propagation should apply the registry in BOTH directions. Models should accept a direction parameter (forward/backward) — currently passed via ModelContext.direction. Implementation is consistent for the baselines; future models should honor the parameter.

5. Cross-arrangement composition. When two arrangements meet (Sc4 coupling), models should compose. Probably via the registry on a product arrangement; needs validation when first cross-arrangement walk is authored.