idkmesh

Mathematical evolution kernel implementation pass

Date: 2026-08-28
Repository: MSKazemi/idkmesh

Owner direction

The owner asked to continue development, make the mathematical and algorithmic foundation substantially more solid and intelligent, and implement the resulting mechanisms using GitHub Actions and other GitHub-native capabilities while keeping the work public in the repository.

Audit findings

The repository already contained substantial mathematical architecture and simulation work:

• IDKGraph as a typed temporal directed hypergraph;
• multi-objective Work Unit value and graph unlock ideas;
• quality-diversity emergence experiments;
• correlated-verifier and independence-aware aggregation experiments;
• guarded self-evolution with Pareto search, simulated annealing, replicator/bandit ideas, homeostasis, and a Lyapunov-like repository potential.

The main implementation gap was not lack of formulas. It was the distance between those formulas and the live GitHub-native evolution loop.

Two concrete weaknesses were found:

1. scripts/evolution_score.py converted events into small direct additive deltas, so uncertainty was not represented and repeated activity could look like progress by construction.
2. .github/workflows/evolution-loop.yml updated state only inside an ephemeral Actions checkout and uploaded it. A later run normally began from the checked-in seed again, so the observer did not have trusted cross-iteration memory.

Implementation

Mathematical kernel

Added scripts/evolution_math.py, a deterministic standard-library-only kernel implementing:

• Beta Bayesian soft-evidence updates, posterior variance, and conservative confidence bounds;
• reliability-weighted Bayesian/log-odds vote aggregation;
• equicorrelation effective sample size for correlated evidence;
• normalized Shannon entropy;
• Jensen-Shannon divergence;
• Pareto non-dominated sorting;
• NSGA-II-style crowding distance;
• multiplicative-weights / discrete-replicator policy updates with an exploration floor;
• UCB1-style exploration allocation;
• discounted downstream graph unlock value;
• quadratic homeostatic/Lyapunov-style potential and non-increase condition.

Every algorithm family has an executable deterministic demonstration.

Tests

Added tests/test_evolution_math.py covering:

• posterior movement and uncertainty reduction;
• entropy/JSD boundary cases;
• loss of effective sample size under correlation;
• correlation-aware vote aggregation;
• Pareto fronts and crowding;
• normalized multiplicative-weights updates with preserved exploration;
• UCB exploration of unseen arms;
• graph unlock ordering;
• Lyapunov/homeostatic improvement;
• deterministic demo replay.

Versioned mathematical policy

Added state/evolution-math-policy.json so coefficients are data rather than hidden code constants. It contains:

• Bayesian prior/evidence parameters;
• signed event evidence hypotheses;
• homeostatic targets/scales/weights;
• UCB exploration coefficient;
• multiplicative-weights learning/exploration parameters;
• diversity thresholds;
• graph unlock decay;
• Pareto objective directions.

These values remain hypotheses and must be calibrated against delayed real outcomes.

Evolution scorer v2

Reworked scripts/evolution_score.py so events produce signed soft evidence rather than additive score declarations.

The scorer now:

• migrates old v1 state into Beta beliefs if needed;
• updates posterior beliefs by dimension;
• reports posterior means and confidence bounds;
• tracks actor/event entropy;
• computes risk-adjusted scalar fitness only as a diagnostic;
• computes a homeostatic potential;
• requires both positive diagnostic delta and a Lyapunov-style condition before calling an observation a meaningful improvement;
• bounds the JSONL event ledger;
• preserves read-only/no-authority semantics.

Evolution state v2

Upgraded state/evolution-state.json to a Bayesian seed containing Beta beliefs, activity counts, and homeostatic/checkpoint signals.

Trusted cross-run Actions memory

Updated .github/workflows/evolution-loop.yml with a read-only checkpoint protocol.

For a trusted main run, the workflow:

1. queries the GitHub Actions API for the previous successful main evolution-loop run;
2. uses first-party actions/download-artifact to restore the previous checkpoint if present;
3. runs the Bayesian update;
4. uploads a new checkpoint artifact.

PR runs cannot become the source of future trusted-main state. The workflow keeps only contents: read and actions: read permissions.

This provides actual iteration-to-iteration memory while issue #35 remains unresolved and main remains unprotected.

Mathematical GitHub Actions gate

Added .github/workflows/mathematical-evolution-kernel.yml.

It runs on relevant pushes/PRs, manual dispatch, and a weekly schedule. On Python 3.11 and 3.13 it:

• compiles the mathematical kernel and scorer;
• runs all invariant tests;
• validates state/policy JSON;
• generates the deterministic mathematical demo;
• smoke-tests the Bayesian scorer;
• publishes replayable artifacts for 30 days;
• publishes a detailed GitHub job summary.

Safety boundary

No new merge, approval, issue-write, PR-write, secret, or repository-content write authority was granted to Actions.

The mathematical algorithms allocate evidence/experiments and produce recommendations. They do not supersede independent verification, branch protection, or human/governance integration authority.

Next scientific step

The next useful mathematical advance is calibration rather than adding more unmeasured formulas.

Build a delayed-outcome dataset linking event/action classes, worker/adapter choices, verification structures, and maintenance policies to real outcomes such as regressions, reverts, verifier disagreement, benchmark movement, review burden, newcomer completion, security findings, and verified-useful-work latency.

Then compare models by held-out predictive calibration and use UCB/multiplicative-weights only for bounded experiments whose outcomes are recorded.

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