Date: 2026-08-28
The project owner asked IDKMesh to develop an innovative graph structure for project tasks and work, and to investigate mathematical, physics, and biology-inspired formulas/algorithms for three coupled problems:
The owner specifically asked whether graph structures, mathematical algorithms, physics models, and biological formulas can support a self-evolving repository after repeated iterations.
The response separated the problem into three coupled but distinct dynamical layers rather than using one formula for everything:
The canonical project representation should be a typed, temporal, multiplex directed hypergraph with stable IDs and append-only semantic events/provenance.
Specialized projections should be generated for problems that need stronger formal constraints:
A single task DAG is too restrictive for conflicting evidence and cyclic knowledge. A global e-graph is inappropriate because most project relations are not equality relations.
Each WorkUnit should be evaluated as a multi-objective vector including:
Useful formulas include:
EIG(T) = H(Theta|D) - E_y[H(Theta|D,y_T)]
and a downstream unlock heuristic:
Unlock(i) = sum_(j in Desc(i)) value_j * exp(-lambda * distance(i,j)).
For cross-disciplinary bridge tasks, graph algebraic connectivity can provide one candidate measure of useful connection gain.
The community should be modeled using more than raw contributor count.
R_c = expected number of new retained contributors generated by one retained contributor/contribution cycle.
A multi-type branching matrix B can represent how one contributor discipline activates another. Its spectral radius rho(B) is a growth indicator, while off-diagonal terms measure cross-disciplinary propagation.
A Hawkes-like model can test whether accepted contributions/releases/experiments create follow-on activity:
lambda(t) = mu(t) + sum_(t_k<t) alpha_k exp(-beta(t-t_k)).
Growth is unhealthy if work arrival exceeds verification/review service capacity:
lambda_work < mu_verification.
Use Little’s Law to monitor backlog/latency, and track:
MaintainerLeverage = verified_useful_output / maintainer_hours.
A logistic model can represent active-contributor saturation while treating carrying capacity as a variable that tooling, documentation, distributed review, and task supply can increase.
Generalized Lotka-Volterra models are proposed only as aggregate research models for mutualism/competition between specialist communities, not as individual-level social policy.
The repository should be treated as a controlled dynamical system with a health vector, not a single fitness number.
Use a MAPE-K-inspired structure:
Monitor -> Analyze -> Plan -> Execute, operating over shared project Knowledge.
Candidate diagnostic terms include:
A Lyapunov-inspired controller can test whether maintenance actions tend to reduce project stress after disturbances.
Represent files, sections, concepts, equations, decisions, tasks, schemas, and references as a graph. Measure orphan ratio, broken-link ratio, navigation distance, decision-document consistency, duplication, and graph fragmentation.
Use MDL thinking to balance duplication against excessive abstraction:
L_total = L(structure) + L(content | structure).
Use spectral/community methods to propose possible document/module/cell boundaries, but require semantic validation before restructuring.
Self-maintenance should use explicit rules with preconditions, transformations, postconditions, and risk classes, for example:
Formal graph-transformation theory such as double-pushout approaches is a useful foundation for disciplined graph rewrites, even if full category-theory machinery is not used in P0.
Candidate repository restructures can be generated and evaluated using multi-objective evolutionary/Pareto methods. Quality-diversity approaches may preserve several good structural niches instead of prematurely converging on one metric optimum.
Simulated annealing is proposed for sandbox exploration where temporarily worse intermediate structures may reach better final states.
These analogies must be converted to measurable experiments before becoming production claims.
Self-evolution must be guarded, not unrestricted.
Core invariant:
observe -> propose -> sandbox -> independent verification/review -> integrate -> measure -> learn.
The same autonomous actor must not propose and solely authorize a protected change. Agents must not silently weaken their own tests, delete contradictory evidence, or rewrite governance/security constraints to satisfy their own fitness function.
Autonomy should progress through stages from observation, to recommendation, to PR proposals, to narrowly deterministic auto-merge, then only later to guarded structural/policy evolution when evidence justifies it.
docs/architecture/IDKGRAPH_TASK_AND_EVOLUTION_MODEL.mddocs/community/COMMUNITY_GROWTH_DYNAMICS.mddocs/architecture/SELF_EVOLVING_REPOSITORY.mdschemas/idkgraph.schema.jsonexamples/idkgraph.example.yamldocs/decisions/ADR-0005-idkgraph-and-guarded-self-evolution.mdImplement P0 IDKGraph repository observatoryBuild the deterministic repository observatory first. It should extract the documentation/task graph, validate machine-readable structure, find broken/orphaned links and other deterministic defects, and produce reproducible reports. Only after this works should semantic AI restructuring agents receive write/proposal capabilities.