IDKMesh

Physarum-Inspired Adaptive Compute Routing

Status: experimental algorithm proposal
Date: 2026-09-22
Scope: adaptive routing inside a future admitted multi-node/federated compute fabric.

1. Why this mechanism

IDKMesh already has:

• hard zero-project-spend compute admission;
• provider-neutral compute offers;
• deterministic offer selection;
• work-unit capability/security filters;
• experimental task-to-worker routing.

What it does not yet have is an adaptive multi-path routing layer for a future compute mesh where:

• several already-authorized nodes/regions can carry work;
• link/node quality changes over time;
• one path may be cheap/fast but fragile;
• another may be slower but more reliable;
• a static best path can become wrong after churn or an outage.

The slime mold Physarum polycephalum is relevant because its transport network adapts tube conductance according to flow. Tero et al. showed a mathematical abstraction balancing transport efficiency, cost, and fault tolerance in adaptive networks (Science 327, 2010, DOI: 10.1126/science.1177894).

The engineering hypothesis is:

A conductance-based adaptive routing rule can retain useful alternative compute paths and recover from changing node/link quality faster than static single-path selection, without bypassing IDKMesh admission or trust policy.

2. Critical authority boundary

Physarum routing is after admission, never before it.

Resource evidence
  -> local authorization
  -> concrete compute offers
  -> Resource -> Compute Admission
  -> hard WorkUnit feasibility/security/cost filter
  -> admitted zero-project-cost graph
  -> Physarum-inspired adaptive route recommendation
  -> bounded execution
  -> ResultManifest
  -> independent VerificationResult
  -> human/governance integration

The adaptive algorithm MUST NOT:

• turn an unavailable provider into an available one;
• relax the repository’s $0 project-spend ceiling;
• invent capabilities;
• weaken worker trust requirements;
• grant repository-write or merge authority;
• treat path popularity as correctness evidence.

If no eligible admitted path exists, the result remains no_eligible_offer / no dispatch.

3. Biological mechanism -> engineering mechanism

In the classical flow-conductivity abstraction:

Q_ij = (D_ij / L_ij) * (p_i - p_j)

where:

• Q_ij = flow;
• D_ij = tube conductivity;
• L_ij = path/edge length or cost;
• p_i - p_j = pressure difference.

Conductivity changes with observed flow and decays without reinforcement.

For the first IDKMesh experiment, use a simpler path-level equivalent-resistance approximation:

R(path) = sum_e L_e / D_e

Conductance(path) = 1 / R(path)

Then combine that with observed reliability:

RouteValue(path) =
    Conductance(path)
  * EstimatedReliability(path)
  * Efficiency(path)

with:

Efficiency(path) = 1 / PathLength(path)

Selection remains stochastic with a small exploration floor.

4. Conductance update

For edge e after one routed WorkUnit:

D_e(t+1) =
  clip(
    (1-rho) * D_e(t)
    + alpha * VerifiedRouteReward * I[e used]
    - penalty * I[e observed failed],
    D_min,
    D_max
  )

where:

• rho = evaporation / forgetting;
• alpha = reinforcement gain;
• verified route reward is larger for successful low-burden paths;
• observed failed edges are explicitly penalized;
• D_min > 0 prevents total extinction of alternative paths.

This is deliberately similar in spirit to biological tube adaptation but is not a claim that compute networks are literal slime molds.

5. Reliability learning

Each admitted edge keeps a simple Beta posterior:

reliability_e ~ Beta(a_e, b_e)

Observed success:

a_e += 1

Observed failure:

b_e += 1

Path reliability is initially approximated as the product of posterior means across its edges.

This is a research simplification. Real deployment would need to distinguish:

• transport failure;
• worker failure;
• provider outage;
• timeout;
• artifact-transfer failure;
• verifier rejection.

Only failures actually attributable to a path/link should update transport reliability.

6. Why this is different from ACO already in IDKMesh

ACO/stigmergy currently addresses which task/worker path deserves attention based on verified useful outcomes.

Physarum routing addresses a different layer:

ACO / AVE:
Which worker/task/verifier strategy should receive work?

Physarum compute routing:
Through which already-admitted compute/federation path should the bounded work travel?

The state variable is edge/path conductance, not task pheromone.

The mechanism should not create a second task scheduler.

7. Baselines

The first simulator compares:

1. shortest-static
   • always use the initially shortest path;
   • no learning.
2. reliability-greedy
   • choose current estimated reliability / path length;
   • no explicit exploration.
3. epsilon-greedy
   • same as reliability greedy with random exploration.
4. Thompson path
   • Bayesian path-level success posterior;
   • samples a route under uncertainty.
5. Physarum
   • edge-level reliability posteriors;
   • adaptive conductance;
   • evaporation;
   • failure penalty;
   • bounded exploration.

The Physarum mechanism only earns further development if it competes with the stronger adaptive baselines, not merely the static shortest path.

8. Dynamic environment

The first fixture intentionally changes during the run.

Before the shift:

• path A is shortest and highly reliable;
• path B is longer but usable;
• path C is longest and highly reliable.

After the shift:

• path A degrades sharply;
• path B improves;
• path C remains stable.

This tests whether the router can:

• exploit a good short path initially;
• retain enough alternate-path knowledge;
• recover after the old route becomes bad;
• avoid paying unnecessary route burden forever.

9. Metrics

Report a Pareto vector:

• overall completion rate;
• pre-shift completion rate;
• post-shift completion rate;
• mean latency/path length on successful tasks;
• mean routing burden;
• path entropy;
• maximum path-selection share;
• adaptation/recovery time;
• optional future energy/donor burden;
• optional future verifier-independence value.

A higher success rate that doubles donor/network burden is not automatically better.

10. Product integration target

If the synthetic mechanism survives baselines and later real-node evidence, integrate as a dry-run planner beside the existing compute router.

Possible future interface:

admitted_graph = compute_admission(...)

plan = adaptive_path_router(
    work_unit,
    admitted_graph,
    observed_path_state,
)

explain(plan)

The initial integration should only explain:

• selected route;
• alternative routes kept alive;
• conductance/reliability state;
• why a path was penalized;
• whether route scarcity caused no dispatch.

It should not execute automatically.

11. Real-node evidence gate

Do not claim an advantage from simulation alone.

A real experiment should use 3-10 controlled nodes or containers and inject:

• latency changes;
• transient node loss;
• one degraded relay/provider;
• bandwidth limits;
• coordinator restart;
• artifact transfer failure.

Compare against:

• deterministic shortest/lowest-wait routing;
• reliability-aware greedy;
• Thompson/contextual-bandit routing.

Retain exact route decisions and failure attribution.

12. Falsification criteria

Reject or simplify the mechanism if:

• Thompson/bandit routing adapts equally well with less state;
• the conductance model adds latency/burden without improving resilience;
• it becomes unstable under noisy reliability observations;
• it over-reinforces early lucky paths;
• D_min exploration produces excessive donor/network cost;
• path failures cannot be attributed accurately enough for safe updates.

13. External research basis

• Tero et al., Rules for biologically inspired adaptive network design, Science 327 (2010), DOI 10.1126/science.1177894.
• Le Verge-Serandour & Alim, Physarum polycephalum: Smart Network Adaptation, Annual Review of Condensed Matter Physics 15 (2024), DOI 10.1146/annurev-conmatphys-040821-115312.
• Gao et al., review of Physarum-based computational models, Physics of Life Reviews 29 (2019), DOI 10.1016/j.plrev.2018.05.002.

The papers motivate the adaptive-network mechanism. They do not establish that the mechanism is better for IDKMesh; that remains an experimental question.

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