Status: review (no behavior change) · Kernel: box-and-box v0.8.0 (8 rungs, 97 laws) Scope: how closely the Graphonomous memory engine (OS-001) already conforms to the [&] governance kernel, rung by rung, and the small set of additive naming/wiring changes that would make it explicitly compliant.
Graphonomous is already structurally isomorphic to the kernel's load-bearing rungs — it just doesn't name them. Its coverage→decision policy is the bridge (feasible ▸ permitted ▸ best); its coverage score is the axiological semiring; its Wilson intervals are the epistemic rung; its cost cap is the resource rung's affine ledger. The gap is vocabulary + two small guarantees, not architecture. Nothing here requires a core refactor; every recommendation is additive.
| Kernel rung | Graphonomous implementation | Compliance |
|---|---|---|
1. alethic (value) | Topology.compute_kappa/2, SCC analysis; node confidence | ✅ ~90% — κ is a first-class Value |
2. axiological (score) | Coverage.weighted_sum/2, Reranker | ◻ ~60% — weighted sum, not a named semiring |
| 3. deontic (norm/govern) | Coverage.pick_decision/4 floor gates (act/learn/escalate) | ◻ ~70% — floor present, 0̲ veto implicit |
| 4. temporal (LTL ▸ supervise) | consolidation cadence; freshness/staleness decay | ◻ ~40% — time-aware, no LTL obligations |
| 5. reflexive (entrenched ring-0) | — (no self-amendment surface) | ✕ out of scope |
| 6. epistemic (knows ▸ believes) | Uncertainty.interval/1 (Wilson), BeliefRevision (AGM) | ✅ ~95% — strongest rung |
| 7. strategic (coalition power) | — (single-agent; delegated to Deliberatic) | ✕ out of scope |
| 8. resource (affine ledger) | CostTracker.budget_exceeded?/0 ($10/day), Forgetter LRU+decay | ◻ ~85% — ledger present |
value) ✅lib/graphonomous/topology.ex compute_kappa/2 (line 134) computes the κ cyclicity invariant — the same Value-family invariant the kernel's value.mjs carries (alethic "what can happen"). Node confidence scores are the truth-degrees over which Value laws L1–L14 range. Already compliant; recommend citing the rung-1 correspondence in the Topology moduledoc so κ is understood as the alethic Value, not a bespoke metric.
score) ◻ → name the semiringlib/graphonomous/coverage.ex weighted_sum/2 (line 604) computes Σ value × weight and clamps to [0,1]. That is the kernel's probability semiring (⊕ = +, ⊗ = ×) from box-and-box/score.mjs. Additive recommendation: document that the coverage score is the axiological rung in the probability semiring, and (optionally) expose a tropical (⊕ = min) "weakest-component" view alongside the weighted mean — so the engine can answer "is any coverage component failing?" the way the kernel's safety floor does, not just "how good on average?".
0̲ veto explicitCoverage.pick_decision/4 (line 392) is the bridge, already implemented:
:act when coverage ≥ floor AND uncertainty ≤ ceiling AND risk ≤ ceiling # feasible ▸ permitted
:learn when (looser floor) # permitted, not yet best
:escalate otherwise # floor not metThis is exactly feasible ▸ permitted ▸ best: the conjunctive thresholds are the un-weakenable safety floor, and decision_confidence/3 (line 409) is the gradient that the bridge's best step optimizes. The one missing guarantee is `0̲` annihilation: in the kernel, a floor violation annihilates the verdict (no amount of gradient can rescue it). Graphonomous approximates this — :escalate is terminal — but the relationship is implicit. Additive recommendation: state in the Coverage moduledoc that a sub-floor signal annihilates to :escalate (the deontic 0̲), and add a property test mirroring the kernel's DB2 annihilation law so the guarantee can't silently regress.
Freshness/staleness decay (coverage.ex line 383) and consolidation cadence are time-aware, but there are no explicit LTL obligations (e.g. "every stored contradiction is eventually resolved"). Out of scope to add now; flagged as the natural next rung if temporal guarantees become first-class. Maps to box-and-box/temporal.mjs (X, ◇).
lib/graphonomous/uncertainty.ex interval/1 (line 28) computes Wilson confidence intervals over evidence counts, with an explicit :no_evidence bottom — this is the kernel's epistemic rung (S5/KD45 "knows ▸ believes") in statistical form. BeliefRevision implements AGM expansion/contraction with contradicts edges. Already compliant at ~95%; recommend naming the :no_evidence case as the epistemic bottom and citing the rung-6 correspondence. This is the rung Graphonomous could claim conformance on today.
lib/graphonomous/cost_tracker.ex budget_exceeded?/0 (line 167) enforces a $10/day cap — an affine ledger: spend is consumed and cannot go negative past the cap. The Forgetter (LRU + priority decay) is resource reclamation. This is the kernel's resource rung (resource.mjs, laws C1–C8). Additive recommendation: emit the daily-budget remaining as a resource signal and name it with the resource-rung vocabulary (consume, overspend → 0̲), so unattended autonomy degrades gracefully via the same algebra the kernel uses.
| Change | File | Risk | Value |
|---|---|---|---|
| Cite κ = alethic Value | topology.ex moduledoc | none | shared vocabulary |
| Name coverage score = probability semiring; optional tropical view | coverage.ex | low | bottleneck visibility |
State the 0̲ annihilation on sub-floor; add DB2-style property test | coverage.ex + test | low | regression guard |
Name Wilson :no_evidence as epistemic bottom | uncertainty.ex moduledoc | none | claim rung-6 conformance |
| Emit resource-ledger remaining with kernel vocabulary | cost_tracker.ex | low | graceful autonomy |
It does not change any decision thresholds, coverage weights, or confidence formulas.
It does not make Graphonomous call the JS kernel at runtime — Graphonomous stays
self-contained Elixir; the kernel is the specification its algebra conforms to.
It does not add the reflexive (rung 5) or strategic (rung 7) rungs — those are
single-agent-out-of-scope and delegated to Delegatic/Deliberatic respectively.
AmpersandBoxDesign/box-and-box/ — the kernel (node test/laws.mjs → 97 laws)
AmpersandBoxDesign/box-and-box/{score,bridge,epistemic,resource}.mjs — the rungs cited
lib/graphonomous/coverage.ex — the bridge + axiological semiring (§ rungs 2–3)
lib/graphonomous/uncertainty.ex — Wilson epistemic intervals (§ rung 6)
lib/graphonomous/cost_tracker.ex — affine resource ledger (§ rung 8)