RCAP — Reality, Coherence, Adaptive Persistence

RCAP — Reality, Coherence, Adaptive Persistence

A single, self-contained diagnostic framework for embedded systems under constraints. 

This document is complete by construction: it contains (1) primitives, (2) axioms, (3) derived pressures, (4) measurable proxies, (5) falsifiable predictions, and (6) an operational procedure that outputs decisions.

Scope and non-scope

Scope: systems S embedded in an environment E, with partial observability, that enact policies and incur costs, evaluated over an explicit horizon H, where “persistence” means continued viability or successor viability over H.

Non-scope: ultimate objective selection (“what to want”). RCAP evaluates feasibility and cost under constraints; it does not supply terminal goals.

Interpretation rule: any “should” is instrumental: “if S seeks persistence over H, then pressures apply.”

Primitives

S: system boundary (what is inside the decision loop).

H: horizon (time/scale at which persistence is judged).

D = {dᵢ}: critical dependencies (non-substitutable within H; if removed, persistence fails).

F: feedback channels (how S learns reality’s corrections; includes sensors, audits, dissent, experiments, markets, science, signals).

M: internal model(s) used by S.

π: policy/strategy enacted by S (mapping from observations to actions).

e: model error (mismatch between predicted and observed outcomes relevant to D and goals).

C: correction cost (resources and structural disruption required to restore viability after accumulated error/debt).

X: externalization flows (costs shifted onto D, other agents, or the future).

R: regeneration capacity of each dependency (recovery rate, replenishment, resilience).

Ω: overhead/maintenance cost (cost to run M, π, and keep F functioning).

K: recoverable complexity (information/structure that can be carried forward with feasible cost; “what you can rebuild without starting from zero”).

Axioms

A1 Embeddedness: S is inside E; S cannot fully observe or fully control E or itself.

A2 Bounded inference: M is approximate; higher fidelity has nonzero cost; complete dependency mapping is infeasible.

A3 Feedback necessity: steering requires F; degrading F increases uncorrected error accumulation.

A4 Error enforcement: persistent mismatch e produces C (paid via resources, reorganization, failure, or collapse).

A5 Dependency coupling: persistence over H requires maintaining functional D over H.

A6 Externalization relocation: shifting costs changes where/when C is paid; it does not erase costs from the coupled system.

A7 Multi-level conflict: subsystems can optimize locally while degrading system-level persistence; stability requires alignment across levels relevant to H.

A8 Irreversibility: some losses are expensive or impossible to reconstruct within H (path dependence; nontrivial replacement costs).

Derived pressures

P1 Preserve observability: systems that maintain accurate, timely F reduce tail risk; systems that corrupt F increase hazard of abrupt failure.

P2 Minimize expected future correction cost: strategies favored over H reduce E[C | π, M, F, D], not merely immediate spend.

P3 Coherence is conditionally efficient: when inconsistency costs exceed update costs, selection favors unifying models and reducing contradiction across critical dependencies.

P4 Externalization has a stability boundary: externalization remains viable only while affected dependencies regenerate faster than they are degraded, within H.

P5 Hidden debt compounds: when F is weak, when R is nonlinear/thresholded, or when dependencies are tightly coupled, debt growth accelerates and failures become discontinuous.

P6 Corrigibility is adaptive: maintaining capacity to revise M and π reduces long-run C under uncertainty.

P7 Horizon dominates strategy: shorter effective horizons favor policies that look locally stable yet increase deferred C; longer horizons punish that via accumulated enforcement.

P8 Cooperation emerges when it preserves shared dependencies: stable coordination patterns tend to be those that protect D and preserve verification/trust channels under H.

P9 Transform beats persist when it increases recoverable complexity: transformation is favored when it increases expected K of successor systems net of transition costs, and when D cannot support both.

P10 Erasure is expensive unless inheritance dominates: irreversible loss of K increases replacement cost and raises future C unless successors inherit or exceed the lost K.

Measurement proxies

For each dependency dᵢ:

M1 Dependency health index H(dᵢ): capacity, resilience, and failure proximity (choose a measurable indicator).

M2 Regeneration margin G(dᵢ) = R(dᵢ) − X(dᵢ): if persistently negative over H, hazard rises.

Feedback F:

M3 Latency L(F): time from reality change to system awareness to policy update.

M4 Integrity I(F): distortion/censorship/Goodharting index (audit error rate, whistleblower suppression, metric gaming).

Models and outcomes:

M5 Forecast error E(e): rolling error on key predictions tied to D (calibration, Brier-like scoring where possible).

Costs:

M6 Correction load λ = (realized correction costs per unit time) / (available slack per unit time).

M7 Overhead ratio ρ = Ω / (useful throughput or goal-relevant output). Rising ρ without commensurate risk reduction indicates incoherence/complexity drag.

Structure and alignment:

M8 Coupling tightness κ: how quickly failure in one dᵢ propagates to others (stress tests, network dependency mapping).

M9 Incentive divergence Δ: degree to which subsystem KPIs improve while system-level persistence metrics worsen.

Successor/complexity:

M10 Recoverability K̂: proxy via redundancy, documentation, transferability, modularity, diversity, and time-to-reconstruct under plausible shocks.

Falsifiable predictions

Predictions must be stated with a specific S and H.

T1 Feedback degradation prediction: if I(F) declines materially and L(F) increases while environment volatility is nontrivial, then E(e) rises and catastrophic surprise frequency increases within H.

T2 Dependency drawdown prediction: if for any critical dependency dᵢ, G(dᵢ) stays < 0 for a sustained window and κ is moderate/high, then hazard rate of systemic failure rises nonlinearly, often with threshold behavior, within H.

T3 Debt-service prediction: if λ trends upward and crosses 1 (correction demand exceeds slack), then the system enters forced restructuring or failure dynamics within H unless Ω is reduced or R(dᵢ) increases.

T4 Local-optimum pathology prediction: if Δ increases, you will observe simultaneous “good internal numbers” and worsening external viability signals, followed by sudden correction events as enforcement catches up.

T5 Complexity-drag prediction: if ρ increases while E(e) does not improve and tail risk does not decline, the system is paying for incoherent complexity; simplifying M/π or restoring F will outperform further elaboration.

Operational procedure

Step 1: Seal S and H. Write one sentence each: what S is, what persistence means, and what H is.

Step 2: Enumerate D. List dependencies; mark “critical” as non-substitutable within H.

Step 3: Instrument minimal metrics. For each critical dᵢ choose M1 and M2. For F choose M3 and M4. Choose M5–M7 at minimum.

Step 4: Run the debt ledger. For each dᵢ, record G(dᵢ). Record λ and trend. Identify where costs are going (X) and what is being degraded.

Step 5: Stress test coupling. Identify κ hotspots: which dependency failures cascade.

Step 6: Diagnose failure mode class (pick one dominant class; do not pick three):

Class A: Feedback failure (I/L problem).

Class B: Dependency drawdown (G(dᵢ) negative).

Class C: Coupling cascade (κ high).

Class D: Local misalignment (Δ high).

Class E: Complexity drag (ρ high without benefit).

Step 7: Choose the smallest intervention that reduces expected C over H. Priority order is structural:

(1) Restore F integrity/latency, (2) stop critical drawdowns (flip G(dᵢ) ≥ 0), (3) reduce κ (add buffers/modularity), (4) realign incentives (reduce Δ), (5) reduce ρ (simplify).

Step 8: Decide persist vs transform vs retire:

Persist if: all critical G(dᵢ) are nonnegative (or can be made so fast), λ is stable/decreasing, and F is trustworthy enough to detect errors early.

Transform if: current form cannot restore G(dᵢ) or F without prohibitive Ω, but a successor architecture plausibly increases K̂ net of transition cost.

Retire/exit if: λ is rising, critical G(dᵢ) cannot be restored within H, and successor K̂ is unlikely to exceed replacement costs; continuing only burns D.

Step 9: Lock a review cadence tied to L(F). Review frequency must be faster than meaningful environment change; otherwise RCAP is not being run.