RPCS-1

The framework underneath RPCS-1

Derived from what an observer has to be

RPCS-1 is the practical layer of the IMM research program. Its current foundation is IMM Paper 18 (Observer Requirements, 2026), which asks the minimal question: what must any bounded system do to estimate a changing world from noisy observations and act on it in time? Each tuning knob then arrives as a forced consequence — with an optimal-setting law — rather than as an assertion.

One-pass summary

bounded observer + changing world + noisy signals + time pressure
    => three forced blocks:  ESTIMATE  ->  DETECT  ->  COMMIT
    => five primitives (TI, UE | SG, FT | AR) = measurement coordinates
    => matching laws: when the world changes faster =>
         integrate less, update faster, look more often,
         liberalize detection, commit sooner

The five primitives are not five independent dimensions. They are a parameterization — a chart — over three coupled blocks. Legitimate as measurement coordinates, wrong as an ontology. Paper 18 supersedes the older "five are forced" claim on exactly this point.

The three blocks

01

Estimate

TI, UE (and the sampling rate ρ)

Track a changing quantity from noisy observations.

Forced by the bare setup: any bounded observer estimating under noise faces the bias–variance trade. TI (how much history) and UE (how fast to update) are provably one control loop in two parameterizations for the minimal observer — they only separate in hierarchical receivers tracking fast state and slow rules at once.

02

Detect

SG, FT

Notice when the world has changed regime.

One alarm channel with two knobs: gain (SG) and criterion (FT). Its value is inherited, not posited — missed changes prolong stale estimates, false alarms reset good ones. Four other processes consume its reset signal, which is why a receiver that goes deaf loses measurably (3.2× in the agent simulation).

03

Commit

AR

Stop deliberating and act, under time pressure.

For discrete, time-bound actions, accumulate-evidence-to-a-bound is the optimal policy class (Wald–Wolfowitz, standard). The bound scales logarithmically with stakes-to-urgency, and drops when the world changes faster — evidence expires.

The matching laws

Every law family answers the same question — how should this knob move as the environment's change rate rises? — and every answer points the same direction. This is what the tuner operationalizes.

R-1 Temporal integration

Integrate less when the world changes faster. Exact 1/λ scaling holds for change-detecting observers; fixed windows get a square-root law.

R-2 Update elasticity

Update faster when the world changes faster. Cross-checked against the exact steady-state Kalman gain.

R-3 Action rate

Look more often when the world changes faster — and disengaging entirely is never optimal under unbounded drift. Freezing is rational only when impact is bounded and looking is costly.

R-4 Detection channel

Turn gain up and liberalize the alarm criterion as the change rate rises. The textbook criterion log-law failed its pre-registered check and was cut.

R-5 Commitment

Commit faster when the world changes faster; thresholds are logarithmic in stakes-to-urgency.

What's derived, what's identified, what's still open

The corpus uses explicit epistemic labels on every claim, and the failures stay visible. If you're evaluating whether to trust the recommendations, this table is the honest basis:

Derived [D]

The R-1…R-5 law families, the three-block synthesis (T-OR-1), the rational-freeze boundary. Derived under named assumptions from standard mathematics — no lemma is claimed as new.

Identified [I]

The bridge from "environmental entropy H" to an operational change rate. An identification, not a derivation — and it now carries empirical weight, which the paper says plainly.

Predicted [P]

A registered battery of LLM tests (under $10 total) with outcomes that would count against the framework pre-stated. Untested as of v0.1.

Failed & reported

Three pre-registered checks failed. One was an algebra error (corrected, then re-run), one is cut from the claims entirely, one was a discretization artifact (resolved at finer step). All three are in the paper.

Also stated plainly in the paper: nothing in the framework creates trading edge, and the three-block count is conditional on regime-switching environments with discrete, time-bound actions — the class that covers support, coding, research, and workflow agents. Outside it, the count degrades predictably, and that degradation is itself testable.

Failure modes, mapped to blocks

oscillation

Over-updating: the estimate loop keeps revisiting the same evidence and cannot settle.

overload

Detection saturation: too much signal gets through and weak evidence drives action.

freeze

Epistemic freeze or an unreachable commitment bound: the receiver stalls when it should act.

underdetermination

Commitment starved under deadline: forced to act before the evidence bound is reached.

This mapping is interpretive [A] and part of the registered test battery — labeled as such, not sold as established.

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