idkmesh

Anytime Drift Guard

Status: experimental mathematical control-plane primitive. Read-only; no repository integration authority.

Purpose

The Sequential Evidence Kernel protects IDKMesh against optional stopping while a bounded common-mean model remains credible. That leaves a separate failure mode: the data-generating regime itself may change.

Pooling evidence across a real regime shift can produce a precise answer to the wrong question. The Anytime Drift Guard therefore tests the common-mean assumption before a strong pooled effect is allowed to become an experiment candidate.

It is a blocking observer, not an actuator.

1. Fixed split test

For bounded observations X_i in [a,b], consider a prefix ending at time t and split it at k:

before = X_1 ... X_k
 after = X_(k+1) ... X_t

Let

D_(t,k) = mean(after) - mean(before).

Under the null hypothesis that both windows have the same expectation, Hoeffding’s inequality for the weighted difference of the two sample means gives

P(|D_(t,k)| >= eps)
  <= 2 exp(
       -2 eps^2 /
       ((b-a)^2 (1/k + 1/(t-k)))
     ).

For pairwise error budget delta_(t,k), the threshold is therefore

tau_(t,k)
  = (b-a)
    sqrt(
      0.5 (1/k + 1/(t-k))
      log(2 / delta_(t,k))
    ).

A fixed pair alarms when

|D_(t,k)| > tau_(t,k).

2. Global error spending over indefinite scanning

A repository can inspect the stream repeatedly and can try many historical split points. Treating every scan as a fresh delta=0.05 test would recreate the optional-stopping problem.

For minimum window size m, scanning begins at t=2m. Define

Z_m = sum_(s=2m..infinity) 1/s^2.

At time t, there are

M_t = t - 2m + 1

admissible split points. The guard allocates

delta_(t,k)
  = delta / (Z_m t^2 M_t).

For each fixed t, summing over all admissible k cancels M_t:

sum_k delta_(t,k)
  = delta / (Z_m t^2).

Then

sum_(t=2m..infinity) sum_k delta_(t,k)
  = delta.

Combining each fixed-pair Hoeffding bound with a union bound controls the probability of any false change alarm over all future observation times and all admissible historical splits by at most delta, under the stated bounded common-mean assumptions.

The implementation evaluates Z_m with the Basel identity

sum_(t=1..infinity) 1/t^2 = pi^2 / 6.

3. What an alarm means

An alarm means:

bounded change detected at the configured sensitivity;
review the regime boundary before pooling evidence.

It does not prove a physical phase transition, causal mechanism, malicious actor, or exact change-point location.

No alarm means only:

no bounded change detected at this sensitivity.

It does not prove stationarity.

4. Multiple metrics

If M metrics are scanned simultaneously, the implementation first allocates

delta_metric = delta / M

and each metric then spends its share over all times and splits. This preserves a total family-wise false-alarm budget across the named metric family rather than treating every repository signal as a separate 5% test.

5. Composition with sequential effect evidence

For paired candidate/baseline evaluation, define the effect stream

E_t = candidate_t - baseline_t,  E_t in [-1,1].

The combined gate splits one total error budget into a drift portion and an effect-evidence portion, then applies the following strict ordering:

hard governance failure
    > detected effect-stream regime change
    > sequential effect evidence.

Operationally:

if hard_guard_ok == false:
    GUARDED
elif anytime_drift_alarm == true:
    OBSERVE_DRIFT
else:
    delegate to paired sequential evidence gate

A strong pooled effect cannot compensate for a detected regime change, and neither statistics nor drift analysis can compensate for a failed governance guard.

6. Evidence preservation

A detected change does not automatically delete, truncate, relabel, or reset historical evidence. The output policy is explicit:

preserve_all_evidence_and_review_regime_boundary

Automatic history deletion would make the detector an evidence-selection actuator and could create a new Goodhart surface. Any later segmentation/reset policy requires separately reviewed semantics and provenance.

7. Assumptions and limitations

The guarantee relies on bounded observations and a common expectation under an independent/common-mean or appropriate bounded martingale model when the null is true. Unknown dependence, adversarially selected telemetry, incorrect bounds, missing-not-at-random observations, and logging-policy errors can invalidate calibration.

The all-splits implementation is deliberately O(n^2). It is intended for low-rate repository/evaluation evidence streams, not high-frequency raw telemetry. If scale requires pruning, a later implementation should preserve an explicit global error budget rather than silently reducing statistical guarantees.

8. Authority boundary

The guard cannot:

Positive/negative outputs are decision support only.

Executable surfaces