Module 002 — Pairwise is not enough
If we measure every pair of guardrails, do we finally know how the stack fails?
No. There exist distributions with identical singleton failure rates and identical pairwise overlaps whose three-way failure probabilities still differ — 0 in one, 0.25 in the other. Pairwise evidence narrows the feasible set; it does not close it.
01Observed / given
Three binary guardrails; every singleton failure rate is 0.5 and every pairwise overlap is 0.25 — the complete first- and second-order evidence, held identical by construction.
03Feasible worlds
Two explicit distributions realize those moments: uniform even-parity and uniform odd-parity. Under even parity the triple failure never occurs; under odd parity it occurs with probability 0.25. All singleton and pairwise evidence leaves the interval [0, 0.25] intact.
04Identification status
Partially identified at every order tested. "We measured every pair, so we know the stack" is false in general: the third moment is not a function of the first two.
05Result or bound
E1's recorded outcome, with its epistemic decision record: the claim survived its controls and was narrowed, not widened — decision: Narrow. The study also showed the product baseline is neither reliably conservative nor reliably optimistic: it understated a common-cause generator fourfold and invented risk under a mutually exclusive one.
06Witness / counterexample
The two parity distributions are the counterexample pair — each is an explicit, checkable world, not an existence argument.
07Claim envelope
CC-003
Supported within scope · Owner-authored, public
CC-Framework's E1 dependence-evidence study established constructively that distributions with identical singleton failure rates (0.5) and identical pairwise overlaps (0.25) can differ in three-way failure probability — 0 under even parity, 0.25 under odd parity — so measuring every pair does not identify a three-guardrail stack. E1 is synthetic; its recorded decision is Narrow.
- Scope
- The frozen study document at the bound commit. Controlled synthetic generators only; no real guardrail was measured.
- Binding
E1_DEPENDENCE_EVIDENCE_STUDY.md @ ee61a710
The study's decision record (verdict: Narrow, standing objections, corrections to its own first draft) lives beside it in the same repository directory.- Dimensions
- visibilityPublicprovenanceOwner-authored, publicsupport roleDocumentmaturityReleased
- Reviewed
- 2026-08-23 · window 120 days
- Triggers
- executable fires when the frozen study document on the default branch changes
- manual E2 produces empirical results — the synthetic scoping here must be restated
- Non-claims
- the parity construction demonstrates possibility, not frequency, in real guardrail stacks — no claim of empirical prevalence
- nothing here validates the framework's practical or deployed value; "we validated CC" is prohibited at every rung of the repository's evidence ladder
- the product-baseline failure directions observed in E1 are properties of the tested generators, not universal constants
Rendered from the same registry as the ledger — one source, two views.
09Falsifier
The executable trigger on CC-003 fires if the frozen study document changes on the default branch. Mathematically: exhibit a proof that singleton + pairwise moments identify the triple in this class, and the module's thesis dies.
10Non-claims
- the parity construction demonstrates possibility, not frequency, in real guardrail stacks — no claim of empirical prevalence
- nothing here validates the framework's practical or deployed value; "we validated CC" is prohibited at every rung of the repository's evidence ladder
- the product-baseline failure directions observed in E1 are properties of the tested generators, not universal constants
- E1 is synthetic end to end; nothing here estimates how often real guardrail stacks exhibit higher-order dependence.
11Reproducibility
The study is frozen with pinned artifacts in cc-framework (docs/research/, artifact identity relocation-invariant); its commands and manifest hashes are recorded in the repository.
12Next unknown
If pairwise evidence cannot close the set, what evidence can — and what does it cost to collect? That is E2's frozen question, on the now page.