Module 006 — Witnesses
Why believe an interval's endpoints are real rather than worst-case rhetoric?
Because they are attained. For every identified interval the kernel returns endpoint witness distributions — explicit feasible worlds that satisfy the declared constraints and achieve the bounds. A wide interval stops being a complaint and becomes a checkable object.
01Observed / given
The same two marginals as module 001: p₁ = p₂ = 0.10, no dependence evidence, both-fail query.
03Feasible worlds
identify() returns the sharp interval [0.0, 0.10] and two distributions over the four atoms (neither, A only, B only, both): the lower witness (0.8, 0.1, 0.1, 0.0) separates the failures entirely; the upper witness (0.9, 0, 0, 0.1) stacks them.
04Identification status
Sharpness made concrete: no value outside the interval is consistent with the evidence, and the endpoints are exhibited, not merely bounded.
05Result or bound
The reproduction script checks, from a clean clone at the bound commit and to a tolerance of 1e-9, that each witness sums to one, is nonnegative, satisfies both marginal constraints, and attains its endpoint — in CI, on every push and weekly.
06Witness / counterexample
The witnesses are the module. What is machine-checked is their feasibility and attainment; what is not checked — and not claimed — is that either world describes any deployed system.
07Claim envelope
CC-004
Supported within scope · Machine-generated, owner-executed
For marginals (0.10, 0.10) and the both-fail query, cc.kernel.strict identify() returns the sharp interval [0.0, 0.10] together with endpoint witness distributions that sum to one, are nonnegative, satisfy both marginal constraints, and attain each endpoint — verified to 1e-9 from a clean clone.
- Scope
- The kernel identification module at the bound commit, re-verified by CI on every push and weekly in the witness stage of scripts/reproduce_cc001.py. No claim about any deployed system.
- Binding
Cubits11/cc-framework @ 167aa1ee
Shares CC-001's bound commit so a single clean-clone checkout reproduces both claims; the reproduction script enforces that the two bindings stay equal.- Dimensions
- visibilityPublicprovenanceMachine-generated, owner-executedsupport roleExecuted outputmaturityReleased
- Reviewed
- 2026-08-23 · window 120 days
- Triggers
- executable fires when the identification module on the default branch diverges from the bound revision
- manual witness API change outside the bound module file
- Non-claims
- endpoint witnesses are feasible mathematical worlds, not observed systems
- attainment does not select a point inside the interval or estimate the true dependence
Rendered from the same registry as the ledger — one source, two views.
09Falsifier
The witness stage of the reproduction fails if the kernel stops returning feasible, endpoint-attaining solutions; the executable trigger on CC-004 fires if the identification module diverges from its binding.
10Non-claims
- endpoint witnesses are feasible mathematical worlds, not observed systems
- attainment does not select a point inside the interval or estimate the true dependence
- Endpoint witnesses are feasible mathematical worlds, not observed systems; exhibiting them selects no point inside the interval.
11Reproducibility
python scripts/reproduce_cc001.py — the witness stage runs identify() and asserts feasibility and attainment against the registry's structured expected values.
12Next unknown
Witnesses at scale: explicit atom enumeration grows as 2^m — how far can witness-carrying identification be pushed before the atoms themselves must be abstracted?