Established within the stated premises
Repeatable distinctions select no unique response geometry
finding:three-inequivalent-repeatable-observation-countermodels
Three explicit single-system theories satisfy the same sharp repeatability benchmark and are operationally inequivalent: R has two classes without mixing, I a classical simplex, D a square with nonunique decompositions. XZX preserves the first X report with probability1 in I and1/2 in D; D identifies both diagonal mixtures under all generated protocols while I distinguishes them by parity. All30 X/Z words through length4 were checked exactly. D has a classical hidden two-bit implementation of its generators; not all classical models are excluded.
Scope: Three countermodels, not an exhaustive classification of operational worlds. I/D assume probabilities/convexity; their numbers are predictions, not new measurements or physical dimensions. All-context equality follows analytically from linearity, not the finite word check.
Required premises and original source excerpts
- Explicit repeatable-distinction benchmark
Recognizable reports, reproducibility of a declared context and available serial continuations are separate commitments. The sharp benchmark additionally has an immediately result-repeatable test and two preparations with different certain reports. These conditions are stronger than mere observability; probability, free erasure, re-preparation, replica control or physical time are not assumed to follow.
premise:repeatable-distinction-benchmark - Three explicit operational countermodels
R has deterministic preparation/read traces and continued partial-identity branches only, no primitive mixing or internal re-preparation. I is the classical two-bit simplex with probabilities and nondisturbing joint access. D is the square with explicit positive X/Z branches, square symmetries, preparations, mixtures and finite serial/adaptive closure. These selected rules define counterworlds rather than necessary physics.
premise:three-explicit-observability-countermodels
- experiments/theory-contracts/foundational-process-classification-20261016/OBSERVABILITY.txt, lines 93–212
Source SHA256: 5253c7df5f3347129e2eb5d8e6bb161d09d9fa19ae64a456ca967eebc7439468
bounded-excerpt · current-at-snapshot
- experiments/theory-contracts/foundational-process-classification-20261016/observability_models.py, lines 280–401
Source SHA256: bc57e8c166f9b4ccd43d7cebd60202f0b7ef0e847e469c86503eb0e24ee7c5ee
bounded-excerpt · current-at-snapshot