Witness and engine

In plain terms

Every foundational programme faces the same temptation. Build a concrete model in which your mechanism visibly works, and it becomes fatally easy to announce that the mechanism explains everything the model contains, but the model had quantum mechanics built into its bones, so of course quantum mechanics came out. The distinction between witness and engine is CSD's vocabulary for resisting that temptation.

The engine is the general machinery, typicality over a preparation region, outcome weights given by volumes, and a measure forced by symmetry. A witness is a concrete arena on which the engine demonstrably runs, with familiar structures such as the space of quantum states and their unitary evolution built in from the start.

The claim that the engine runs and here is a witness is provable, and it's proved. The claim that quantum mechanics is therefore derived would be an overclaim, and the corpus's own guard documents exist to keep it from being made.

In CSD

The finite-dimensional quantum-mechanical closure is the flagship example, a concrete projective witness carrying the symmetric measure and unitary evolution, on which the full reconstruction pipeline executes. It demonstrates the engine, and it isn't quantum mechanics derived from CSD, because the witness supplies structures a derivation would have to earn.

The distinction is enforced and not just stated. A manifest names exactly which end- to-end claims are backed by theorems, an automated check rejects phrasings that have been retracted as overclaims, and results are labelled by which side of the line between realisation and derivation they sit on.

Mathematically

The witness tier is SectorData instances on CP^(N-1) and on the Kahler arena, with the measure bridge proved instance-by-instance rather than assumed abstractly, and the engine tier is the frequency and volume theorems quantified over the structures, consuming the postulates as hypotheses.

The audit tier is mechanical, as the connectivity manifest and the claims guard are scripts that fail the build when prose claims outrun the proved connectivity.

Related entries

• LF1 main theoremIn a deterministic world with repeated preparations, the frequencies you observe converge to volume ratios with probability one, and the theorem is machine-checked with no randomness anywhere in the dynamics.
• What exactly is machine-checked in CSD?Every theorem in the CSD corpus is verified by a proof assistant from zero imported axioms, and the list of what such checking can't certify is published alongside it.
• Measurement flowA deterministic, volume-preserving flow carries out a measurement, and the volumes of its pointer blocks are the Born weights, for every preparation.
• Born volume ratioIn every finite dimension the Born weight of an outcome equals a ratio of volumes in the space of quantum states, for every outcome and every state, with no genericity condition attached.
• De-isolationNothing collapses, as a measured system stops being isolated, and measurement is what de-isolation dynamics looks like from inside.