Computability infrastructure for finite candidate tests and SAT reference semantics

## Proposed contribution

Add proved computability infrastructure for future formalizations about candidate algorithms and feasible SAT search:

- exhaustive finite candidate/input prefixes, least partial counterexample bounds, and checked finite certificates;
- explicit clocks and canonical enumeration of clocked binary descriptions;
- structured 3-CNF semantics with a proved exhaustive reference checker, followed by a validated binary parser.

The first two PRs are independent additions to `FormalConjecturesForMathlib`, with regression tests and reproducible axiom audits. They introduce no research conjecture or new dependency.

## Literature and scope

The longer-term motivation is Igor C. Oliveira, [Meta-Mathematics of Computational Complexity Theory, ECCC TR25-041](https://eccc.weizmann.ac.il/report/2025/041/), §5.1.2, equation (4) and Open Problem 5.3. That problem concerns unprovability of SAT-search guarantees in PV₁; stating it faithfully needs arithmetic syntax and representation results beyond these additions.

Scott Aaronson, [P =? NP](https://www.scottaaronson.com/papers/pnp.pdf), §2.2.1 and §3.1, provides the decision/search and truth/provability background. The proposed finite-prefix results are elementary finite-set arguments, not a formalization of an independence theorem. No polynomial-time SAT solver, TM2 simulation, or P-versus-NP result is claimed.

Subsequent targets are canonical formula parsing, a concrete machine interpretation, and only then the arithmetic representation bridge. PR descriptions will identify the exact implemented declarations, source roles, encoding conventions, and checks.

Implementation is AI-assisted using Codex.

The issue names FormalConjecturesForMathlib but no source files, tests, or entry points. Start by locating the proposed finite-prefix, certificate, clock, enumeration, and 3-CNF additions. Done means proved infrastructure, regression tests, reproducible axiom audits, and the validated parser described in the scope.

Written by the indexing model from the issue text.