feat(M15.5-M15.7): add clock dynamics and entropic synthesis

[jagg-ix]

Combined M15.5–M15.7

Completes the next three relational-clock targets in one direct-to-main PR, pinned to the latest entropic-physlib-linear-full TIP b44d8ab215568d2239ab2ea20aca483df3b1076b.

M15.5 — conditioned four-clock dynamics

• transports exact direct system evolution through the finite Page–Wootters conditioning equality;
• composes Page–Wootters, modular, entropic and proper-time calibration maps;
• verifies path commutation, invertibility, strict temporal order and non-collapsing proper-time readings.

M15.6 — functorial conditioning

• verifies that deterministic post-processing preserves exact conditioning;
• transports observables and predicates from conditioned to direct states;
• checks exact post-processing composition;
• conjugates Page–Wootters endomorphisms through the calibrated entropic clock and verifies identity, composition and injectivity.

M15.7 — entropic-clock synthesis

• verifies injectivity of the cyclic clock driver and residue-shift compatibility;
• verifies exact KL preservation under one reversible clock step;
• checks the tick-force virial identity using a finite canonical ensemble;
• checks the shared-randomness CHSH ceiling and the eight-clock 2√2 quantum value;
• checks the periodic primitive-root clock, one-step age advance and complex-energy damping laws.

Formal authority

Pins:

• ThreeClockClosure.lean@979aca0d;
• ThreeClockDynamics.lean@3fd7da75;
• ThreeClockFunctoriality.lean@c9dcb1f1;
• EntropicClockSynthesis.lean@f5570588;
• formal branch TIP b44d8ab215568d2239ab2ea20aca483df3b1076b.

Claim boundary

The result is a conditional-relational-clock-synthesis model. The finite conditioning equality, clock equivalences, strict physical calibration maps and selected thermodynamic inputs remain explicit premises. This PR does not claim a global preferred time, automatic equivalence of arbitrary clocks, one action deriving all clock/information/force/correlation faces, a Pinsker-type information-correlation bound, or Einstein equations derived from a Bell certificate.

Validation

• Python compilation passed;
• three formal ledgers parsed;
• focused tests: 3 passed;
• M15.5 acceptance: 8/8;
• M15.6 acceptance: 9/9;
• M15.7 acceptance: 11/11;
• tick-force finite-difference error: 4.86e-11;
• no workflow file was added or modified.

Branch audit

• base: main@1c0e66fe5f2eba55c16928bd7c7b6ec2053bbc7e
• head: 736c47b32a3b8c373b8371e68caa209dc02f38d1
• one commit
• 16 changed files
• zero commits behind main