v0.431.0 — THE CAP THEOREM SHIP

B270 (PAPER_2265): the derivation session Daniel ordered - the L_buoy
variational attempt at the cap theorem. The road B269 named is walked.

- The cap upgrades: POSTULATE -> DERIVED MODULO ONE NAMED LEMMA.
- PAPER_1065's EOM supplies produce/remove/drain as its OWN three
  terms (gravity seed, buoyancy pair, phonon).
- The surplus is EXACTLY F_TRZ: F_UBi carries (1+F_TRZ), F_UBii
  carries k_spring*(1+E_n) - at the balance zone the unit parts cancel
  and the overshoot is structural, not fitted.
- TRZ-carried: PAPER_072 (F_TRZ = the fraction entering the zone) +
  PAPER_009 (D_TRZ = 0.900, canonical 10 pct removal); the (2R-1)
  negative branch opposes production.
- THE DERIVATION DISCRIMINATES: bare TRZ (0.90) and quadratic TRZ
  (0.81) are ELIMINATED - only projected-linear lands on 17/20.
- The removed 3/20 drains through g_phonon - the EOM's own third term,
  the 1.25 THz LENR carrier - closing 17/20 + 3/20 = 1.
- ONE step remains, NAMED: the bridge lemma (D_BSFG/D_phys projection
  weight from mode counting, linear action on production) - a
  registry-tracked OPEN target, not a claim. Clay machinery separately
  OPEN as ledgered.

Gate 6,093/0. Dispatch 2,316 keys. Registry 7,093 rows. Acceptance
109/109 (simulator v1.90.0 untouched).
