← NS Zone · NS-FCBP

NS-FCBP

Navier–Stokes Forest Coercive Budget Program · Cycle VI · 6/6 built · global regularity OPEN

NS-FCBP continues from the forest coercive budget problem left by NS-CFOP Cycle V: can a forest functional be found that is simultaneously globally finite, near-critical on the dangerous cut, and stable under branching/fragmentation? Six rounds carry this forward: FCBP-01 proves the energy-class forcing upper bound and the critical forcing topology differ by exactly one spatial derivative; FCBP-02 tests the filtered vorticity architecture and finds four remaining obstructions; FCBP-03 proves this cycle's first real breakthrough — a non-summable "slow-scale critical lift window"; FCBP-04 closes filter compatibility but reveals a new time-thickness barrier; FCBP-05 proves a sharp half-exponent time threshold; FCBP-06 completes the Cycle VI final audit.

Cycle VI does not produce an unconditional forest coercive budget — FCBP-06 proves the replication-gate NO-GO (inserting the dangerous causal marker itself as an observation coordinate cannot count as a new coercive bridge), a native CAR compiler, and a conditional paid-side absorption compiler, concluding the surviving obstruction is no longer a scale/filter/scheduling construction problem but minimal non-tautological obstruction extraction and rigidity — formally handing off to "NS-MORP: Navier–Stokes Minimal Obstruction Rigidity Program." NS-MORP → NS-DCRP are therefore three consecutive segments of one research line: FCBP (Cycle VI) → MORP (Cycle VII) → DCRP.