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Localize Beatty barriers to finite non-descent prefixes - #30
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The inherited Beatty accumulator argument assumed that an orbit never descends. This change proves a time cap from non-descent at one index, an accumulator cap from non-descent only through a finite prefix, and conditional first-crossing descent within the certificate reach. It also adds a sound balanced interval checker. Crossing existence remains open, and mathematical priority is unestablished.
Validation: Lean compilation; five theorem axiom footprints across the two new modules; 344,004 independently evaluated exact non-descent prefixes; four rejected false certificates across the two modules; repository proof-escape scan over 5,523 Lean files. CI runs the finite Beatty audit.