Family hunt, phases 1-2: exact fiber determination; invariant still doesn't separate - #15
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…uses to separate
Phase 1 (fiber determination for the weighted-lift family): for any
target (A,B,C) with C != 0, the w-values of the preimages are exactly
the real roots of E(w) = -H(w) + w(H'(0) + BC) - AC^2 -- CONSTANT
leading coefficient, so no degree drop anywhere (unlike F's wall) --
with the chart lifting each root off the escape locus {BC = p(w)}.
Both the inverse identity E(u*gamma) == 0 and the chart identity
x(BC - p(w)) == C are verified symbolically at import. n1 is now a
certified count (no Groebner, no artifacts): phase 0's odd values 1, 3
were eliminant artifacts and vanish.
Findings through phase 2: certified n1 value sets are {0, 2, 4} for
BOTH same-degree members; numeric n2 (60-digit, relative thresholds,
486 targets incl. wide log-scaled search) attains {0,2,4,6,8,10,12} for
BOTH; neither reaches 14 or 16 yet. Through n2 the multiplicity
invariant does not separate the pair -- the completeness question is
live. Next: certify max ess-range(n2) per member, then n3 or the
wall-gluing data.
Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
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Phase 1: exact fiber determination for the weighted-lift family (inverse equation E(w) with constant leading coefficient + chart, both identities verified symbolically at import) — n₁ is now certified, and phase 0's odd values are confirmed chart artifacts. Phase 2: certified n₁ sets {0,2,4} and numeric n₂ sets {0,2,4,6,8,10,12} are IDENTICAL for both same-degree members through 486 targets including wide log-scaled search. The completeness question is live. Tracking in #14.
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