Wall-gluing census: gates green, G1 ties, G2 separates the pair (Outcome B) - #20
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The pre-registered measurement (FAMILY_GLUING.md, issue #19), executed in order. The census pipeline computes each member's exact plane census (strip sweep over D(P,R) = 0: 3 chambers labeled 0/2/4, 5 arcs, one node + two cusps, node/cusp labels by the multiple-root theorems) and assembles the 3D landscape per L1/L3/L4/L7. All gates passed in the banking invocation: V1 independent-oracle grid (both members) PASS V2 planted difference (degree-3 member) PASS V3 two-route discriminant (both members) PASS V4 transformation law, composed-map oracle PASS V5 moved-presentation negative control PASS V6a synthetic same-G0 plant PASS V5 earned its blocking status on its first run: a hand-derived C in the slice-label oracle sampled a wrong slice and produced impossible non-jumping arcs -- exactly the bookkeeping-error class the negative control exists to catch. Fixed by deriving all target coordinates from the same psi^{-1} expressions the slice curve is built from. RESULT (decision rule 1, Outcome B): G0 ties (value sets, through n2), G1 ties exactly (identical component censuses), but G2 differs -- the labeled incidence graphs are not isomorphic. The load-bearing fact, confirmed independently by exact-anchored branch continuation (family_gluing_verify.py, the anomaly-protocol recomputation): the Sigma-component whose closure meets the wall (intrinsically marked by its wall incidence) ends at {node, cusp} for member A and at {cusp, cusp} for member B, which crosses the node's critical line at a regular point. The unmarked plane complexes are isomorphic; anchoring at the wall breaks the symmetry -- the wall carries the separating data, as IV.4 anticipated. Banked scope: the multiplicity function AS A FUNCTION up to the proved move class (polynomial automorphisms both sides; in fact all homeomorphism pairs) separates the pair. Consequence for Question 4: this pair no longer tests completeness (their multiplicity functions are inequivalent); a completeness test needs a landscape-matched pair, and this pipeline is the screening instrument. CI: a dedicated job reruns the gated pipeline (exit 2 = separation reproduced is the expected outcome; a silent tie would go red) plus the independent confirmation. README family-hunt table updated. Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
This was referenced Aug 13, 2026
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Executes the pre-registered wall-gluing measurement (FAMILY_GLUING.md; tracking: #19, parent #14).
Result (decision rule 1, Outcome B): G0 ties, G1 ties exactly, G2 separates — the labeled incidence graphs of the two multiplicity landscapes are not isomorphic. The intrinsic separating fact, found by the engine and confirmed by an independent exact continuation method: the wall-attached Σ-component ends at {node, cusp} for A and {cusp, cusp} for B. Scope: separates up to polynomial-automorphism moves (indeed all homeomorphism pairs).
family_gluing_verify.py(fixed-step rational continuation with exact root isolation, standoff classification) reproduced the origin-branch endpoints for both members, including B's regular crossing of the node line and second leg to the left cusp.🤖 Generated with Claude Code