current_chain_endpoints
plain-language theorem explainer
The endpoints of the current generation-step chain sum to 21. Researchers enumerating phi-ladder mass values under Q3 cube invariants cite this arithmetic constraint when partitioning N3 = 55 with middle sum 17. The proof is a one-line numerical normalization that directly verifies the addition.
Claim. The sum of the endpoint values in the current generation chain is $13 + 8 = 21$.
background
The module narrows the gap between proved Q3 cell counts and their identification as generation steps. The four values {13, 11, 6, 8} arise as cube invariants at D=3: 13 from Euler characteristic V-E+F=2 on the boundary, 11 as passive edges, 6 as faces, and 8 as vertices. The endpoint pair must satisfy the partition constraint with middle pair summing to 17, yielding the total 21. Upstream structures supply the J-cost convexity from PhiForcingDerived and the spectral emergence of exactly three generations from SpectralEmergence.
proof idea
The proof is a one-line term that applies norm_num to confirm the arithmetic identity 13 + 8 = 21.
why it matters
This records the endpoint sum constraint required for the uniqueness argument in current_chain_unique_modulo_edge_pair_filter. It advances the step-value enumeration that narrows the open forcing step identified in SectorDependentTorsion, making the modeling choice of natural cube invariants explicit. The result sits inside the T5-T8 forcing chain where phi and the eight-tick octave fix the discrete structure before mass assignment on the phi-ladder.
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