jcost_two_channel_coeff_unique
plain-language theorem explainer
The theorem asserts uniqueness of the real coefficient c in the cubic perturbative expansion of twice the J-cost at one plus the fine-structure constant. Mass derivations in Recognition Science cite it to fix the radiative correction term unambiguously before extracting topology counts or ledger fractions. The proof is a one-line term application of an upstream existence-uniqueness lemma for the two-channel J-cost form.
Claim. There exists a unique real number $c$ such that $2 J(1 + α) = α² + c α³$, where $α$ is the fine-structure constant and $J$ denotes the J-cost function.
background
The J-cost function is the cost quantity (abbreviated from Quantity CostUnit) that measures recognition effort under the Recognition Composition Law. The fine-structure constant α is defined as the reciprocal of its derived inverse, kept symbolic in this module. The local setting is the Mass-Layer J-Cost Perturbation Bridge, which upstreams the O4 perturbative closure and certifies the Jcost(1+α) channel form together with its explicit α² + 12α³ decomposition.
proof idea
The proof is a direct term application of the upstream lemma exists_unique_two_jcost_channel_coeff, which already encodes the unique existence for the cubic coefficient in the doubled J-cost expansion.
why it matters
This uniqueness pins the canonical cubic-channel coefficient that is extracted in the sibling definitions jcost_two_channel_coeff and jcost_two_channel_coeff_spec. It closes the O4 perturbative channel inside the mass-layer bridge, feeding mass topology counts and ledger-fraction derivations. The result aligns with the Recognition framework landmark that places the inverse fine-structure constant inside the narrow interval (137.030, 137.039).
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