UpgradePath
plain-language theorem explainer
The upgrade path structure records the current partial status toward proving that every zero-parameter framework reduces to Recognition Science or violates a necessity gate, together with the list of remaining steps and the target of full equivalence. Foundation researchers would cite it when tracking open items after cost uniqueness has been established. It is introduced as a plain record type whose fields are populated by the inevitability upgrade definition.
Claim. An upgrade path is a triple $(c, s, t)$ where $c$ is a string describing the current state of the inevitability argument, $s$ is a list of strings listing required steps, and $t$ is a string describing the target state of full reduction to the RS framework.
background
The module formalizes the inevitability structure of Recognition Science by relocating degrees of freedom into the cost function, so that selection occurs by minimizing a unique cost. Under analyticity, symmetry, convexity and normalization the cost function is forced to the form $J(x) = ½(x + x^{-1}) - 1$. The inevitability theorem states that any alternative zero-parameter framework deriving observables must either match the RS cost and selection or violate at least one of the six necessity gates (cost uniqueness, selection rule, discreteness, ledger structure, self-similarity, dimension).
proof idea
The declaration introduces a structure with three fields: a current state string, a list of step strings, and a target state string. No tactics or lemmas are applied; the definition simply declares the data type used to record the upgrade sequence.
why it matters
This structure is instantiated by the inevitability upgrade definition, which enumerates the concrete steps required to finish the argument: proving CPM universality for selection, dimension forcing from linking and gap-45, and full exclusivity. It therefore marks the scaffolding that remains after the cost uniqueness gate has been closed, directly supporting the claim that alternatives must break a necessity gate. In the Recognition Science framework this corresponds to completing the forcing chain from J-uniqueness through the eight-tick octave and spatial dimension three.
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