zero_parameter
Why this theorem is linked from Proximal Policy Optimization Algorithms unclear
Pith linked this Lean declaration because the review connected a specific passage in the paper to this theorem. The relation tag says how strong that connection is; it is not a generic placeholder.
ε = 0.2 chosen by hyperparameter search; Atari uses linearly annealed ε and Adam stepsize; multiple epochs K, GAE λ=0.95, etc., all hand-tuned
Relation between the paper passage and the cited Recognition theorem.
plain-language theorem explainer
A framework F is zero-parameter exactly when its parameters field is zero. Researchers formalizing the no-alternatives claim cite this predicate to restrict attention to parameter-free candidates. The definition is a direct field projection from the AlternativeFramework structure.
Claim. An alternative framework $F$ is zero-parameter when the number of free parameters satisfies $F.parameters = 0$.
background
The module formalizes inevitability structure under a cost-as-foundation approach. Alternatives are organized into three buckets: choices about the cost functional itself, the meaning of existence, and the admissible class of frameworks. Any zero-parameter framework that derives observables must either match RS or violate one of the six necessity gates (cost uniqueness, selection rule, discreteness, ledger structure, self-similarity, dimension).
proof idea
One-line definition that projects the parameters field of the AlternativeFramework structure and asserts equality to zero.
why it matters
This definition supplies the zero-parameter hypothesis for the downstream inevitability theorem, which asserts that any such framework deriving observables must reduce to RS or violate a gate. It operationalizes the module's core claim that selection occurs by minimizing a unique cost and that alternatives must break a necessity gate. The construction directly supports the T5 J-uniqueness and T6 phi-forcing steps of the Recognition Science chain.
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papers checked against this theorem (showing 2 of 2)
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Shallow quantum circuit guarantees a 0.6924 cut on cubic graphs
"depends on an integer parameter p ... 2p angles (γ,β)"
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Clipping a single ratio replaces the trust region in policy gradients
"ε = 0.2 chosen by hyperparameter search; Atari uses linearly annealed ε and Adam stepsize; multiple epochs K, GAE λ=0.95, etc., all hand-tuned"