block_capacity
block_capacity supplies the dimensionless capacity of the n-th shell as phi to the power 2n in the periodic table proxy. Recognition Science chemists cite it when scaling shell energies via the E_coh factor. The implementation is a direct one-line power expression drawn from the imported Constants bundle.
claimThe capacity of the n-th shell is $C(n) = phi^{2n}$, where $phi$ is the self-similar fixed point supplied by the Constants structure.
background
The PeriodicBlocks module models periodic table block structure via phi-packing of orbitals. The module documentation states: 'We model a dimensionless capacity φ^(2n) for the n-th shell and an energy-like shell scale E_coh * φ^(2n), yielding a direct identity used by certificates and reports.' This depends on the Constants structure from LawOfExistence, an abstract bundle containing phi along with other CPM constants such as Knet.
proof idea
This is a one-line definition that directly assigns block_capacity n to Constants.phi raised to the power of 2 times n.
why it matters in Recognition Science
The definition supplies the capacity factor invoked by the shell definition and the blocks_holds theorem, which states shell n equals E_coh times block_capacity n. It realizes the phi-packing proxy for orbital capacities, linking to the self-similar fixed point phi from the unified forcing chain in the Recognition framework.
scope and limits
- Does not derive phi or E_coh from first principles.
- Does not compute numerical capacities for specific elements.
- Does not address electron configurations or chemical reactivity.
formal statement (Lean)
15noncomputable def block_capacity (n : Nat) : ℝ := Constants.phi ^ (2 * n)
proof body
Definition body.
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