pith. sign in
def

parityCount

definition
show as:
module
IndisputableMonolith.Foundation.IntegrationGap
domain
Foundation
line
48 · github
papers citing
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plain-language theorem explainer

parityCount defines the number of independent ledger parities as the square of dimension d. Foundation and cosmology researchers cite it when assembling the integration gap of 45 at D=3. The definition is a direct algebraic assignment with no additional computation required.

Claim. In dimension $d$, the parity count equals $d^2$.

background

The Integration Gap module treats the integration gap as the product of parity count and configuration dimension, which equals 45 at D=3. parityCount d supplies the $D^2$ factor that counts independent ledger parities. D is the spatial dimension fixed at 3 by linking arguments. Upstream, the parity concept appears in LedgerPostingAdjacency.parity as a pattern on ledger states, while Gap45.Derivation.gap supplies the overall 45-unit target.

proof idea

The declaration is a one-line definition that directly assigns the value $d$ squared to parityCount d.

why it matters

This definition supplies the parity factor for integrationGap, which appears in IntegrationGapCert and feeds into the eta_B rung derivations in Cosmology.EtaBExactRungDerivation. It contributes to the combinatorial structure that, with coprimality, restricts D to 3. The result aligns with the forced dimension D=3 and the 45-unit gap in the Recognition Science chain.

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