IndisputableMonolith.Foundation.PostingExtensivity
The PostingExtensivity module defines the posting potential as the shifted J-cost satisfying the d'Alembert equation inside zero-parameter comparison ledgers. Researchers deriving the T5 to T6 bridge would cite it when establishing extensivity from ledger composition. The module supplies a sequence of definitions and lemmas that connect the J-cost to phi-forcing properties.
claimThe posting potential is the shifted J-cost satisfying the d'Alembert equation: $\Pi(x) = J(x) + 1 = \frac12(x + x^{-1})$, where $J(x) = \frac12(x + x^{-1}) - 1$.
background
The module sits inside the Recognition Science forcing chain and imports the ZeroParameterComparisonLedger from LedgerCanonicality. That ledger packages a countable carrier for discrete states, local binary comparison with symmetric cost, and a conserved log-charge scalar. It also imports HierarchyEmergence, whose doc-comment states that a zero-parameter comparison ledger with multilevel composition necessarily produces a minimal hierarchy and forces phi as the unique admissible scale.
proof idea
This is a definition module, no proofs.
why it matters in Recognition Science
The module feeds the posting potential and its extensivity lemmas directly into HierarchyDynamics. That downstream module closes the T5 to T6 gap by deriving the Fibonacci recurrence from primitive ledger axioms, as described in its doc-comment on resolving the deepest structural gap in the Recognition Science forcing chain.
scope and limits
- Does not derive numerical values for constants such as alpha or G.
- Does not address continuous limits or field-theoretic extensions.
- Does not treat multi-particle interactions beyond binary comparisons.
used by (1)
depends on (3)
declarations in this module (11)
-
def
PostingPotential -
theorem
posting_one -
theorem
posting_pos -
theorem
posting_dalembert -
theorem
posting_scales_compose -
theorem
closure_forces_additive -
theorem
additive_closure_golden -
theorem
discrete_fibonacci_from_minimality -
theorem
posting_extensivity_forces_phi -
theorem
posting_gives_unit_recurrence -
theorem
posting_coefficients_minimal