IndisputableMonolith.LedgerUnits
The LedgerUnits module defines the cyclic subgroup of the integers generated by a parameter δ and specializes to δ equal to one to obtain an order isomorphism with the integers. It supplies conversion maps between the subgroup and the integers together with uniqueness and round-trip lemmas. Researchers working on discrete ledger models in complexity theory would reference these units. The module consists entirely of definitions and elementary lemmas with no non-trivial proofs.
claimThe subgroup $\langle \delta \rangle \leq \mathbb{Z}$ generated by $\delta$, equipped with order-isomorphism maps between the subgroup and $\mathbb{Z}$ when $\delta = 1$.
background
The module establishes the subgroup of the integers generated by a parameter δ. The doc-comment states: 'The subgroup of ℤ generated by δ. We specialize to δ = 1 for a clean order isomorphism.' It defines the subgroup and supplies the conversion maps together with lemmas on specification, uniqueness, and the round-trip identities. The setting is purely algebraic and imports only Mathlib.
proof idea
This is a definition module, no proofs.
why it matters in Recognition Science
This module supplies the basic unit conversions imported by the ComputationBridge scaffold. That downstream module is explicitly marked as a scaffold exploring a hypothetical P versus NP framework based on ledger-style dual complexity and lies outside the verified certificate chain.
scope and limits
- Does not form part of the main certificate chain.
- Does not contain any results from the forcing chain T0 to T8.
- Does not address physical constants or mass formulas.
- Specializes the subgroup exclusively to the case δ = 1.
used by (1)
declarations in this module (23)
-
def
DeltaSub -
def
fromZ_one -
def
toZ_one -
lemma
toZ_fromZ_one -
lemma
fromZ_toZ_one -
def
equiv_delta_one -
def
fromZ -
def
toZ -
lemma
toZ_spec -
lemma
rep_unique -
lemma
toZ_fromZ -
lemma
fromZ_toZ -
lemma
toZ_succ -
def
rungOf -
lemma
rungOf_fromZ -
lemma
rungOf_step -
def
equiv_delta -
def
fromNat -
def
kOf -
lemma
kOf_fromZ -
lemma
kOf_fromNat -
lemma
kOf_step_succ -
theorem
quantization