HA + independent Lean evidence · Research, not Alpha admission

ND0400 — NatExpAtanhRecurrence

Full irrationality (IR072/G121) remains open. Stable: 432. Alpha v35: 4,318. This checkpoint changes neither catalogue.

Conservative definition

Parameters: b, c, L, D

S D ≤ S (1 · c) ∧ (∃ x. b = x · S (1 · c) + D) ∧ (S (2 · D) ≤ S (2 · c) ∧ (∃ x. b = x · S (2 · c) + 2 · D) ∧ (∀ x. ∀ y. ∀ z. ∀ n. S S S x ≤ L → S y ≤ S (S x · c) ∧ (∃ m. b = m · S (S x · c) + y) → S z ≤ S (S S x · c) ∧ (∃ m. b = m · S (S S x · c) + z) → S n ≤ S (S S S x · c) ∧ (∃ m. b = m · S (S S S x · c) + n) → S S x · n = x · y + 2 · z))

Definition prerequisites

PD0013 · PD0002

Theorem uses (notation, not proof premises)

CV002 · CV029 · CV031 · CV034