# Source Fidelity And Positioning

## Mathematical Lineage

Krasikov and Lagarias developed the finite difference-inequality method and
published exponent `0.84` in:

> Ilia Krasikov and Jeffrey C. Lagarias, “Bounds for the 3x + 1 Problem using
> Difference Inequalities,” *Acta Arithmetica* 109 (2003), 237–258.

The earlier Proof Atlas package `collatz_predecessor_088` formalized a
level-15 certificate with exponent `0.881` and derived the public exponent
`0.88`.

This package keeps the same map, counting convention, target assumptions, and
asymptotic transport while replacing the finite input by a level-18
`0.901` certificate. The fixed fallback used at level 15 does not supply the
bounded potential needed at level 18. The new Lean development proves an
adaptive least-potential fallback and its compatibility with both coefficient
comparison and the time-local minimizing-lift argument.

The standalone extraction byte-preserves every retained proof module except
`Erdos1135/Terras/Core/Defs.lean` and
`Erdos1135/KrasikovLagarias/EliminationNormalizer.lean`. The foundational
Terras file is deliberately reduced to the exact accelerated-map definition
and two branch equations used by this proof, with the same defining expression
as the completed source commit. Removing its unused standard-map and
odd-only-map declarations also removes the unrelated `FormalConjectures`
import path. The normalizer differs only by removal of an unused level-15
import and its level-15 convenience corollary; its generic normalization
definitions and proofs are unchanged. This keeps the release dependency
closure specific to the level-18 theorem.

## Checked Versus Explanatory Claims

Lean checks the exact declarations in `STATEMENT_MAP.md`. Independent Python
and C++ programs replay the finite certificates. Historical, novelty, and
priority statements are separate literature-review questions and are not
implied by Lean.

Public wording should say that this release improves the earlier checked
`0.88` result. Any broader priority claim should remain qualified until its
literature review is recorded.

## Source-Paper Gaps

The inherited formalization does not rely on unsupported repeated-residue
subtree-isomorphism or order-independence claims. Its elimination route uses
explicit normalizers, critical histories, finite-potential termination, and
checked target transport.