Lean verification registry · Authored proofs · The Logos Architecture

Loop Halting Guarantee

Verified sequents with unresolved formal parts
Axiom-free: true · 1 checked theorem statements.

Lean establishes the listed formal statements and dependencies. The exact authored source, Ground, known premise meanings, application validation and empirical evidence remain separately typed. No unencoded section is certified by a neighboring theorem.

Original source author: Maclain Hunter. Machine formalization: Replit Agent. No original wording was rewritten.

Source registered: not established (not original authorship).
Formalized: 2026-10-03T10:37:05.082Z.
Checked: 2026-10-03T10:40:01.752Z.
Independent timestamp: 2026-10-03T10:42:55.000Z.

Authored source SHA-256: 9bca977c1c264cbc7b860f19a086650304fa6c7c8495d1566b6cafb552eba3dd

Lean source · Verification JSON · Exact archived source JSON · Compiler report · Current authored source page · Signed release and verification instructions

Kernel output

Lean (version 4.7.0, commit v4.7.0, Release)
exitCode=0
'HunterAuthored.fuel_iteration_bound' does not depend on any axioms

Source-bound formal statements

fuel_iteration_bound · Kernel-verified · axiom-free

{
  "name": "Loop Halting Guarantee",
  "formal": "∀config.maxDepth ∈ ℕ⁺: mcbLoop terminates in ≤ maxDepth iterations",
  "proof": "Strictly increasing counter bounded by finite maxDepth",
  "implementation": "mcbLoop(initial, transform, config): MCBComputationUnit[]"
}

For every total transform, including early stopping, the finite-fuel loop executes at most maxDepth steps. This checks the mathematical counter argument, not termination of uninstrumented external callbacks.

Exact authored source in the timestamped release

{
  "name": "Loop Halting Guarantee",
  "formal": "∀config.maxDepth ∈ ℕ⁺: mcbLoop terminates in ≤ maxDepth iterations",
  "proof": "Strictly increasing counter bounded by finite maxDepth",
  "implementation": "mcbLoop(initial, transform, config): MCBComputationUnit[]"
}