Pith Number

pith:V2F6FVEA

pith:2025:V2F6FVEAMO3J6DX7FROIPU6UYV

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The Orientation Boundary for Step-Duplicating Recursors: Mechanized Impossibility, Escape, and Certification

Moses Rahnama

A mechanized theorem proves that a fixed step-duplicating recursor lies outside all named direct termination measure classes.

arxiv:2512.00081 v10 · 2025-11-26 · cs.LO · math.LO

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Claims

C1strongest claim

We formalize the orientation boundary for first-order step-duplicating recursors: a mechanized object-level barrier theorem, proved without reductions or undecidability, showing that a fixed terminating recursor lies outside named direct termination-measure classes.

C2weakest assumption

The twelve base measure classes (additive, transparency-constrained compositional, scalar growth families, tracked vector and pair families) together with the arctic/tropical extensions and scalar-dominance data exhaust the relevant direct termination measures for the recursor in question.

C3one line summary

Lean 4 formalization establishes an object-level orientation boundary showing fixed step-duplicating recursors lie outside explicit direct termination-measure classes, with three escape routes and tool connections.

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-22T01:03:51.384121Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ae8be2d48063b69f0eff2c5c87d3d4c54aa31b55367959b0ffdaa3af1f439d09

Aliases

arxiv: 2512.00081 · arxiv_version: 2512.00081v10 · doi: 10.48550/arxiv.2512.00081 · pith_short_12: V2F6FVEAMO3J · pith_short_16: V2F6FVEAMO3J6DX7 · pith_short_8: V2F6FVEA

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/V2F6FVEAMO3J6DX7FROIPU6UYV \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: ae8be2d48063b69f0eff2c5c87d3d4c54aa31b55367959b0ffdaa3af1f439d09

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "674c705d1b0b391475396cfbb17af5cf07c5d51709dd71be75b0d101425b407e",
    "cross_cats_sorted": [
      "math.LO"
    ],
    "license": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
    "primary_cat": "cs.LO",
    "submitted_at": "2025-11-26T00:50:17Z",
    "title_canon_sha256": "5425051c777fdf576fae9f18a5996e2e72817cf984b15de85b4e9316dbb495a9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2512.00081",
    "kind": "arxiv",
    "version": 10
  }
}