Pith Number

pith:QVFJIAQC

pith:2025:QVFJIAQCQJ2ACJ5UVJFK7ZV23D

not attested not anchored not stored refs pending

Encoding Peano Arithmetic in a Minimal Fragment of Separation Logic

Makoto Tatsuta, Sohei Ito

Pi-0-1 formulas of Peano arithmetic are valid in the standard model exactly when their translations are valid in this minimal separation logic fragment.

arxiv:2507.00465 v4 · 2025-07-01 · cs.LO

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\usepackage{pith}
\pithnumber{QVFJIAQCQJ2ACJ5UVJFK7ZV23D}

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Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

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The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Claims

C1strongest claim

a formula in Peano arithmetic is valid in the standard model if and only if its translation in this fragment is valid in the standard interpretation

C2weakest assumption

The translation from Pi-0-1 formulas to the separation logic fragment preserves validity exactly under the standard model of arithmetic and the standard heap interpretation of the logic (as stated in the equivalence claim).

C3one line summary

Encodes Pi-0-1 formulas of Peano arithmetic into a minimal separation logic fragment (intuitionistic points-to, 0, successor) and proves validity equivalence, implying undecidability.

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-25T02:01:05.237346Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

854a94020282740127b4aa4aafe6bad8fc7cd9e31459a4ddacbe5e4343f04089

Aliases

arxiv: 2507.00465 · arxiv_version: 2507.00465v4 · doi: 10.48550/arxiv.2507.00465 · pith_short_12: QVFJIAQCQJ2A · pith_short_16: QVFJIAQCQJ2ACJ5U · pith_short_8: QVFJIAQC

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/QVFJIAQCQJ2ACJ5UVJFK7ZV23D \
  | 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: 854a94020282740127b4aa4aafe6bad8fc7cd9e31459a4ddacbe5e4343f04089

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "006d6df61e793a54d84d22b4de199efbbf42ca300191887879b3424c5d8d8214",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.LO",
    "submitted_at": "2025-07-01T06:26:14Z",
    "title_canon_sha256": "0be7992262459b36a382012a88d5814d4e763406bb76103e3da69966caa1319d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2507.00465",
    "kind": "arxiv",
    "version": 4
  }
}