Pith Number

pith:AECX3NFX

pith:2025:AECX3NFXYYGSS4SFVP3MPOL2TR

not attested not anchored not stored refs pending

A Dichotomy for $k$-automatic expansions of Presburger Arithmetic

Alexi Block Gorman, Chris Schulz, Jason Bell

arxiv:2508.04851 v2 · 2025-08-06 · math.LO · cs.FL

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{AECX3NFXYYGSS4SFVP3MPOL2TR}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

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.

Receipt and verification

First computed	2026-05-18T02:44:33.434156Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

01057db4b7c60d297245abf6c7b97a9c7827e4d2ccf846303954d9f4b053cb5d

Aliases

arxiv: 2508.04851 · arxiv_version: 2508.04851v2 · doi: 10.48550/arxiv.2508.04851 · pith_short_12: AECX3NFXYYGS · pith_short_16: AECX3NFXYYGSS4SF · pith_short_8: AECX3NFX

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/AECX3NFXYYGSS4SFVP3MPOL2TR \
  | 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: 01057db4b7c60d297245abf6c7b97a9c7827e4d2ccf846303954d9f4b053cb5d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "73218b03f8d7bd37dd463f3b0917de4db08cd6475cdd5962592499ae294884e9",
    "cross_cats_sorted": [
      "cs.FL"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.LO",
    "submitted_at": "2025-08-06T19:55:28Z",
    "title_canon_sha256": "3aad1f52d86f646d39768f69bc1aaf002d5fe19a339dfd0d34139e3eeec23949"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2508.04851",
    "kind": "arxiv",
    "version": 2
  }
}