Pith Number

pith:RTLOLY66

pith:2003:RTLOLY66L2PUYYZI7K4JKN6XJ3

not attested not anchored not stored refs pending

The First Order Definability of Graphs: Upper Bounds for Quantifier Rank

Helmut Veith, Oleg Pikhurko, Oleg Verbitsky

arxiv:math/0311041 v1 · 2003-11-04 · math.CO · math.LO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{RTLOLY66L2PUYYZI7K4JKN6XJ3}

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	2026-05-18T01:05:28.541739Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8cd6e5e3de5e9f4c6328fab89537d74ecd61fb73211ffc506356c3d73de99f8b

Aliases

arxiv: math/0311041 · arxiv_version: math/0311041v1 · doi: 10.48550/arxiv.math/0311041 · pith_short_12: RTLOLY66L2PU · pith_short_16: RTLOLY66L2PUYYZI · pith_short_8: RTLOLY66

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/RTLOLY66L2PUYYZI7K4JKN6XJ3 \
  | 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: 8cd6e5e3de5e9f4c6328fab89537d74ecd61fb73211ffc506356c3d73de99f8b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fbac4e97aa0ef6b3170fe9aca193bce6ad4001df4c641a39d10f9f3d17f1197b",
    "cross_cats_sorted": [
      "math.LO"
    ],
    "license": "",
    "primary_cat": "math.CO",
    "submitted_at": "2003-11-04T19:07:42Z",
    "title_canon_sha256": "01e1f6dba11d08b9ce991bee0e540c7a93db32553e644dd1e46f4a107b1ae730"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0311041",
    "kind": "arxiv",
    "version": 1
  }
}