Pith Number

pith:GDTSX3TB

pith:2013:GDTSX3TBVPHI4UEONI3XVQWF3E

not attested not anchored not stored refs pending

Outerstring graphs are $\chi$-bounded

Alexandre Rok, Bartosz Walczak

arxiv:1312.1559 v4 · 2013-12-05 · math.CO · cs.CG · cs.DM

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{GDTSX3TBVPHI4UEONI3XVQWF3E}

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	2026-05-17T23:59:26.859786Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

30e72bee61abce8e508e6a377ac2c5d933eaca6a1ffa96e1a960ca59c8d9bdc0

Aliases

arxiv: 1312.1559 · arxiv_version: 1312.1559v4 · doi: 10.48550/arxiv.1312.1559 · pith_short_12: GDTSX3TBVPHI · pith_short_16: GDTSX3TBVPHI4UEO · pith_short_8: GDTSX3TB

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/GDTSX3TBVPHI4UEONI3XVQWF3E \
  | 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: 30e72bee61abce8e508e6a377ac2c5d933eaca6a1ffa96e1a960ca59c8d9bdc0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0191529dbe41ccb2b1dd98911cc1dcc0d779149d9d01d65d5090a03432ef0bc2",
    "cross_cats_sorted": [
      "cs.CG",
      "cs.DM"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2013-12-05T14:24:54Z",
    "title_canon_sha256": "2a593db4ebe23fbe96f1dd260f45710be88bec24a170e0ff906fc96eb4df80d2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1312.1559",
    "kind": "arxiv",
    "version": 4
  }
}