Pith Number

pith:VFMEICSG

pith:2016:VFMEICSG6TMT3IDKFBSMBUVTGF

not attested not anchored not stored refs pending

The Erdos-Posa Property for Directed Graphs

Ken-ichi Kawarabayashi, Paul Wollan, Saeed Akhoondian Amiri, Stephan Kreutzer

arxiv:1603.02504 v3 · 2016-03-08 · cs.DM · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{VFMEICSG6TMT3IDKFBSMBUVTGF}

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	2026-05-18T01:19:10.645771Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a958440a46f4d93da06a2864c0d2b3314a9e1d6ffdb95f34a439a74809bb912f

Aliases

arxiv: 1603.02504 · arxiv_version: 1603.02504v3 · doi: 10.48550/arxiv.1603.02504 · pith_short_12: VFMEICSG6TMT · pith_short_16: VFMEICSG6TMT3IDK · pith_short_8: VFMEICSG

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/VFMEICSG6TMT3IDKFBSMBUVTGF \
  | 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: a958440a46f4d93da06a2864c0d2b3314a9e1d6ffdb95f34a439a74809bb912f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "20a176be36dcd0bc3c7cbe09f84e618440b608b39b32c46b8fa91b37f8f3face",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.DM",
    "submitted_at": "2016-03-08T12:48:38Z",
    "title_canon_sha256": "ecffd7c35bbb896ed11c4bcc785cf375445f363cc921000521684072939fef62"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1603.02504",
    "kind": "arxiv",
    "version": 3
  }
}