Pith Number

pith:XPIW7PDL

pith:2016:XPIW7PDLZRVIIVE3TEVI73NUVG

not attested not anchored not stored refs pending

Homomorphism bounds and edge-colourings of $K_4$-minor-free graphs

Florent Foucaud, Laurent Beaudou, Reza Naserasr

arxiv:1610.03999 v2 · 2016-10-13 · math.CO · cs.DS

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{XPIW7PDLZRVIIVE3TEVI73NUVG}

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	2026-05-18T00:24:53.172361Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bbd16fbc6bcc6a84549b992a8fedb4a9963e2742be1d4db3b78785866b4a7685

Aliases

arxiv: 1610.03999 · arxiv_version: 1610.03999v2 · doi: 10.48550/arxiv.1610.03999 · pith_short_12: XPIW7PDLZRVI · pith_short_16: XPIW7PDLZRVIIVE3 · pith_short_8: XPIW7PDL

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/XPIW7PDLZRVIIVE3TEVI73NUVG \
  | 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: bbd16fbc6bcc6a84549b992a8fedb4a9963e2742be1d4db3b78785866b4a7685

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "564302e57cd6f2367877e9eaae576733a8d4113c575a7aa8a9d4c3e7f3fc15fc",
    "cross_cats_sorted": [
      "cs.DS"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2016-10-13T09:52:58Z",
    "title_canon_sha256": "d69bf9bf77b91139ae92a7902694b7a8b7efe6ea504ce498ce20a9551a1e27dc"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1610.03999",
    "kind": "arxiv",
    "version": 2
  }
}