Pith Number

pith:FCIPMSG6

pith:2012:FCIPMSG6FLGT3SNCTH5TAA5KTT

not attested not anchored not stored refs pending

Short proofs of coloring theorems on planar graphs

Alexandr V. Kostochka, Bernard Lidick\'y, Matthew Yancey, Oleg V. Borodin

arxiv:1211.3981 v1 · 2012-11-16 · math.CO · 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{FCIPMSG6FLGT3SNCTH5TAA5KTT}

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	2026-05-18T00:54:58.457235Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2890f648de2acd3dc9a299fb3003aa9cd68899b19727703df6247cd954a3820d

Aliases

arxiv: 1211.3981 · arxiv_version: 1211.3981v1 · doi: 10.48550/arxiv.1211.3981 · pith_short_12: FCIPMSG6FLGT · pith_short_16: FCIPMSG6FLGT3SNC · pith_short_8: FCIPMSG6

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/FCIPMSG6FLGT3SNCTH5TAA5KTT \
  | 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: 2890f648de2acd3dc9a299fb3003aa9cd68899b19727703df6247cd954a3820d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1adcfb9f6f7c7b99805c915d320b6da5bae78212d0fdc317cd1034db4a6b4712",
    "cross_cats_sorted": [
      "cs.DM"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2012-11-16T18:19:43Z",
    "title_canon_sha256": "e1ada59021363000676a5bb0023d50f4b8e10daa55d049376575aeee1875b790"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1211.3981",
    "kind": "arxiv",
    "version": 1
  }
}