Pith Number

pith:TMDF76VQ

pith:2019:TMDF76VQ7UGXTLIJH3NKIQT2NB

not attested not anchored not stored refs pending

A new upper bound on the chromatic number of graphs with no odd $K_t$ minor

Sergey Norin, Zi-Xia Song

arxiv:1912.07647 v1 · 2019-12-16 · 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{TMDF76VQ7UGXTLIJH3NKIQT2NB}

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	2026-07-05T00:26:24.704134Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9b065ffab0fd0d79ad093edaa4427a684bba14dee9a959d1f8f383b5483ed8ff

Aliases

arxiv: 1912.07647 · arxiv_version: 1912.07647v1 · doi: 10.48550/arxiv.1912.07647 · pith_short_12: TMDF76VQ7UGX · pith_short_16: TMDF76VQ7UGXTLIJ · pith_short_8: TMDF76VQ

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/TMDF76VQ7UGXTLIJH3NKIQT2NB \
  | 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: 9b065ffab0fd0d79ad093edaa4427a684bba14dee9a959d1f8f383b5483ed8ff

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6aa152bc60b57c410a19ae3e3b9effbbd95ed88fb45765e2b1f3c562e24f6901",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2019-12-16T19:27:28Z",
    "title_canon_sha256": "aee7487758a970a273ef120a80e54c3010e08b48d10a1b54e82f1c34b48e41c2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1912.07647",
    "kind": "arxiv",
    "version": 1
  }
}