Pith Number

pith:4ZX66BRC

pith:2012:4ZX66BRCTCHKK4MYYRCMZV27WC

not attested not anchored not stored refs pending

A short proof that $\chi$ can be bounded $\epsilon$ away from $\Delta+1$ towards $\omega$

Andrew D. King, Bruce A. Reed

arxiv:1211.1410 v1 · 2012-11-06 · 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{4ZX66BRCTCHKK4MYYRCMZV27WC}

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	2026-05-18T03:41:20.996376Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e66fef0622988ea57198c444ccd75fb098003ea84ffe6c8083f1c7b2eda46ffe

Aliases

arxiv: 1211.1410 · arxiv_version: 1211.1410v1 · doi: 10.48550/arxiv.1211.1410 · pith_short_12: 4ZX66BRCTCHK · pith_short_16: 4ZX66BRCTCHKK4MY · pith_short_8: 4ZX66BRC

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/4ZX66BRCTCHKK4MYYRCMZV27WC \
  | 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: e66fef0622988ea57198c444ccd75fb098003ea84ffe6c8083f1c7b2eda46ffe

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ffb58a618f2e25e017dc2be2bdeaa7ca0b479c9638c82b5a93a7bf1b5c9a623c",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.DM",
    "submitted_at": "2012-11-06T22:02:27Z",
    "title_canon_sha256": "d9a462b866b3636fb2ef2c60e5d4773a021c99678897839a4ba8bb090d77ae5e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1211.1410",
    "kind": "arxiv",
    "version": 1
  }
}