Pith Number

pith:4OZUWTIY

pith:2011:4OZUWTIY6S3LZSUAIPGZUJUTRO

not attested not anchored not stored refs pending

A brief, simple proof of Vizing's conjecture

Elliot Krop

arxiv:1109.0707 v2 · 2011-09-04 · 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{4OZUWTIY6S3LZSUAIPGZUJUTRO}

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	2026-05-18T04:12:55.548824Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e3b34b4d18f4b6bcca8043cd9a26938badde109b9ef65171bdcd61e958ea01ad

Aliases

arxiv: 1109.0707 · arxiv_version: 1109.0707v2 · doi: 10.48550/arxiv.1109.0707 · pith_short_12: 4OZUWTIY6S3L · pith_short_16: 4OZUWTIY6S3LZSUA · pith_short_8: 4OZUWTIY

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/4OZUWTIY6S3LZSUAIPGZUJUTRO \
  | 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: e3b34b4d18f4b6bcca8043cd9a26938badde109b9ef65171bdcd61e958ea01ad

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "95a634ef8cadbbb9643ddee2ec9694a57baeceaab37a2ff0458ebc40af0c3eb6",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2011-09-04T12:07:25Z",
    "title_canon_sha256": "ce15ef8ca232faaf1adf06ca41c474fe79299bd33d526a2d2cbb567672d39566"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1109.0707",
    "kind": "arxiv",
    "version": 2
  }
}