Pith Number

pith:7J5V5RC7

pith:2011:7J5V5RC7GXJYUFOMSXQEZ7FM66

not attested not anchored not stored refs pending

On the game chromatic number of sparse random graphs

Alan Frieze, Mikhail Lavrov, Simi Haber

arxiv:1201.0046 v6 · 2011-12-30 · 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{7J5V5RC7GXJYUFOMSXQEZ7FM66}

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	2026-05-18T00:13:48.789088Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fa7b5ec45f35d38a15cc95e04cfcacf7a1919c35a322e52643d37dda55adcadf

Aliases

arxiv: 1201.0046 · arxiv_version: 1201.0046v6 · doi: 10.48550/arxiv.1201.0046 · pith_short_12: 7J5V5RC7GXJY · pith_short_16: 7J5V5RC7GXJYUFOM · pith_short_8: 7J5V5RC7

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/7J5V5RC7GXJYUFOMSXQEZ7FM66 \
  | 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: fa7b5ec45f35d38a15cc95e04cfcacf7a1919c35a322e52643d37dda55adcadf

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1b6179832e5d93352040c878d05fea469b44028d2c6c44c10f2516552e23adb0",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2011-12-30T01:15:04Z",
    "title_canon_sha256": "e7e7be97b69fa160de1705c8cfb294b7c87ebf829e254685ad8b8f0e72a569c1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1201.0046",
    "kind": "arxiv",
    "version": 6
  }
}