Pith Number

pith:6VGNULUP

pith:2016:6VGNULUPCVJ3EBZ5AB4YXAOTQT

not attested not anchored not stored refs pending

The structure of typical eye-free graphs and a Turan-type result for two weighted colours

Peter Keevash, William Lochet

arxiv:1608.08990 v1 · 2016-08-31 · 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{6VGNULUPCVJ3EBZ5AB4YXAOTQT}

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	2026-05-18T01:06:39.506727Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f54cda2e8f1553b2073d00798b81d384f5af3342e2b08d987096f04b7d6bcc1f

Aliases

arxiv: 1608.08990 · arxiv_version: 1608.08990v1 · doi: 10.48550/arxiv.1608.08990 · pith_short_12: 6VGNULUPCVJ3 · pith_short_16: 6VGNULUPCVJ3EBZ5 · pith_short_8: 6VGNULUP

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/6VGNULUPCVJ3EBZ5AB4YXAOTQT \
  | 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: f54cda2e8f1553b2073d00798b81d384f5af3342e2b08d987096f04b7d6bcc1f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "76a60fbd2090d169b14a8d8da629ccde46e0e7e371912647a7debec8925f151e",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2016-08-31T18:46:34Z",
    "title_canon_sha256": "1005e03182d20a5e42b1694ff686b99daed53159ac12a1ea65947a435f301f40"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1608.08990",
    "kind": "arxiv",
    "version": 1
  }
}