Pith Number

pith:N3SUNISL

pith:2009:N3SUNISLPYQWFIS6I4J5X6NEFJ

not attested not anchored not stored refs pending

Dense H-free graphs are almost (\chi(H)-1)-partite

Peter Allen (DIMAP, University of Warwick)

arxiv:0907.3815 v3 · 2009-07-22 · 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{N3SUNISLPYQWFIS6I4J5X6NEFJ}

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	2026-05-18T04:28:36.584185Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6ee546a24b7e2162a25e4713dbf9a42a50c274429b969571233a7ef7d1e7030c

Aliases

arxiv: 0907.3815 · arxiv_version: 0907.3815v3 · doi: 10.48550/arxiv.0907.3815 · pith_short_12: N3SUNISLPYQW · pith_short_16: N3SUNISLPYQWFIS6 · pith_short_8: N3SUNISL

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/N3SUNISLPYQWFIS6I4J5X6NEFJ \
  | 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: 6ee546a24b7e2162a25e4713dbf9a42a50c274429b969571233a7ef7d1e7030c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b2d4fcfe51fb7a412b455a8e7fb5d5b09b5bd6a00ed07f54d3a177438262e373",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2009-07-22T11:05:35Z",
    "title_canon_sha256": "1486db56b3166373a2cc7732dd775084fc824aaafec1274fab45bc8ea2d26e10"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0907.3815",
    "kind": "arxiv",
    "version": 3
  }
}