Pith Number

pith:7W32NSZ3

pith:2018:7W32NSZ3J53UULSQ3JUDT4B5KX

not attested not anchored not stored refs pending

Linearity of Saturation for Berge Hypergraphs

Abhishek Methuku, D\'aniel Gerbner, Michael Tait, Sean English

arxiv:1807.06947 v1 · 2018-07-18 · 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{7W32NSZ3J53UULSQ3JUDT4B5KX}

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	2026-05-18T00:10:25.253902Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fdb7a6cb3b4f774a2e50da6839f03d55d0b1a3be7926abacfe03d111733d09ed

Aliases

arxiv: 1807.06947 · arxiv_version: 1807.06947v1 · doi: 10.48550/arxiv.1807.06947 · pith_short_12: 7W32NSZ3J53U · pith_short_16: 7W32NSZ3J53UULSQ · pith_short_8: 7W32NSZ3

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/7W32NSZ3J53UULSQ3JUDT4B5KX \
  | 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: fdb7a6cb3b4f774a2e50da6839f03d55d0b1a3be7926abacfe03d111733d09ed

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2a8a64fedf8eabeff29306b1078ea3e98788597209a1b0eed1f1776a156c06ca",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2018-07-18T14:01:55Z",
    "title_canon_sha256": "9f727aae2279290264c2799c614dae4ded4ce76e2603fed721e1c287c64261e0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1807.06947",
    "kind": "arxiv",
    "version": 1
  }
}