Pith Number

pith:4SP3JAGO

pith:2018:4SP3JAGOY7F26RMLZTFHE3ABFG

not attested not anchored not stored refs pending

The bipartite $K_{2,2}$-free process and bipartite Ramsey number $b(2, t)$

Deepak Bal, Patrick Bennett

arxiv:1808.02139 v1 · 2018-08-06 · 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{4SP3JAGOY7F26RMLZTFHE3ABFG}

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	2026-05-18T00:08:47.496699Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e49fb480cec7cbaf458bccca726c012998ad46a568e37cc15cc5c52d16f26f21

Aliases

arxiv: 1808.02139 · arxiv_version: 1808.02139v1 · doi: 10.48550/arxiv.1808.02139 · pith_short_12: 4SP3JAGOY7F2 · pith_short_16: 4SP3JAGOY7F26RML · pith_short_8: 4SP3JAGO

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/4SP3JAGOY7F26RMLZTFHE3ABFG \
  | 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: e49fb480cec7cbaf458bccca726c012998ad46a568e37cc15cc5c52d16f26f21

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "cbd55443cf6febbbe22f31cefeed31400e1cfd0797fa6b238dad5df9387d6d4f",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2018-08-06T22:28:33Z",
    "title_canon_sha256": "bf3238b8459687988949d49b9b249e3a59713533ee5d6a57248877d6b1bd8cc4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1808.02139",
    "kind": "arxiv",
    "version": 1
  }
}