Pith Number

pith:UBG4CA3X

pith:2025:UBG4CA3XM7G7CBW3TGHKHIFJGJ

not attested not anchored not stored refs pending

Weak saturation numbers of large complete bipartite graphs

Ilya Vorobyev, Maksim Zhukovskii, Margarita Akhmejanova

arxiv:2508.19435 v1 · 2025-08-26 · 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{UBG4CA3XM7G7CBW3TGHKHIFJGJ}

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	2026-07-05T12:00:11.464739Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a04dc1037767cdf106db998ea3a0a9326545ad366f27fb9831daef748f28fa41

Aliases

arxiv: 2508.19435 · arxiv_version: 2508.19435v1 · doi: 10.48550/arxiv.2508.19435 · pith_short_12: UBG4CA3XM7G7 · pith_short_16: UBG4CA3XM7G7CBW3 · pith_short_8: UBG4CA3X

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/UBG4CA3XM7G7CBW3TGHKHIFJGJ \
  | 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: a04dc1037767cdf106db998ea3a0a9326545ad366f27fb9831daef748f28fa41

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "450b259777b5a94e8b80c80bd11f36f0b3e7ee9dde9d0f0421dbc7c4cf6ae7d6",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2025-08-26T21:09:45Z",
    "title_canon_sha256": "c1a22b80e08a7dda63560453e220ee0c90f0419d8b43c654b6b0532c202a220c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2508.19435",
    "kind": "arxiv",
    "version": 1
  }
}