Pith Number

pith:YNXB6YD4

pith:2017:YNXB6YD4LPBRXWKQGKRW6TEPBG

not attested not anchored not stored refs pending

Cubic graphs with small independence ratio

Alexandr Kostochka, J\'ozsef Balogh, Xujun Liu

arxiv:1708.03996 v2 · 2017-08-14 · 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{YNXB6YD4LPBRXWKQGKRW6TEPBG}

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	2026-05-17T23:54:26.686911Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c36e1f607c5bc31bd95032a36f4c8f09b4ab35902d5260691c30691def7ba934

Aliases

arxiv: 1708.03996 · arxiv_version: 1708.03996v2 · doi: 10.48550/arxiv.1708.03996 · pith_short_12: YNXB6YD4LPBR · pith_short_16: YNXB6YD4LPBRXWKQ · pith_short_8: YNXB6YD4

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/YNXB6YD4LPBRXWKQGKRW6TEPBG \
  | 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: c36e1f607c5bc31bd95032a36f4c8f09b4ab35902d5260691c30691def7ba934

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "10945612d8fb229bb797c2b16cf4e46350de728ae9dd9edaad77d7f5910501e0",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2017-08-14T02:46:37Z",
    "title_canon_sha256": "1c5719d713d04221274c86d46b64fd8d692f5ba80c6d48ecda3fcef051569c3b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1708.03996",
    "kind": "arxiv",
    "version": 2
  }
}