Pith Number

pith:Z5JPJKGU

pith:2019:Z5JPJKGUBPKQMCVRHAIMNKEBOI

not attested not anchored not stored refs pending

Some exact results on $4$-cycles: stability and supersaturation

Jialin He, Jie Ma, Tianchi Yang

arxiv:1912.00986 v4 · 2019-12-02 · 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{Z5JPJKGUBPKQMCVRHAIMNKEBOI}

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	2026-07-05T10:12:12.076689Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cf52f4a8d40bd5060ab13810c6a881721b3a670f5b9af4d26ffa30b86e5e8376

Aliases

arxiv: 1912.00986 · arxiv_version: 1912.00986v4 · doi: 10.48550/arxiv.1912.00986 · pith_short_12: Z5JPJKGUBPKQ · pith_short_16: Z5JPJKGUBPKQMCVR · pith_short_8: Z5JPJKGU

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/Z5JPJKGUBPKQMCVRHAIMNKEBOI \
  | 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: cf52f4a8d40bd5060ab13810c6a881721b3a670f5b9af4d26ffa30b86e5e8376

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0fa8b096151325a226f5926e7f7b35fd1852a2eca06740db69e7fbb86f7a566b",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2019-12-02T18:24:46Z",
    "title_canon_sha256": "713b6dfc00c0a6d4c1be29d25e48c015f5707c8341ede71b6f367ae1053f5128"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1912.00986",
    "kind": "arxiv",
    "version": 4
  }
}