Pith Number

pith:BC3WL352

pith:2021:BC3WL352B4AW2NUNWKQQKB6IKU

not attested not anchored not stored refs pending

Upper bounds on the extremal number of the 4-cycle

Jie Ma, Tianchi Yang

arxiv:2107.11601 v3 · 2021-07-24 · 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{BC3WL352B4AW2NUNWKQQKB6IKU}

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	2026-07-05T03:21:56.450539Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

08b765efba0f016d368db2a10507c8553d3eba5cd240b3a793fe275ce1c74fb3

Aliases

arxiv: 2107.11601 · arxiv_version: 2107.11601v3 · doi: 10.48550/arxiv.2107.11601 · pith_short_12: BC3WL352B4AW · pith_short_16: BC3WL352B4AW2NUN · pith_short_8: BC3WL352

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/BC3WL352B4AW2NUNWKQQKB6IKU \
  | 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: 08b765efba0f016d368db2a10507c8553d3eba5cd240b3a793fe275ce1c74fb3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5220ad7baba43923037fa7ecc8d0a06e0c173fbc411d5a78c0c50206679a89b5",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2021-07-24T13:30:40Z",
    "title_canon_sha256": "abd72f45dfd71a00fae097e5330912b42c412ef4cc2dc8fbf8b00580b4bf83dc"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2107.11601",
    "kind": "arxiv",
    "version": 3
  }
}