Pith Number

pith:N4AF4XOB

pith:2019:N4AF4XOBHNDUYTWXCXOA3EYZFZ

not attested not anchored not stored refs pending

An Improved Error Term for Tur$\acute{\rm a}$n Number of Expanded Non-degenerate 2-graphs

Guiying Yan, Xin Xu, Yucong Tang

arxiv:1904.00146 v1 · 2019-03-30 · 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{N4AF4XOBHNDUYTWXCXOA3EYZFZ}

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	2026-05-17T23:49:49.309776Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6f005e5dc13b474c4ed715dc0d93192e6b120cc2e1b2cba23a786f4fa372643d

Aliases

arxiv: 1904.00146 · arxiv_version: 1904.00146v1 · doi: 10.48550/arxiv.1904.00146 · pith_short_12: N4AF4XOBHNDU · pith_short_16: N4AF4XOBHNDUYTWX · pith_short_8: N4AF4XOB

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/N4AF4XOBHNDUYTWXCXOA3EYZFZ \
  | 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: 6f005e5dc13b474c4ed715dc0d93192e6b120cc2e1b2cba23a786f4fa372643d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b1abfc837b21d059e3cd4f42cd8d191be725981567328d38fe7c487b6de8d07c",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2019-03-30T04:22:36Z",
    "title_canon_sha256": "f1ab3df181e6fc58996c374d72cf2c7ca1ca5a2b4b5b7bcb2a276be9eeabc5a4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1904.00146",
    "kind": "arxiv",
    "version": 1
  }
}