Pith Number

pith:ZQGBMEND

pith:2024:ZQGBMENDWOEDN5DMW24GYB4I7M

not attested not anchored not stored refs pending

On $3$-graphs with vanishing codegree Tur\'{a}n density

Ander Lamaison, Haotian Yang, Hong Liu, Laihao Ding, Shuaichao Wang

arxiv:2407.08771 v1 · 2024-07-11 · 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{ZQGBMENDWOEDN5DMW24GYB4I7M}

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	2026-07-05T08:42:55.922174Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cc0c1611a3b38836f46cb6b86c0788fb38f126f17ac94f945d6eb288d7fd5c03

Aliases

arxiv: 2407.08771 · arxiv_version: 2407.08771v1 · doi: 10.48550/arxiv.2407.08771 · pith_short_12: ZQGBMENDWOED · pith_short_16: ZQGBMENDWOEDN5DM · pith_short_8: ZQGBMEND

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/ZQGBMENDWOEDN5DMW24GYB4I7M \
  | 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: cc0c1611a3b38836f46cb6b86c0788fb38f126f17ac94f945d6eb288d7fd5c03

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "22ecae1a0b2572835425277c638576d93ca7a85a6bb995a356d4834b4811c1ea",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/publicdomain/zero/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2024-07-11T17:55:01Z",
    "title_canon_sha256": "f068df1321413370df82e4d94ff3c30d189a352f945ff162682fff2dcf6a4288"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2407.08771",
    "kind": "arxiv",
    "version": 1
  }
}