Pith Number

pith:SE64HJOD

pith:2026:SE64HJODRJPRO3WA77DHYFP377

not attested not anchored not stored refs pending

Vanishing orders, suspensions and zero degree Tur\'an densities

Haotian Yang, Hong Liu, Jiangdong Ai, Laihao Ding

arxiv:2603.05973 v2 · 2026-03-06 · 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{SE64HJODRJPRO3WA77DHYFP377}

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	2026-07-01T01:17:48.367673Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

913dc3a5c38a5f176ec0ffc67c15fbfffd0fa882f9c1540a6c9c1bad3d0daa04

Aliases

arxiv: 2603.05973 · arxiv_version: 2603.05973v2 · doi: 10.48550/arxiv.2603.05973 · pith_short_12: SE64HJODRJPR · pith_short_16: SE64HJODRJPRO3WA · pith_short_8: SE64HJOD

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/SE64HJODRJPRO3WA77DHYFP377 \
  | 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: 913dc3a5c38a5f176ec0ffc67c15fbfffd0fa882f9c1540a6c9c1bad3d0daa04

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1d88ac6545f0b44c5d5cd9e923882463399665df9cbbcc9e95661d1599ff047b",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2026-03-06T07:13:04Z",
    "title_canon_sha256": "818ca8bd67a8058e91367c8130419f8fbe58c6dca9d34b6a7d0e2eef83196c18"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2603.05973",
    "kind": "arxiv",
    "version": 2
  }
}