Pith Number

pith:LD3Y4WFZ

pith:2025:LD3Y4WFZJB2I62NMRQMR2S5TM6

not attested not anchored not stored refs pending

On the characterizations of $\mathcal{D}_{k} \backslash \mathcal{D}_{k-2}$

Hong-Jian Lai, Jing Zeng, Lihua You, Xinghui Zhao

arxiv:2508.07332 v2 · 2025-08-10 · 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{LD3Y4WFZJB2I62NMRQMR2S5TM6}

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	2026-06-12T01:09:12.097974Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

58f78e58b948748f69ac8c191d4bb36787d5ae4a1ac498a2ce4fcc5fe4e97816

Aliases

arxiv: 2508.07332 · arxiv_version: 2508.07332v2 · doi: 10.48550/arxiv.2508.07332 · pith_short_12: LD3Y4WFZJB2I · pith_short_16: LD3Y4WFZJB2I62NM · pith_short_8: LD3Y4WFZ

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/LD3Y4WFZJB2I62NMRQMR2S5TM6 \
  | 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: 58f78e58b948748f69ac8c191d4bb36787d5ae4a1ac498a2ce4fcc5fe4e97816

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "54f9eb6eb5eddfb7a780adf84468b519e4a1505ba48d39bbc621f1d1a58eaa7d",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2025-08-10T13:17:57Z",
    "title_canon_sha256": "4d87bcea4e33d0f6419f9484c18dc529d7c1e8486bd8410efd53477404318eb4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2508.07332",
    "kind": "arxiv",
    "version": 2
  }
}