Pith Number

pith:5A5YHB2E

pith:2023:5A5YHB2EDI72B2QFIBA4JV62PW

not attested not anchored not stored refs pending

Proof of a conjecture on distribution of Laplacian eigenvalues and diameter, and beyond

Bo Zhou, Leyou Xu

arxiv:2303.11503 v2 · 2023-03-20 · 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{5A5YHB2EDI72B2QFIBA4JV62PW}

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	2026-07-05T06:22:01.726164Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e83b8387441a3fa0ea054041c4d7da7db56ab8781d6fa35b6d0ccd5d00a848b8

Aliases

arxiv: 2303.11503 · arxiv_version: 2303.11503v2 · doi: 10.48550/arxiv.2303.11503 · pith_short_12: 5A5YHB2EDI72 · pith_short_16: 5A5YHB2EDI72B2QF · pith_short_8: 5A5YHB2E

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/5A5YHB2EDI72B2QFIBA4JV62PW \
  | 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: e83b8387441a3fa0ea054041c4d7da7db56ab8781d6fa35b6d0ccd5d00a848b8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ac8c2de66adf5832d5a29f4009df63a03e85945c6c59be4d9a72f94cb487eb4d",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2023-03-20T23:47:36Z",
    "title_canon_sha256": "a5b29d3d440dfbde45eeeaa873031cedeeaba2daf8cbe6d9cb5257f7fee4db84"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2303.11503",
    "kind": "arxiv",
    "version": 2
  }
}