Pith Number

pith:IJBSUSBL

pith:2013:IJBSUSBLZEYBMPCIUWPMGMJ7GW

not attested not anchored not stored refs pending

Estimates of the gaps between consecutive eigenvalues of Laplacian

Daguang Chen, Hongcang Yang, Tao Zheng

arxiv:1309.7446 v1 · 2013-09-28 · math.DG

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{IJBSUSBLZEYBMPCIUWPMGMJ7GW}

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	2026-05-18T01:18:10.443381Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

42432a482bc930163c48a59ec3313f35a865ad5393346ad6915b729a3f79955c

Aliases

arxiv: 1309.7446 · arxiv_version: 1309.7446v1 · doi: 10.48550/arxiv.1309.7446 · pith_short_12: IJBSUSBLZEYB · pith_short_16: IJBSUSBLZEYBMPCI · pith_short_8: IJBSUSBL

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/IJBSUSBLZEYBMPCIUWPMGMJ7GW \
  | 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: 42432a482bc930163c48a59ec3313f35a865ad5393346ad6915b729a3f79955c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4a047b2c1dbff53cd1f865185bf08d7df18e74d6d5d6ae3617b88bad6fb30132",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/3.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2013-09-28T10:19:17Z",
    "title_canon_sha256": "ddecc9f02d0b520753cc0cfcdb85e1fdd6c3882c7cb9c7a6d29b2b930849e74f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1309.7446",
    "kind": "arxiv",
    "version": 1
  }
}