Pith Number

pith:DPGRZ7VR

pith:2011:DPGRZ7VRNUWO4QS44VP62XCK5H

not attested not anchored not stored refs pending

Mysteries around the graph Laplacian eigenvalue 4

Ernest Woei, Naoki Saito, Yuji Nakatsukasa

arxiv:1112.4526 v2 · 2011-12-19 · math.NA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{DPGRZ7VRNUWO4QS44VP62XCK5H}

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	2026-05-18T03:48:23.362143Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1bcd1cfeb16d2cee425ce55fed5c4ae9fd822559055f871ec320315d82995849

Aliases

arxiv: 1112.4526 · arxiv_version: 1112.4526v2 · doi: 10.48550/arxiv.1112.4526 · pith_short_12: DPGRZ7VRNUWO · pith_short_16: DPGRZ7VRNUWO4QS4 · pith_short_8: DPGRZ7VR

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/DPGRZ7VRNUWO4QS44VP62XCK5H \
  | 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: 1bcd1cfeb16d2cee425ce55fed5c4ae9fd822559055f871ec320315d82995849

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "09a3161f374916014509cb93a4c895dec14788667e96178a79aa4b621e253a79",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NA",
    "submitted_at": "2011-12-19T23:05:07Z",
    "title_canon_sha256": "b09722d9bafe1fe08c59dcf27d875c3aba4d09fa0d47c8318dab3ee15b022b92"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1112.4526",
    "kind": "arxiv",
    "version": 2
  }
}