Pith Number

pith:SWX2ADO5

pith:2015:SWX2ADO5QNOFOOG5OAHVL2LP6D

not attested not anchored not stored refs pending

On the spectrum of the normalized Laplacian of iterated triangulations of graphs

Francesc Comellas, Pinchen Xie, Zhongzhi Zhang

arxiv:1509.04882 v1 · 2015-09-16 · math.SP · 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{SWX2ADO5QNOFOOG5OAHVL2LP6D}

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	2026-05-18T01:17:52.499761Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

95afa00ddd835c5738dd700f55e96ff0f339bc5260252c42feb09527df8f92e7

Aliases

arxiv: 1509.04882 · arxiv_version: 1509.04882v1 · doi: 10.48550/arxiv.1509.04882 · pith_short_12: SWX2ADO5QNOF · pith_short_16: SWX2ADO5QNOFOOG5 · pith_short_8: SWX2ADO5

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/SWX2ADO5QNOFOOG5OAHVL2LP6D \
  | 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: 95afa00ddd835c5738dd700f55e96ff0f339bc5260252c42feb09527df8f92e7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ac977bce43fb7f030a18e17edce0b54ed3bab3bb505cfce5f913e28ba0b1342d",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.SP",
    "submitted_at": "2015-09-16T10:54:10Z",
    "title_canon_sha256": "c8509c6566acc0a558c590cc732605195ffb03edb3cf010df082177774557701"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1509.04882",
    "kind": "arxiv",
    "version": 1
  }
}