Pith Number

pith:4I7DHCG7

pith:2013:4I7DHCG7FOWNZMBSQS6OJZK4VP

not attested not anchored not stored refs pending

Interpreting the von Neumann entropy of graph Laplacians, and coentropic graphs

Niel de Beaudrap, Richard Wilson, Simone Severini, Vittorio Giovannetti

arxiv:1304.7946 v1 · 2013-04-30 · 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{4I7DHCG7FOWNZMBSQS6OJZK4VP}

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	2026-05-18T03:26:51.345284Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e23e3388df2bacdcb03284bce4e55cabf099cb6974b9620dc33bcd53a192ee4b

Aliases

arxiv: 1304.7946 · arxiv_version: 1304.7946v1 · doi: 10.48550/arxiv.1304.7946 · pith_short_12: 4I7DHCG7FOWN · pith_short_16: 4I7DHCG7FOWNZMBS · pith_short_8: 4I7DHCG7

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/4I7DHCG7FOWNZMBSQS6OJZK4VP \
  | 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: e23e3388df2bacdcb03284bce4e55cabf099cb6974b9620dc33bcd53a192ee4b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4c5a7fea988e9cf7d7505e20818e0fcf38d250c61ddafc35edf3a270ff2f2eb8",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2013-04-30T10:38:59Z",
    "title_canon_sha256": "695aa8d24282fafe8cc462b0a2cc386b665572e2c7f9f35c7de627a91362c6e6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1304.7946",
    "kind": "arxiv",
    "version": 1
  }
}