Pith Number

pith:RRFNAQYB

pith:2012:RRFNAQYBW7MR4L3UNQDMHAPA63

not attested not anchored not stored refs pending

On the spectral density function of the Laplacian of a graph

Herbert Koch, Wolfgang Lueck

arxiv:1205.2321 v2 · 2012-05-10 · 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{RRFNAQYBW7MR4L3UNQDMHAPA63}

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	2026-05-18T02:26:39.602736Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8c4ad04301b7d91e2f746c06c381e0f6f1fa7d7405bdaf0db86834133196b4fc

Aliases

arxiv: 1205.2321 · arxiv_version: 1205.2321v2 · doi: 10.48550/arxiv.1205.2321 · pith_short_12: RRFNAQYBW7MR · pith_short_16: RRFNAQYBW7MR4L3U · pith_short_8: RRFNAQYB

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/RRFNAQYBW7MR4L3UNQDMHAPA63 \
  | 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: 8c4ad04301b7d91e2f746c06c381e0f6f1fa7d7405bdaf0db86834133196b4fc

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5229454c19a23b6478bd01158c3630fe4f17835e92c584f28709a4bf07b6107a",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2012-05-10T17:34:19Z",
    "title_canon_sha256": "b7c0a7cdc3e81de42ef17628eb2402945cf9d77318221c291bdcefc88d815e4c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1205.2321",
    "kind": "arxiv",
    "version": 2
  }
}