Pith Number

pith:3PZYZ53W

pith:2016:3PZYZ53WPS6NTSFIJOIRH4USKB

not attested not anchored not stored refs pending

Spectral properties of the hierarchical product of graphs

Kirsti Wash, Per Sebastian Skardal

arxiv:1606.03930 v2 · 2016-06-13 · nlin.AO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{3PZYZ53WPS6NTSFIJOIRH4USKB}

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	2026-05-18T00:56:46.002481Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

dbf38cf7767cbcd9c8a84b9113f2925054005924c1af2065d78cd5cddc2632e6

Aliases

arxiv: 1606.03930 · arxiv_version: 1606.03930v2 · doi: 10.48550/arxiv.1606.03930 · pith_short_12: 3PZYZ53WPS6N · pith_short_16: 3PZYZ53WPS6NTSFI · pith_short_8: 3PZYZ53W

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/3PZYZ53WPS6NTSFIJOIRH4USKB \
  | 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: dbf38cf7767cbcd9c8a84b9113f2925054005924c1af2065d78cd5cddc2632e6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3132a8b8cc07e6c8139a654bd528bfd0513f885894eaf2d5ec5e8e307b6ff358",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "nlin.AO",
    "submitted_at": "2016-06-13T13:01:09Z",
    "title_canon_sha256": "31500352d810d8e95a823f01a7d13f5259ae50d2c53ca8df083ffd624d12defb"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1606.03930",
    "kind": "arxiv",
    "version": 2
  }
}