Pith Number

pith:4LPKSSOL

pith:2016:4LPKSSOLGMKMU5D3O27W455XW3

not attested not anchored not stored refs pending

Average Shortest Path Length of Graphs of Diameter 3

Nobutaka Shimizu, Ryuhei Mori

arxiv:1606.05119 v1 · 2016-06-16 · cs.DM · cs.DS

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{4LPKSSOLGMKMU5D3O27W455XW3}

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	2026-05-18T01:12:21.980607Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e2dea949cb3314ca747b76bf6e77b7b6df37ff203dca3fe74aba4f2e4401a935

Aliases

arxiv: 1606.05119 · arxiv_version: 1606.05119v1 · doi: 10.48550/arxiv.1606.05119 · pith_short_12: 4LPKSSOLGMKM · pith_short_16: 4LPKSSOLGMKMU5D3 · pith_short_8: 4LPKSSOL

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/4LPKSSOLGMKMU5D3O27W455XW3 \
  | 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: e2dea949cb3314ca747b76bf6e77b7b6df37ff203dca3fe74aba4f2e4401a935

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "140e69ec629be668cb9a53adba80b5443ebfa75eaffc3001b5e9e854ad6e349d",
    "cross_cats_sorted": [
      "cs.DS"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.DM",
    "submitted_at": "2016-06-16T10:04:18Z",
    "title_canon_sha256": "b2cb7262bcb4ad61bffc9731c4a5bf71072cfcf94ef0093ccf99dda4263b7631"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1606.05119",
    "kind": "arxiv",
    "version": 1
  }
}