Pith Number

pith:4QB5C6AA

pith:2011:4QB5C6AA4IDR7SBRNIRNHKCDSB

not attested not anchored not stored refs pending

A Combinatorial Algorithm for All-Pairs Shortest Paths in Directed Vertex-Weighted Graphs with Applications to Disc Graphs

Andrzej Lingas, Dzmitry Sledneu

arxiv:1111.6519 v1 · 2011-11-28 · 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{4QB5C6AA4IDR7SBRNIRNHKCDSB}

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	2026-05-18T03:01:11.412983Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e403d17800e2071fc8316a22d3a84390785ece085987febabf83ce007b0753a0

Aliases

arxiv: 1111.6519 · arxiv_version: 1111.6519v1 · doi: 10.48550/arxiv.1111.6519 · pith_short_12: 4QB5C6AA4IDR · pith_short_16: 4QB5C6AA4IDR7SBR · pith_short_8: 4QB5C6AA

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/4QB5C6AA4IDR7SBRNIRNHKCDSB \
  | 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: e403d17800e2071fc8316a22d3a84390785ece085987febabf83ce007b0753a0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "61c3e4d26c4e3637e5b7ed92e7f5792e32083b576966105503527422a0897696",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.DS",
    "submitted_at": "2011-11-28T17:14:26Z",
    "title_canon_sha256": "8c5e19b3097e4d50e0c3eded07ab13050e2982767c34757fc88581fb21f4342a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1111.6519",
    "kind": "arxiv",
    "version": 1
  }
}