Pith Number

pith:K36SLX7H

pith:2023:K36SLX7HN3P2X7N7KXK2XNPTO6

not attested not anchored not stored refs pending

On the Number of Shortest Paths in Graphs

Elad Tzalik, Itai Benjamini

arxiv:2311.10014 v1 · 2023-11-16 · math.CO · math.MG · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{K36SLX7HN3P2X7N7KXK2XNPTO6}

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	2026-07-05T07:13:36.438200Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

56fd25dfe76edfabfdbf55d5abb5f37787584c0dcd87c09789dd12be5bfe4691

Aliases

arxiv: 2311.10014 · arxiv_version: 2311.10014v1 · doi: 10.48550/arxiv.2311.10014 · pith_short_12: K36SLX7HN3P2 · pith_short_16: K36SLX7HN3P2X7N7 · pith_short_8: K36SLX7H

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/K36SLX7HN3P2X7N7KXK2XNPTO6 \
  | 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: 56fd25dfe76edfabfdbf55d5abb5f37787584c0dcd87c09789dd12be5bfe4691

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "dcf585df2589d7da87f8ffcd0891799a3cc6f0dda3fa223580df8f740dfb3ee4",
    "cross_cats_sorted": [
      "math.MG",
      "math.PR"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2023-11-16T16:56:30Z",
    "title_canon_sha256": "e77a5b4611d54aae31d43f92a2db49142fb0d0d8162ea2f693c81f90252fc90e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2311.10014",
    "kind": "arxiv",
    "version": 1
  }
}