Pith Number

pith:XOZZFYFJ

pith:2011:XOZZFYFJPM2D3ARKFQVYJQJUDK

not attested not anchored not stored refs pending

Max-plus objects to study the complexity of graphs

Cristiano Bocci, Fabio Rapallo, Luca Chiantini

arxiv:1111.1352 v2 · 2011-11-05 · math.PR · 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{XOZZFYFJPM2D3ARKFQVYJQJUDK}

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	2026-05-18T04:09:24.882276Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bbb392e0a97b343d822a2c2b84c1341ab9240aa4941b9b20aa8ea28bb49189cb

Aliases

arxiv: 1111.1352 · arxiv_version: 1111.1352v2 · doi: 10.48550/arxiv.1111.1352 · pith_short_12: XOZZFYFJPM2D · pith_short_16: XOZZFYFJPM2D3ARK · pith_short_8: XOZZFYFJ

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/XOZZFYFJPM2D3ARKFQVYJQJUDK \
  | 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: bbb392e0a97b343d822a2c2b84c1341ab9240aa4941b9b20aa8ea28bb49189cb

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "853e40f77c1e60ac0d3fe0f6eac12f8345627d6bc948cc1c1e32100a89e38fd8",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2011-11-05T21:38:29Z",
    "title_canon_sha256": "b90ec10b973bcd97fe19ae22b0c7741b4ca583d04278f09f83c149bf77383bdc"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1111.1352",
    "kind": "arxiv",
    "version": 2
  }
}