Pith Number

pith:3XSJVT6N

pith:2016:3XSJVT6N5XQMPTX6FQDYSB3T3L

not attested not anchored not stored refs pending

Hyperbolicity of direct products of graphs

Alvaro Mart\'inez-P\'erez, Amauris de la Cruz, Jos\'e M. Rodr\'iguez, Walter Carballosa

arxiv:1611.04372 v1 · 2016-11-14 · math.MG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{3XSJVT6N5XQMPTX6FQDYSB3T3L}

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	2026-05-18T00:59:16.801180Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

dde49acfcdede0c7cefe2c07890773dad169c14a83d7270148dc5b3ce7cc0759

Aliases

arxiv: 1611.04372 · arxiv_version: 1611.04372v1 · doi: 10.48550/arxiv.1611.04372 · pith_short_12: 3XSJVT6N5XQM · pith_short_16: 3XSJVT6N5XQMPTX6 · pith_short_8: 3XSJVT6N

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/3XSJVT6N5XQMPTX6FQDYSB3T3L \
  | 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: dde49acfcdede0c7cefe2c07890773dad169c14a83d7270148dc5b3ce7cc0759

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a55247f66e04909e9d4a7d26ab2fda9a1142c7fdf1be657fa3e1d6e4f609deae",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.MG",
    "submitted_at": "2016-11-14T13:03:17Z",
    "title_canon_sha256": "7420f728a5b9347be63fce04cc901e8929c87cc97f7e39a5564b9337c689ba78"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1611.04372",
    "kind": "arxiv",
    "version": 1
  }
}