Pith Number

pith:5XLBPS36

pith:2014:5XLBPS36RWM4FIU5HB2XENYQR6

not attested not anchored not stored refs pending

A strong geometric hyperbolicity property for directed graphs and monoids

Mark Kambites, Robert Gray

arxiv:1401.0752 v2 · 2014-01-03 · math.GR · 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{5XLBPS36RWM4FIU5HB2XENYQR6}

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	2026-05-18T02:40:18.548539Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

edd617cb7e8d99c2a29d38757237108f9ff43943166c622a0b61ceada3f1885d

Aliases

arxiv: 1401.0752 · arxiv_version: 1401.0752v2 · doi: 10.48550/arxiv.1401.0752 · pith_short_12: 5XLBPS36RWM4 · pith_short_16: 5XLBPS36RWM4FIU5 · pith_short_8: 5XLBPS36

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/5XLBPS36RWM4FIU5HB2XENYQR6 \
  | 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: edd617cb7e8d99c2a29d38757237108f9ff43943166c622a0b61ceada3f1885d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "952fb25a3561f59789cde2d6f031231c031b6f44ce8ed4096b7128ce3a1f3ed7",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2014-01-03T23:11:52Z",
    "title_canon_sha256": "fe61d5a52920391589036e299a77f6634714c016f7594cd9f7f2bf2e5579a4a4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1401.0752",
    "kind": "arxiv",
    "version": 2
  }
}