Pith Number

pith:BMNJUV73

pith:2015:BMNJUV73W23QF3XCGOHABVF5YV

not attested not anchored not stored refs pending

Sphere boundaries of hyperbolic groups

Benjamin Beeker, Nir Lazarovich

arxiv:1512.00866 v2 · 2015-12-02 · math.GR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{BMNJUV73W23QF3XCGOHABVF5YV}

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	2026-05-18T00:20:59.987913Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0b1a9a57fbb6b702eee2338e00d4bdc55a7a515e41bafd012cd6c6e195fa9ee7

Aliases

arxiv: 1512.00866 · arxiv_version: 1512.00866v2 · doi: 10.48550/arxiv.1512.00866 · pith_short_12: BMNJUV73W23Q · pith_short_16: BMNJUV73W23QF3XC · pith_short_8: BMNJUV73

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/BMNJUV73W23QF3XCGOHABVF5YV \
  | 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: 0b1a9a57fbb6b702eee2338e00d4bdc55a7a515e41bafd012cd6c6e195fa9ee7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "819273d5cc810a2646590c213cba53150b3364e3a3fd2ef8070544b27e825bcf",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2015-12-02T21:05:06Z",
    "title_canon_sha256": "ffcf8b39bce0eaebcdfe3d28149a86c942d505754029fc0d408cd001418cc702"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1512.00866",
    "kind": "arxiv",
    "version": 2
  }
}