Pith Number

pith:CB24SMNJ

pith:2014:CB24SMNJIVLT3OIGMQ56YYIG74

not attested not anchored not stored refs pending

Hyperbolic graphs for free products, and the Gromov boundary of the graph of cyclic splittings

Camille Horbez

arxiv:1408.0544 v3 · 2014-08-03 · math.GR · math.GT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{CB24SMNJIVLT3OIGMQ56YYIG74}

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	2026-05-18T00:44:28.884721Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1075c931a945573db906643bec6106ff2016a141bd244410ba3a816c7117cc62

Aliases

arxiv: 1408.0544 · arxiv_version: 1408.0544v3 · doi: 10.48550/arxiv.1408.0544 · pith_short_12: CB24SMNJIVLT · pith_short_16: CB24SMNJIVLT3OIG · pith_short_8: CB24SMNJ

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/CB24SMNJIVLT3OIGMQ56YYIG74 \
  | 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: 1075c931a945573db906643bec6106ff2016a141bd244410ba3a816c7117cc62

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "09a45585eaeb48ed4d84fa8ef05e09ecb8d88d7dbdccb7ea966de933d08fe87e",
    "cross_cats_sorted": [
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2014-08-03T21:11:36Z",
    "title_canon_sha256": "f705143cc80e06f3bf63e637312ac5020280a1bb975a3c6aece9b550fdf9f0e2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1408.0544",
    "kind": "arxiv",
    "version": 3
  }
}