Pith Number

pith:U7ZAT54Z

pith:2016:U7ZAT54Z6GTL72AO3BYTJZG5Y6

not attested not anchored not stored refs pending

Graphs of hyperbolic groups and a limit set intersection theorem

Pranab Sardar

arxiv:1606.07264 v2 · 2016-06-23 · math.GT · 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{U7ZAT54Z6GTL72AO3BYTJZG5Y6}

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	2026-05-18T01:04:43.253296Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a7f209f799f1a6bfe80ed87134e4ddc7b25d61925c9f7b5ed147e0a4dfbbcda2

Aliases

arxiv: 1606.07264 · arxiv_version: 1606.07264v2 · doi: 10.48550/arxiv.1606.07264 · pith_short_12: U7ZAT54Z6GTL · pith_short_16: U7ZAT54Z6GTL72AO · pith_short_8: U7ZAT54Z

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/U7ZAT54Z6GTL72AO3BYTJZG5Y6 \
  | 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: a7f209f799f1a6bfe80ed87134e4ddc7b25d61925c9f7b5ed147e0a4dfbbcda2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "31a4c797df21640182664446a231d2cf2a000c8529f28937561ab2f59d72097f",
    "cross_cats_sorted": [
      "math.GR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2016-06-23T10:40:33Z",
    "title_canon_sha256": "81a468844072f65980cefc9f37241a99cf2f2dfcfcfaf9b7d3b7e48f1ff6cc39"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1606.07264",
    "kind": "arxiv",
    "version": 2
  }
}