Pith Number

pith:7RFB3A6F

pith:2014:7RFB3A6FPPLC2UMUZNFDGJWZYH

not attested not anchored not stored refs pending

Locally compact lacunary hyperbolic groups

Adrien Le Boudec

arxiv:1409.8041 v2 · 2014-09-29 · 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{7RFB3A6FPPLC2UMUZNFDGJWZYH}

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	2026-05-18T01:20:29.877857Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fc4a1d83c57bd62d5194cb4a3326d9c1d52b1794a6d796d879b2c7b9156bc49b

Aliases

arxiv: 1409.8041 · arxiv_version: 1409.8041v2 · doi: 10.48550/arxiv.1409.8041 · pith_short_12: 7RFB3A6FPPLC · pith_short_16: 7RFB3A6FPPLC2UMU · pith_short_8: 7RFB3A6F

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/7RFB3A6FPPLC2UMUZNFDGJWZYH \
  | 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: fc4a1d83c57bd62d5194cb4a3326d9c1d52b1794a6d796d879b2c7b9156bc49b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0b8b4ca1662c5a66084d58c895761af9d9e6850c3d16e14264dad2581d263917",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2014-09-29T09:28:41Z",
    "title_canon_sha256": "cfd66894f8b13a7b602001e3a976696617ee1a555428fc06bf7ab611a615c06c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1409.8041",
    "kind": "arxiv",
    "version": 2
  }
}