Pith Number

pith:QJ7XNGBP

pith:2011:QJ7XNGBPLUZVXQ3QQI5NT4MQL2

not attested not anchored not stored refs pending

Random Walk on a Co-Compact Fuchsian Group

S\'ebastien Gou\"ezel, Steven P. Lalley

arxiv:1107.5591 v3 · 2011-07-27 · math.PR · 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{QJ7XNGBPLUZVXQ3QQI5NT4MQL2}

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	2026-05-18T03:55:23.879782Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

827f76982f5d335bc370823ad9f1905eb1730c36e79664c8ead755d15bad69f0

Aliases

arxiv: 1107.5591 · arxiv_version: 1107.5591v3 · doi: 10.48550/arxiv.1107.5591 · pith_short_12: QJ7XNGBPLUZV · pith_short_16: QJ7XNGBPLUZVXQ3Q · pith_short_8: QJ7XNGBP

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/QJ7XNGBPLUZVXQ3QQI5NT4MQL2 \
  | 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: 827f76982f5d335bc370823ad9f1905eb1730c36e79664c8ead755d15bad69f0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5d86c71c87fa9691c9b3d64402bed7982b2ecd052191e6d675a476a7cb36fac8",
    "cross_cats_sorted": [
      "math.GR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2011-07-27T20:31:52Z",
    "title_canon_sha256": "d18112237bfeea68ac2a4bcafbccf3f145d2ebae00daa7cdea215990fd510023"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1107.5591",
    "kind": "arxiv",
    "version": 3
  }
}