Pith Number

pith:P7LHA56A

pith:2013:P7LHA56AGACD2WXJ66ZLNEPITL

not attested not anchored not stored refs pending

Martin boundary of random walks with unbounded jumps in hyperbolic groups

S\'ebastien Gou\"ezel (IRMAR)

arxiv:1302.5388 v2 · 2013-02-21 · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{P7LHA56AGACD2WXJ66ZLNEPITL}

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	2026-05-18T01:28:06.281090Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7fd67077c030043d5ae9f7b2b691e89afb8216716b434156f2285fa837f6354b

Aliases

arxiv: 1302.5388 · arxiv_version: 1302.5388v2 · doi: 10.48550/arxiv.1302.5388 · pith_short_12: P7LHA56AGACD · pith_short_16: P7LHA56AGACD2WXJ · pith_short_8: P7LHA56A

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/P7LHA56AGACD2WXJ66ZLNEPITL \
  | 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: 7fd67077c030043d5ae9f7b2b691e89afb8216716b434156f2285fa837f6354b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f31e6baf29cbb71524fbf45b8f79250458b5ae90979506341e15c3f2666c6803",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2013-02-21T19:50:35Z",
    "title_canon_sha256": "c8206ef63708a42897f692e519458d2ee646b536051a1169c174c56d4bc0cec0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1302.5388",
    "kind": "arxiv",
    "version": 2
  }
}