Pith Number

pith:3DG7S5SP

pith:2012:3DG7S5SPAVIXJAU2GSGSMYHO72

not attested not anchored not stored refs pending

Random walks on nilpotent groups driven by measures supported on powers of generators

Laurent Saloff-Coste, Tianyi Zheng

arxiv:1211.3003 v1 · 2012-11-13 · math.PR · math.FA · 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{3DG7S5SPAVIXJAU2GSGSMYHO72}

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	2026-05-18T03:40:52.120799Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d8cdf9764f055174829a348d2660eefe896bb0f4c2d3ddc14cd0f08b7a198f4f

Aliases

arxiv: 1211.3003 · arxiv_version: 1211.3003v1 · doi: 10.48550/arxiv.1211.3003 · pith_short_12: 3DG7S5SPAVIX · pith_short_16: 3DG7S5SPAVIXJAU2 · pith_short_8: 3DG7S5SP

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/3DG7S5SPAVIXJAU2GSGSMYHO72 \
  | 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: d8cdf9764f055174829a348d2660eefe896bb0f4c2d3ddc14cd0f08b7a198f4f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8a804be490a51e7bbea809f1bf7a5e6e41239b188ce2dc5a17d153da40bb2f9f",
    "cross_cats_sorted": [
      "math.FA",
      "math.GR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2012-11-13T14:40:36Z",
    "title_canon_sha256": "6e562c22493ae871f0b8c50811faa2d3fae5285b1cd9357ffc1e8c9f7ed15e6e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1211.3003",
    "kind": "arxiv",
    "version": 1
  }
}