Pith Number

pith:AF7JGRCU

pith:2015:AF7JGRCUY3BY3W7ST4CY63P2BU

not attested not anchored not stored refs pending

Intrinsic random walks and sub-Laplacians in sub-Riemannian geometry

Luca Rizzi, Robert Neel, Ugo Boscain

arxiv:1503.00725 v4 · 2015-03-02 · math.DG · math.AP · math.OC · 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{AF7JGRCUY3BY3W7ST4CY63P2BU}

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	2026-05-18T00:42:49.139143Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

017e934454c6c38ddbf29f058f6dfa0d09fd7dc0f658e8533e4da8e40d7805c2

Aliases

arxiv: 1503.00725 · arxiv_version: 1503.00725v4 · doi: 10.48550/arxiv.1503.00725 · pith_short_12: AF7JGRCUY3BY · pith_short_16: AF7JGRCUY3BY3W7S · pith_short_8: AF7JGRCU

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/AF7JGRCUY3BY3W7ST4CY63P2BU \
  | 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: 017e934454c6c38ddbf29f058f6dfa0d09fd7dc0f658e8533e4da8e40d7805c2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1c2335bf986c4fb09fa1d2208f40a9321f7da06de579479ed131a0e2635426fc",
    "cross_cats_sorted": [
      "math.AP",
      "math.OC",
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2015-03-02T21:00:13Z",
    "title_canon_sha256": "b0cfbb300813ae734e83b44ea9565de64a1f59c2b36f0e67eae1f04343fcfe47"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1503.00725",
    "kind": "arxiv",
    "version": 4
  }
}