Pith Number

pith:Y4HVB3FH

pith:2013:Y4HVB3FHPWZQGOFFSYUKOXENGJ

not attested not anchored not stored refs pending

On free stochastic processes and their derivatives

Daniel Alpay, Guy Salomon, Palle Jorgensen

arxiv:1311.3239 v1 · 2013-11-13 · math.OA · math.FA · 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{Y4HVB3FHPWZQGOFFSYUKOXENGJ}

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	2026-05-18T03:07:12.598138Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c70f50eca77db30338a59628a75c8d327c442d448a3d2f07c067f6733a50de8a

Aliases

arxiv: 1311.3239 · arxiv_version: 1311.3239v1 · doi: 10.48550/arxiv.1311.3239 · pith_short_12: Y4HVB3FHPWZQ · pith_short_16: Y4HVB3FHPWZQGOFF · pith_short_8: Y4HVB3FH

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/Y4HVB3FHPWZQGOFFSYUKOXENGJ \
  | 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: c70f50eca77db30338a59628a75c8d327c442d448a3d2f07c067f6733a50de8a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0f51725a8e66c814f7c3f6db8bc677288208761cc8e15d2839bd2ef5d420b9fc",
    "cross_cats_sorted": [
      "math.FA",
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OA",
    "submitted_at": "2013-11-13T18:24:56Z",
    "title_canon_sha256": "50e901ae3b54e2815667fa5a55e32724841c0b39b3dda0c90300089a68dc2dd1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1311.3239",
    "kind": "arxiv",
    "version": 1
  }
}