Pith Number

pith:ZTPUWKSK

pith:2011:ZTPUWKSKH3KCJUYFRX3CJIFZDA

not attested not anchored not stored refs pending

Stochastic processes induced by singular operators

Daniel Alpay, Palle Jorgensen

arxiv:1109.5273 v1 · 2011-09-24 · math.PR · math.FA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{ZTPUWKSKH3KCJUYFRX3CJIFZDA}

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	2026-05-18T04:12:20.183455Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ccdf4b2a4a3ed424d3058df624a0b9182ba9e61ae03c83fb2d22c4d73093cebc

Aliases

arxiv: 1109.5273 · arxiv_version: 1109.5273v1 · doi: 10.48550/arxiv.1109.5273 · pith_short_12: ZTPUWKSKH3KC · pith_short_16: ZTPUWKSKH3KCJUYF · pith_short_8: ZTPUWKSK

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/ZTPUWKSKH3KCJUYFRX3CJIFZDA \
  | 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: ccdf4b2a4a3ed424d3058df624a0b9182ba9e61ae03c83fb2d22c4d73093cebc

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ff7b53c6d180ba3c1ae817586d98c876a6257576d06ecfaed08ee44290a91be0",
    "cross_cats_sorted": [
      "math.FA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2011-09-24T14:32:39Z",
    "title_canon_sha256": "f82df16a4604f9e460cfda263d933784d0a11ed3ef8a4fb7f065c5923cb82093"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1109.5273",
    "kind": "arxiv",
    "version": 1
  }
}