Pith Number

pith:H33SOP5P

pith:2011:H33SOP5PPRSC7XOQ4PEIVBH7WJ

not attested not anchored not stored refs pending

Multidimensional Yamada-Watanabe theorem and its applications to particle systems

Jacek Malecki, Piotr Graczyk

arxiv:1108.1459 v4 · 2011-08-06 · 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{H33SOP5PPRSC7XOQ4PEIVBH7WJ}

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	2026-05-18T03:40:51.509590Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3ef7273faf7c642fddd0e3c88a84ffb2443670ef50b0d260dc1df38b6f85aab1

Aliases

arxiv: 1108.1459 · arxiv_version: 1108.1459v4 · doi: 10.48550/arxiv.1108.1459 · pith_short_12: H33SOP5PPRSC · pith_short_16: H33SOP5PPRSC7XOQ · pith_short_8: H33SOP5P

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/H33SOP5PPRSC7XOQ4PEIVBH7WJ \
  | 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: 3ef7273faf7c642fddd0e3c88a84ffb2443670ef50b0d260dc1df38b6f85aab1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "815ffb59c3704115b0294a7cdaa87bed1ea6dae91561d829765c6476e365ced3",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2011-08-06T07:42:11Z",
    "title_canon_sha256": "380f878aee120442599331c9e41940d313d9fff3314f2f14a781ff876b05a5f3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1108.1459",
    "kind": "arxiv",
    "version": 4
  }
}