Pith Number

pith:6GTJPBBO

pith:2016:6GTJPBBOJ772ABXR3LCMUQWDBH

not attested not anchored not stored refs pending

Williams decomposition for superprocesses

Renming Song, Rui Zhang, Yan-Xia Ren

arxiv:1609.03265 v1 · 2016-09-12 · 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{6GTJPBBOJ772ABXR3LCMUQWDBH}

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	2026-05-18T01:04:47.343563Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f1a697842e4fffa006f1dac4ca42c309eaf4b688b5557a393e27c1e5fd7abbce

Aliases

arxiv: 1609.03265 · arxiv_version: 1609.03265v1 · doi: 10.48550/arxiv.1609.03265 · pith_short_12: 6GTJPBBOJ772 · pith_short_16: 6GTJPBBOJ772ABXR · pith_short_8: 6GTJPBBO

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/6GTJPBBOJ772ABXR3LCMUQWDBH \
  | 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: f1a697842e4fffa006f1dac4ca42c309eaf4b688b5557a393e27c1e5fd7abbce

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9f6e8329687f40b6a351fef9bcb7b33fdce6ed5447b1a7bece29ac28ebcf674c",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2016-09-12T04:50:49Z",
    "title_canon_sha256": "322d4e3e13c3c1a1439b5237d37d27de2ea0cfc737a2f93998b563ffdafe0cbe"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1609.03265",
    "kind": "arxiv",
    "version": 1
  }
}