Pith Number

pith:USUDC7DD

pith:2016:USUDC7DDUFVKI6ZTI65HFDQNDW

not attested not anchored not stored refs pending

Reflections at infinity of time changed RBMs on a domain with Liouville branches

Masatoshi Fukushima, Zhen-Qing Chen

arxiv:1611.05772 v1 · 2016-11-17 · 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{USUDC7DDUFVKI6ZTI65HFDQNDW}

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	2026-05-18T00:58:02.618518Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a4a8317c63a16aa47b3347ba728e0d1da2f1ede79f44c59deabb90c3b0fbca0b

Aliases

arxiv: 1611.05772 · arxiv_version: 1611.05772v1 · doi: 10.48550/arxiv.1611.05772 · pith_short_12: USUDC7DDUFVK · pith_short_16: USUDC7DDUFVKI6ZT · pith_short_8: USUDC7DD

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/USUDC7DDUFVKI6ZTI65HFDQNDW \
  | 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: a4a8317c63a16aa47b3347ba728e0d1da2f1ede79f44c59deabb90c3b0fbca0b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d9610dfe02037266a47123e5a340141bd75f5e8d59fef3268e3b984bbf18ad37",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2016-11-17T16:40:41Z",
    "title_canon_sha256": "6057d04c96333efb8eccd5e74c7f8e1fd61f1e2a6bc4f02a2ee71f70631ef7fb"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1611.05772",
    "kind": "arxiv",
    "version": 1
  }
}