Pith Number

pith:S4YZYJOA

pith:2011:S4YZYJOAXFPSUYRDBCDEEFXDZN

not attested not anchored not stored refs pending

Exponential return times in a zero-entropy process

Michal Kupsa, Paulina Grzegorek

arxiv:1101.1828 v1 · 2011-01-10 · math.DS · 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{S4YZYJOAXFPSUYRDBCDEEFXDZN}

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	2026-05-18T04:31:51.714598Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

97319c25c0b95f2a622308864216e3cb5416ae32607ca4060c1de250dc1760e7

Aliases

arxiv: 1101.1828 · arxiv_version: 1101.1828v1 · doi: 10.48550/arxiv.1101.1828 · pith_short_12: S4YZYJOAXFPS · pith_short_16: S4YZYJOAXFPSUYRD · pith_short_8: S4YZYJOA

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/S4YZYJOAXFPSUYRDBCDEEFXDZN \
  | 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: 97319c25c0b95f2a622308864216e3cb5416ae32607ca4060c1de250dc1760e7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a1c5ae8cc65e1959e76c8d421f1706b7a4a7b330759c7dc8832ed828162b3fa6",
    "cross_cats_sorted": [
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2011-01-10T14:28:19Z",
    "title_canon_sha256": "7e95ff0ee8b53fac4f14e58fdb341c493de489fede70dc0a3f48fb27bcf9750e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1101.1828",
    "kind": "arxiv",
    "version": 1
  }
}