Pith Number

pith:HX7RWQX2

pith:2016:HX7RWQX2Y55XUR5R3YN3HRGE35

not attested not anchored not stored refs pending

Thin annuli property and exponential distribution of return times for Weakly Markov systems

Anna Zdunik, {\L}ukasz Pawelec, Mariusz Urba\'nski

arxiv:1605.06917 v4 · 2016-05-23 · math.DS

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{HX7RWQX2Y55XUR5R3YN3HRGE35}

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	2026-05-17T23:57:06.251336Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3dff1b42fac77b7a47b1de1bb3c4c4df736bd95ec8014c1ba5fa7f88129a10ea

Aliases

arxiv: 1605.06917 · arxiv_version: 1605.06917v4 · doi: 10.48550/arxiv.1605.06917 · pith_short_12: HX7RWQX2Y55X · pith_short_16: HX7RWQX2Y55XUR5R · pith_short_8: HX7RWQX2

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/HX7RWQX2Y55XUR5R3YN3HRGE35 \
  | 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: 3dff1b42fac77b7a47b1de1bb3c4c4df736bd95ec8014c1ba5fa7f88129a10ea

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6e42564e733f6c55a0d373573f2e82c4d995a70d1355c70ed021fa2041d86935",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2016-05-23T07:21:52Z",
    "title_canon_sha256": "440074cabce6abb1c488fbc104127ac30a3db845a0482ced17d52f3d0931a9aa"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1605.06917",
    "kind": "arxiv",
    "version": 4
  }
}