Pith Number

pith:CIATMAKB

pith:2016:CIATMAKBS5UJSMYMFSENGME3GM

not attested not anchored not stored refs pending

Under recurrence in the Khintchine recurrence theorem

M\'at\'e Wierdl, Michael Boshernitzan, Nikos Frantzikinakis

arxiv:1603.07720 v3 · 2016-03-24 · math.DS · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{CIATMAKBS5UJSMYMFSENGME3GM}

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	2026-05-18T00:55:39.290641Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1201360141976899330c2c88d3309b3327bb911b30991d14c9f10e46fc6b25b0

Aliases

arxiv: 1603.07720 · arxiv_version: 1603.07720v3 · doi: 10.48550/arxiv.1603.07720 · pith_short_12: CIATMAKBS5UJ · pith_short_16: CIATMAKBS5UJSMYM · pith_short_8: CIATMAKB

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/CIATMAKBS5UJSMYMFSENGME3GM \
  | 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: 1201360141976899330c2c88d3309b3327bb911b30991d14c9f10e46fc6b25b0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a883b673bb1920b19956d1e446ca61300fc616131b02f5914397ae84b8cfe720",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2016-03-24T19:49:17Z",
    "title_canon_sha256": "0c842b5bb45fdc68d30c6182b12717d749dd053f084e19ff7c780b91408ca2fa"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1603.07720",
    "kind": "arxiv",
    "version": 3
  }
}