Pith Number

pith:U6DFJEF4

pith:2008:U6DFJEF46GQ455DDU6BQ6VJEYV

not attested not anchored not stored refs pending

Entropy and Poincar\'e recurrence from a geometrical viewpoint

Paulo Varandas

arxiv:0809.2938 v2 · 2008-09-17 · 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{U6DFJEF46GQ455DDU6BQ6VJEYV}

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	2026-05-18T02:15:34.443913Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a7865490bcf1a1cef463a7830f5524c54474b3e73ce7799f37df0059552c4d16

Aliases

arxiv: 0809.2938 · arxiv_version: 0809.2938v2 · doi: 10.48550/arxiv.0809.2938 · pith_short_12: U6DFJEF46GQ4 · pith_short_16: U6DFJEF46GQ455DD · pith_short_8: U6DFJEF4

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/U6DFJEF46GQ455DDU6BQ6VJEYV \
  | 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: a7865490bcf1a1cef463a7830f5524c54474b3e73ce7799f37df0059552c4d16

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "82e47d3c6ade6515a13ea74beb4b53b86536c8894a32fa4c7ea14400d35f6549",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2008-09-17T14:42:29Z",
    "title_canon_sha256": "e9781eca706309870873ff056282a5700fdec070bc63ab0294f4cc3ceea523a6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0809.2938",
    "kind": "arxiv",
    "version": 2
  }
}