Pith Number

pith:E22HY45T

pith:2010:E22HY45TWFFSE4TYSMHKUBBKF6

not attested not anchored not stored refs pending

Entropy-expansiveness for partially hyperbolic diffeomorphisms

Jose L. Vieitez, Lorenzo J. Diaz, Maria J. Pacifico, Todd Fisher

arxiv:1010.0721 v2 · 2010-10-04 · 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{E22HY45TWFFSE4TYSMHKUBBKF6}

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	2026-05-18T04:10:48.331469Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

26b47c73b3b14b227278930eaa042a2f8e21b1409942988fdaa714c7a60fecac

Aliases

arxiv: 1010.0721 · arxiv_version: 1010.0721v2 · doi: 10.48550/arxiv.1010.0721 · pith_short_12: E22HY45TWFFS · pith_short_16: E22HY45TWFFSE4TY · pith_short_8: E22HY45T

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/E22HY45TWFFSE4TYSMHKUBBKF6 \
  | 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: 26b47c73b3b14b227278930eaa042a2f8e21b1409942988fdaa714c7a60fecac

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1191f08a36d1efe71d0721160cc066a4f5bbb465ea5e4adfbbbbce02aed8617a",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2010-10-04T22:19:05Z",
    "title_canon_sha256": "eb246fe61910914de309aab65e09e721216d0d625bfc47383fbc2b0b4c74a732"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1010.0721",
    "kind": "arxiv",
    "version": 2
  }
}