Pith Number

pith:2PTOST4G

pith:2015:2PTOST4GEKBFAGV3Z5OHHUJ3E7

not attested not anchored not stored refs pending

A short proof of unique ergodicity of horospherical foliations on infinite volume hyperbolic manifolds

Barbara Schapira (LAMFA)

arxiv:1505.05648 v1 · 2015-05-21 · 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{2PTOST4GEKBFAGV3Z5OHHUJ3E7}

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	2026-05-18T02:03:53.873304Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d3e6e94f862282501abbcf5c73d13b27f94e792e41e7b6d84dd2e99bb2d3c29b

Aliases

arxiv: 1505.05648 · arxiv_version: 1505.05648v1 · doi: 10.48550/arxiv.1505.05648 · pith_short_12: 2PTOST4GEKBF · pith_short_16: 2PTOST4GEKBFAGV3 · pith_short_8: 2PTOST4G

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/2PTOST4GEKBFAGV3Z5OHHUJ3E7 \
  | 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: d3e6e94f862282501abbcf5c73d13b27f94e792e41e7b6d84dd2e99bb2d3c29b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a41ee23b48cc8d0a254b58511873b648e532396729242cb2a28a697d648a25cc",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2015-05-21T09:11:20Z",
    "title_canon_sha256": "8fd319fe5bc7f8fec5632b829e28f5ae9d656f4675765d43ee3bd46f59d67363"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1505.05648",
    "kind": "arxiv",
    "version": 1
  }
}