Pith Number

pith:3KS73BNH

pith:2018:3KS73BNHQMUKVQXAOUUD7B42RN

not attested not anchored not stored refs pending

On the Patterson-Sullivan measure for geodesic flows on rank $1$ manifolds without focal points

Fang Wang, Fei Liu, Weisheng Wu

arxiv:1812.04398 v1 · 2018-12-11 · math.DS · math.DG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{3KS73BNHQMUKVQXAOUUD7B42RN}

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	2026-05-17T23:58:32.300873Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

daa5fd85a78328aac2e075283f879a8b6aacce1943242953fb604347b79e972d

Aliases

arxiv: 1812.04398 · arxiv_version: 1812.04398v1 · doi: 10.48550/arxiv.1812.04398 · pith_short_12: 3KS73BNHQMUK · pith_short_16: 3KS73BNHQMUKVQXA · pith_short_8: 3KS73BNH

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/3KS73BNHQMUKVQXAOUUD7B42RN \
  | 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: daa5fd85a78328aac2e075283f879a8b6aacce1943242953fb604347b79e972d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "cd1e023d37360e44542469687c8d44e15e4db8f6b28e3a69e402d062affc03e8",
    "cross_cats_sorted": [
      "math.DG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2018-12-11T13:56:38Z",
    "title_canon_sha256": "8a7a54226d532401cc19c2006478552b682b5e3bb3a2e306dd675f8cabd76ec5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1812.04398",
    "kind": "arxiv",
    "version": 1
  }
}