Pith Number

pith:RBX6F3AT

pith:2018:RBX6F3ATHKF75CSBTP2D654XZV

not attested not anchored not stored refs pending

On the ergodicity of geodesic flows on surfaces without focal points

Fang Wang, Fei Liu, Weisheng Wu

arxiv:1812.04409 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{RBX6F3ATHKF75CSBTP2D654XZV}

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	2026-05-17T23:58:32.253558Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

886fe2ec133a8bfe8a419bf43f7797cd7d9f5cec9b319bf93a15a2d09f8f9c6b

Aliases

arxiv: 1812.04409 · arxiv_version: 1812.04409v1 · doi: 10.48550/arxiv.1812.04409 · pith_short_12: RBX6F3ATHKF7 · pith_short_16: RBX6F3ATHKF75CSB · pith_short_8: RBX6F3AT

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/RBX6F3ATHKF75CSBTP2D654XZV \
  | 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: 886fe2ec133a8bfe8a419bf43f7797cd7d9f5cec9b319bf93a15a2d09f8f9c6b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "35b2cbee1092ad7d032007704734df5759741c53331e1631de8ee014d049d6b5",
    "cross_cats_sorted": [
      "math.DG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2018-12-11T14:06:56Z",
    "title_canon_sha256": "823368d960527c31cec32e13bebc21f37e7d27c7189c4063f215bc16cbce4a4f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1812.04409",
    "kind": "arxiv",
    "version": 1
  }
}