Pith Number

pith:BNTW4AXZ

pith:2013:BNTW4AXZQSYA4SW6G5H6FM6RAZ

not attested not anchored not stored refs pending

On the ergodicity of geodesic flows on surfaces of nonpositive curvature

Weisheng Wu

arxiv:1309.6539 v4 · 2013-09-25 · 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{BNTW4AXZQSYA4SW6G5H6FM6RAZ}

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	2026-05-18T02:20:00.419142Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0b676e02f984b00e4ade374fe2b3d10662f17df480fffe0711bb31300999f3c5

Aliases

arxiv: 1309.6539 · arxiv_version: 1309.6539v4 · doi: 10.48550/arxiv.1309.6539 · pith_short_12: BNTW4AXZQSYA · pith_short_16: BNTW4AXZQSYA4SW6 · pith_short_8: BNTW4AXZ

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/BNTW4AXZQSYA4SW6G5H6FM6RAZ \
  | 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: 0b676e02f984b00e4ade374fe2b3d10662f17df480fffe0711bb31300999f3c5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "acd801754b1d4f3389b1ee79c2f6d670b7f8c1f8b4d566892a92de5bbefc6f11",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2013-09-25T15:03:30Z",
    "title_canon_sha256": "2879908e7cdd1f0b3368b186178964e3e30dcf0970de47f1bd798c0b40d111a8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1309.6539",
    "kind": "arxiv",
    "version": 4
  }
}