Pith Number

pith:YEKV6TYZ

pith:2015:YEKV6TYZYVNJSU7NQW6GTCGQM5

not attested not anchored not stored refs pending

Uniform hyperbolicity of invariant cylinder

Chong-Qing Cheng

arxiv:1509.03160 v1 · 2015-09-10 · 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{YEKV6TYZYVNJSU7NQW6GTCGQM5}

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	2026-05-18T01:33:25.200496Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c1155f4f19c55a9953ed85bc6988d0677f4ee946f27ba047aa32c13785d2add4

Aliases

arxiv: 1509.03160 · arxiv_version: 1509.03160v1 · doi: 10.48550/arxiv.1509.03160 · pith_short_12: YEKV6TYZYVNJ · pith_short_16: YEKV6TYZYVNJSU7N · pith_short_8: YEKV6TYZ

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/YEKV6TYZYVNJSU7NQW6GTCGQM5 \
  | 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: c1155f4f19c55a9953ed85bc6988d0677f4ee946f27ba047aa32c13785d2add4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9ec60efc3ee539e67e0ae848a901461fd38d2706108614318c40c2c576b64627",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2015-09-10T13:58:13Z",
    "title_canon_sha256": "0138100a17646894a5bcd4ecd61fa12b1946d61d81ea30477a9612dd9deb7053"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1509.03160",
    "kind": "arxiv",
    "version": 1
  }
}