Pith Number

pith:XRTJNPBS

pith:2010:XRTJNPBSJZ4NDHLCZDDC5I3GTV

not attested not anchored not stored refs pending

Squaring the Circle and Cubing the Sphere: Circular and Spherical Copulas

Jon A. Wellner (University of Washington, Michael D. Perlman (University of Washington, Seattle)

arxiv:1101.0145 v1 · 2010-12-30 · stat.OT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{XRTJNPBSJZ4NDHLCZDDC5I3GTV}

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	2026-05-18T04:32:10.972036Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bc6696bc324e78d19d62c8c62ea3669d64c0e19a8feb30b6ea344d4334ea70fb

Aliases

arxiv: 1101.0145 · arxiv_version: 1101.0145v1 · doi: 10.48550/arxiv.1101.0145 · pith_short_12: XRTJNPBSJZ4N · pith_short_16: XRTJNPBSJZ4NDHLC · pith_short_8: XRTJNPBS

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/XRTJNPBSJZ4NDHLCZDDC5I3GTV \
  | 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: bc6696bc324e78d19d62c8c62ea3669d64c0e19a8feb30b6ea344d4334ea70fb

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "932e8211420eb817cc9acd2b660b69817037f175eb15b4fb6355fca609622349",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "stat.OT",
    "submitted_at": "2010-12-30T19:52:48Z",
    "title_canon_sha256": "271e7698025e78d9eed9878bd85cb38bfa379b29dbf1cb2696118192b2d90788"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1101.0145",
    "kind": "arxiv",
    "version": 1
  }
}