Pith Number

pith:KZJMIJJ6

pith:2011:KZJMIJJ6ESIYOW5F5WJGZEPLMZ

not attested not anchored not stored refs pending

Smoothness of Densities on Compact Lie Groups

David Applebaum

arxiv:1109.3051 v1 · 2011-09-14 · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{KZJMIJJ6ESIYOW5F5WJGZEPLMZ}

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	2026-05-18T04:13:06.398849Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5652c4253e2491875ba5ed926c91eb667580b5c6afcedba976d6ff2949e7c7f3

Aliases

arxiv: 1109.3051 · arxiv_version: 1109.3051v1 · doi: 10.48550/arxiv.1109.3051 · pith_short_12: KZJMIJJ6ESIY · pith_short_16: KZJMIJJ6ESIYOW5F · pith_short_8: KZJMIJJ6

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/KZJMIJJ6ESIYOW5F5WJGZEPLMZ \
  | 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: 5652c4253e2491875ba5ed926c91eb667580b5c6afcedba976d6ff2949e7c7f3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "597b1926f05a63d93dddf5f3929fae6a671af9080ea1b830dc0689aed0ea4109",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2011-09-14T11:24:52Z",
    "title_canon_sha256": "2a657566ea3fc068e078f92bb908aa2319a3b65fadcf73b032ce668a13b7878f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1109.3051",
    "kind": "arxiv",
    "version": 1
  }
}