Pith Number

pith:W4TZG3XY

pith:2013:W4TZG3XYJGUMWNLZZC55P4UVEV

not attested not anchored not stored refs pending

Global functional calculus for operators on compact Lie groups

Jens Wirth, Michael Ruzhansky

arxiv:1307.1464 v2 · 2013-07-04 · math.FA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{W4TZG3XYJGUMWNLZZC55P4UVEV}

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	2026-05-18T02:51:57.048044Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b727936ef849a8cb3579c8bbd7f2952540d0e5a7329cb1a47113be476c7fd2e8

Aliases

arxiv: 1307.1464 · arxiv_version: 1307.1464v2 · doi: 10.48550/arxiv.1307.1464 · pith_short_12: W4TZG3XYJGUM · pith_short_16: W4TZG3XYJGUMWNLZ · pith_short_8: W4TZG3XY

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/W4TZG3XYJGUMWNLZZC55P4UVEV \
  | 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: b727936ef849a8cb3579c8bbd7f2952540d0e5a7329cb1a47113be476c7fd2e8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7c82c93c538435bf16be75f6de35d7d28ae1ec8397bc891c2549726c7e89717e",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2013-07-04T19:52:58Z",
    "title_canon_sha256": "59190d693ed7d2b7128dd7b3af50d3a785858fdff757faf5d78048afadaf3e0e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1307.1464",
    "kind": "arxiv",
    "version": 2
  }
}