Pith Number

pith:BX7G5ESZ

pith:2012:BX7G5ESZANZ5ZKHLNEKIMQ4NCS

not attested not anchored not stored refs pending

Invariant differential operators and central Fourier multipliers on exponential Lie groups

Oliver Ungermann

arxiv:1202.5007 v1 · 2012-02-22 · math.GR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{BX7G5ESZANZ5ZKHLNEKIMQ4NCS}

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	2026-05-18T04:01:40.046813Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0dfe6e92590373dca8eb691486438d148acfa6bc5e9f27fe6c2247a1b5c8b068

Aliases

arxiv: 1202.5007 · arxiv_version: 1202.5007v1 · doi: 10.48550/arxiv.1202.5007 · pith_short_12: BX7G5ESZANZ5 · pith_short_16: BX7G5ESZANZ5ZKHL · pith_short_8: BX7G5ESZ

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/BX7G5ESZANZ5ZKHLNEKIMQ4NCS \
  | 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: 0dfe6e92590373dca8eb691486438d148acfa6bc5e9f27fe6c2247a1b5c8b068

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "09806124cccb245ae90891d1386f318f10bf96079d17d3e6338a9cec86c7d471",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2012-02-22T19:05:11Z",
    "title_canon_sha256": "b1a4638ea6de2b7a0321c026da51c234e0109091e6fed028370c515e549b8317"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1202.5007",
    "kind": "arxiv",
    "version": 1
  }
}