Pith Number

pith:FPUJKBCC

pith:2009:FPUJKBCC25T4QRPSVKR7XT7Y27

not attested not anchored not stored refs pending

Introduction to Lie groups, isometric and adjoint actions and some generalizations

Marcos M. Alexandrino, Renato G. Bettiol

arxiv:0901.2374 v3 · 2009-01-16 · math.DG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{FPUJKBCC25T4QRPSVKR7XT7Y27}

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	2026-05-18T04:41:44.178140Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2be8950442d767c845f2aaa3fbcff8d7d3152951d06270b11dff8b6f944edc47

Aliases

arxiv: 0901.2374 · arxiv_version: 0901.2374v3 · doi: 10.48550/arxiv.0901.2374 · pith_short_12: FPUJKBCC25T4 · pith_short_16: FPUJKBCC25T4QRPS · pith_short_8: FPUJKBCC

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/FPUJKBCC25T4QRPSVKR7XT7Y27 \
  | 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: 2be8950442d767c845f2aaa3fbcff8d7d3152951d06270b11dff8b6f944edc47

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1f903ffde32e465fb572b0558a8b633a842bcbec57431235a8ca1a21a88d7e3b",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2009-01-16T00:40:38Z",
    "title_canon_sha256": "e94709eeb961ffb70050c177a2eda847e7efd7a1ae77a1bdd04331fcb6911637"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0901.2374",
    "kind": "arxiv",
    "version": 3
  }
}