Pith Number

pith:SG6CAZM2

pith:2012:SG6CAZM2CSS5RF7E5DCQZ5VHO2

not attested not anchored not stored refs pending

Smooth actions of Lie groups and Lie algebras on manifolds

Morris W. Hirsch

arxiv:1204.1690 v1 · 2012-04-07 · 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{SG6CAZM2CSS5RF7E5DCQZ5VHO2}

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	2026-05-18T03:58:23.420094Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

91bc20659a14a5d897e4e8c50cf6a776ba886a12ccd9d6993cdb2eb747b4c327

Aliases

arxiv: 1204.1690 · arxiv_version: 1204.1690v1 · doi: 10.48550/arxiv.1204.1690 · pith_short_12: SG6CAZM2CSS5 · pith_short_16: SG6CAZM2CSS5RF7E · pith_short_8: SG6CAZM2

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/SG6CAZM2CSS5RF7E5DCQZ5VHO2 \
  | 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: 91bc20659a14a5d897e4e8c50cf6a776ba886a12ccd9d6993cdb2eb747b4c327

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0860465ebcfa01efd315a6027fd075c6c47dbe476f522e3ba24bb128b88990d5",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2012-04-07T23:07:38Z",
    "title_canon_sha256": "00acd5e8bf8d58cd97bfba487216936355e753a3f287e66fe4d2128fb08e4180"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1204.1690",
    "kind": "arxiv",
    "version": 1
  }
}