Pith Number

pith:O3ZBODL2

pith:2017:O3ZBODL2QC3TE6XFPFNUGLT3FE

not attested not anchored not stored refs pending

The topological entropy of endomorphisms of Lie groups

Mauro Patr\~ao

arxiv:1711.02562 v4 · 2017-11-06 · math.DS · 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{O3ZBODL2QC3TE6XFPFNUGLT3FE}

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	2026-05-18T00:17:18.958406Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

76f2170d7a80b7327ae5795b432e7b291780cff5fa7c7b3ca561c7471690aff7

Aliases

arxiv: 1711.02562 · arxiv_version: 1711.02562v4 · doi: 10.48550/arxiv.1711.02562 · pith_short_12: O3ZBODL2QC3T · pith_short_16: O3ZBODL2QC3TE6XF · pith_short_8: O3ZBODL2

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/O3ZBODL2QC3TE6XFPFNUGLT3FE \
  | 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: 76f2170d7a80b7327ae5795b432e7b291780cff5fa7c7b3ca561c7471690aff7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "81277f2cf0713fdb393910670c0a6daeff332ec4b22a4d857a82f4f7a2a0232e",
    "cross_cats_sorted": [
      "math.GR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2017-11-06T18:44:37Z",
    "title_canon_sha256": "2a243c7546e6b5a244cddd9c64712b3b1bc0436f04a142c45112abc7ca39b220"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1711.02562",
    "kind": "arxiv",
    "version": 4
  }
}