Pith Number

pith:Q43LCIWZ

pith:2011:Q43LCIWZ4N56UJEHVJUZOPS7VF

not attested not anchored not stored refs pending

Entropy of automorphisms, homology and the intrinsic polynomial structure of nilpotent groups

Thomas Koberda

arxiv:1107.4129 v2 · 2011-07-20 · math.GR · math.GT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{Q43LCIWZ4N56UJEHVJUZOPS7VF}

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	2026-05-18T04:11:41.585455Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8736b122d9e37bea2487aa69973e5fa97124c03c0da9a4d0350f4954a69c9d43

Aliases

arxiv: 1107.4129 · arxiv_version: 1107.4129v2 · doi: 10.48550/arxiv.1107.4129 · pith_short_12: Q43LCIWZ4N56 · pith_short_16: Q43LCIWZ4N56UJEH · pith_short_8: Q43LCIWZ

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/Q43LCIWZ4N56UJEHVJUZOPS7VF \
  | 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: 8736b122d9e37bea2487aa69973e5fa97124c03c0da9a4d0350f4954a69c9d43

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5adda2b89002c0fb724969cf802e9d18331a6a24d3911ec2a07707084f138e71",
    "cross_cats_sorted": [
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2011-07-20T22:08:34Z",
    "title_canon_sha256": "45f10f9a00a4052bdbd4311f2af88ad7be81608ad7b257d8f2d17d4b7df70a88"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1107.4129",
    "kind": "arxiv",
    "version": 2
  }
}