Pith Number

pith:2ASWI7PZ

pith:2016:2ASWI7PZQCIWMA74IDVNKQUUKY

not attested not anchored not stored refs pending

Nilpotent Lie algebras and systolic growth of nilmanifolds

Yves Cornulier

arxiv:1612.00818 v2 · 2016-12-02 · math.GR · 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{2ASWI7PZQCIWMA74IDVNKQUUKY}

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	2026-05-17T23:44:43.622520Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d025647df980916603fc40ead5429456306a4eec82d35744263989d356d1a760

Aliases

arxiv: 1612.00818 · arxiv_version: 1612.00818v2 · doi: 10.48550/arxiv.1612.00818 · pith_short_12: 2ASWI7PZQCIW · pith_short_16: 2ASWI7PZQCIWMA74 · pith_short_8: 2ASWI7PZ

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/2ASWI7PZQCIWMA74IDVNKQUUKY \
  | 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: d025647df980916603fc40ead5429456306a4eec82d35744263989d356d1a760

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "aa7fb5a466faddda12d60d93ce519ef0c25a96535b493e158b658e6649cba9ff",
    "cross_cats_sorted": [
      "math.DG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2016-12-02T20:09:40Z",
    "title_canon_sha256": "fb86d4da0cf3071673c1737e6a318b33249154e84787e8eb548f3376c33d8e4d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1612.00818",
    "kind": "arxiv",
    "version": 2
  }
}