Pith Number

pith:ATO7YZXL

pith:2017:ATO7YZXL6PIN72NLC5C2IMS4OW

not attested not anchored not stored refs pending

A family of complex nilmanifolds with infinitely many real homotopy types

Adela Latorre, Luis Ugarte, Raquel Villacampa

arxiv:1712.07820 v1 · 2017-12-21 · math.DG · math.AT · math.RA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{ATO7YZXL6PIN72NLC5C2IMS4OW}

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	2026-05-18T00:27:29.669418Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

04ddfc66ebf3d0dfe9ab1745a4325c75acfc8c2ac8dc5b09e79482c9bc4b3301

Aliases

arxiv: 1712.07820 · arxiv_version: 1712.07820v1 · doi: 10.48550/arxiv.1712.07820 · pith_short_12: ATO7YZXL6PIN · pith_short_16: ATO7YZXL6PIN72NL · pith_short_8: ATO7YZXL

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/ATO7YZXL6PIN72NLC5C2IMS4OW \
  | 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: 04ddfc66ebf3d0dfe9ab1745a4325c75acfc8c2ac8dc5b09e79482c9bc4b3301

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0054be0751d7579b5443e4c908678ac37a914c0bf24948c208c7a8bcd1d59b18",
    "cross_cats_sorted": [
      "math.AT",
      "math.RA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2017-12-21T08:00:25Z",
    "title_canon_sha256": "d8459580140493f98b754841394125c15fadcfbc966088c7eaccf4a8063721cb"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1712.07820",
    "kind": "arxiv",
    "version": 1
  }
}