Pith Number

pith:EX2Q25QA

pith:2012:EX2Q25QAISX7BWOEVNT4Z4KGXB

not attested not anchored not stored refs pending

Representation equivalent Bieberbach groups and strongly isospectral flat manifolds

Emilio A. Lauret

arxiv:1210.0894 v2 · 2012-10-02 · math.DG · math.RT · math.SP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{EX2Q25QAISX7BWOEVNT4Z4KGXB}

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	2026-05-18T02:53:54.139431Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

25f50d760044aff0d9c4ab67ccf146b847acfab12edd0b7a5291e30df6ece7b6

Aliases

arxiv: 1210.0894 · arxiv_version: 1210.0894v2 · doi: 10.48550/arxiv.1210.0894 · pith_short_12: EX2Q25QAISX7 · pith_short_16: EX2Q25QAISX7BWOE · pith_short_8: EX2Q25QA

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/EX2Q25QAISX7BWOEVNT4Z4KGXB \
  | 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: 25f50d760044aff0d9c4ab67ccf146b847acfab12edd0b7a5291e30df6ece7b6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5abf8dad8c1cb8740b1f0b7048dcda8d67605274d02d58f61c3a677bff531087",
    "cross_cats_sorted": [
      "math.RT",
      "math.SP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2012-10-02T19:48:30Z",
    "title_canon_sha256": "0473a657273efe0eb0986e741d43be39d614b0376e3a13d1138f1ea68aa5195f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1210.0894",
    "kind": "arxiv",
    "version": 2
  }
}