Pith Number

pith:AMZGTPQO

pith:2012:AMZGTPQO3AUEXVTBH7VLB4RCVI

not attested not anchored not stored refs pending

Lyapunov spectrum of ball quotients with applications to commensurability questions

Andr\'e Kappes, Martin Moeller

arxiv:1207.5433 v4 · 2012-07-23 · math.AG · 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{AMZGTPQO3AUEXVTBH7VLB4RCVI}

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	2026-05-18T01:21:05.721579Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

033269be0ed8284bd6613feab0f222aa0dc82b7c1e3f4f1ab7dfe1651b516d7b

Aliases

arxiv: 1207.5433 · arxiv_version: 1207.5433v4 · doi: 10.48550/arxiv.1207.5433 · pith_short_12: AMZGTPQO3AUE · pith_short_16: AMZGTPQO3AUEXVTB · pith_short_8: AMZGTPQO

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/AMZGTPQO3AUEXVTBH7VLB4RCVI \
  | 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: 033269be0ed8284bd6613feab0f222aa0dc82b7c1e3f4f1ab7dfe1651b516d7b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "24e3f3ef3fec8405c777a7744a16e2bc5f56bc865065f4ff003492eadcd8afeb",
    "cross_cats_sorted": [
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2012-07-23T16:06:55Z",
    "title_canon_sha256": "1746c90133cc5e44a0cc0e6d3a91fa50fd8a307019a154408737885230396b15"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1207.5433",
    "kind": "arxiv",
    "version": 4
  }
}