Pith Number

pith:MLOLQSHT

pith:2011:MLOLQSHTTFY5SP6WU36AI2TPO3

not attested not anchored not stored refs pending

Quantitative spectral gap for thin groups of hyperbolic isometries

Michael Magee

arxiv:1112.2004 v3 · 2011-12-09 · math.SP · math.NT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{MLOLQSHTTFY5SP6WU36AI2TPO3}

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	2026-05-18T03:10:46.093336Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

62dcb848f39971d93fd6a6fc046a6f76c7cd1f82d993581181ef51a83a14d18b

Aliases

arxiv: 1112.2004 · arxiv_version: 1112.2004v3 · doi: 10.48550/arxiv.1112.2004 · pith_short_12: MLOLQSHTTFY5 · pith_short_16: MLOLQSHTTFY5SP6W · pith_short_8: MLOLQSHT

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/MLOLQSHTTFY5SP6WU36AI2TPO3 \
  | 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: 62dcb848f39971d93fd6a6fc046a6f76c7cd1f82d993581181ef51a83a14d18b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "53d9f27886d9e103b32ff5b55f7ed5292a8fa8eae73caa78378e7d1f64562db6",
    "cross_cats_sorted": [
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.SP",
    "submitted_at": "2011-12-09T02:11:34Z",
    "title_canon_sha256": "e698798ef4ca2c114f0b28e75aa958fc1cda4a0ec19b19adc23ada3aca2d78a2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1112.2004",
    "kind": "arxiv",
    "version": 3
  }
}