Pith Number

pith:LIPT3GX6

pith:2012:LIPT3GX6S2GR4XJZJNEGUO2PEO

not attested not anchored not stored refs pending

Lagrange Spectra in Teichm\"uller Dynamics via renormalization

Corinna Ulcigrai, Luca Marchese, Pascal Hubert

arxiv:1209.0183 v2 · 2012-09-02 · math.DS · 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{LIPT3GX6S2GR4XJZJNEGUO2PEO}

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	2026-05-18T03:19:35.234261Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5a1f3d9afe968d1e5d394b486a3b4f23bbba671fb3f523dd869e5205c1dd7151

Aliases

arxiv: 1209.0183 · arxiv_version: 1209.0183v2 · doi: 10.48550/arxiv.1209.0183 · pith_short_12: LIPT3GX6S2GR · pith_short_16: LIPT3GX6S2GR4XJZ · pith_short_8: LIPT3GX6

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/LIPT3GX6S2GR4XJZJNEGUO2PEO \
  | 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: 5a1f3d9afe968d1e5d394b486a3b4f23bbba671fb3f523dd869e5205c1dd7151

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "209dd0be3a0648a2940c219c44fafa2b8e1c78328fb8acedcec0c36f6253341a",
    "cross_cats_sorted": [
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2012-09-02T15:38:57Z",
    "title_canon_sha256": "d892f1a10b9698404a1fbb9d8274580a52bec925211a796ebe2158217da8310a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1209.0183",
    "kind": "arxiv",
    "version": 2
  }
}