Pith Number

pith:ZVVZ4GSZ

pith:2013:ZVVZ4GSZ7Q4BQCKYFVD4ZW5M44

not attested not anchored not stored refs pending

Lyapunov exponents for surface groups representations

Bertrand Deroin, Romain Dujardin

arxiv:1305.0049 v2 · 2013-04-30 · math.GT · math.CV

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{ZVVZ4GSZ7Q4BQCKYFVD4ZW5M44}

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	2026-05-18T03:16:51.017245Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cd6b9e1a59fc381809582d47ccdbace70e4385570aeaaee2274f4b05a609d8a2

Aliases

arxiv: 1305.0049 · arxiv_version: 1305.0049v2 · doi: 10.48550/arxiv.1305.0049 · pith_short_12: ZVVZ4GSZ7Q4B · pith_short_16: ZVVZ4GSZ7Q4BQCKY · pith_short_8: ZVVZ4GSZ

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/ZVVZ4GSZ7Q4BQCKYFVD4ZW5M44 \
  | 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: cd6b9e1a59fc381809582d47ccdbace70e4385570aeaaee2274f4b05a609d8a2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "db307bc0b0038dfa51ad7c41f23ee65fe38f74f0e11bc6e41b916544dce0d399",
    "cross_cats_sorted": [
      "math.CV"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2013-04-30T22:52:15Z",
    "title_canon_sha256": "d548a2aa4a9a883c2fc52022e83536dda78bdfe117ebf16fa02ac8f2ead8b5cc"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1305.0049",
    "kind": "arxiv",
    "version": 2
  }
}