Pith Number

pith:C6NGFIIV

pith:2011:C6NGFIIV3YGJAHQZHKWSFRDOEL

not attested not anchored not stored refs pending

Lyapunov exponents in Hilbert geometry

Micka\"el Crampon (IRMA)

arxiv:1105.6275 v1 · 2011-05-31 · math.DS · math.DG · math.MG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{C6NGFIIV3YGJAHQZHKWSFRDOEL}

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	2026-05-17T23:53:36.580590Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

179a62a115de0c901e193aad22c46e22f7925e3a6af823eb04b19b0c3e2d96cc

Aliases

arxiv: 1105.6275 · arxiv_version: 1105.6275v1 · doi: 10.48550/arxiv.1105.6275 · pith_short_12: C6NGFIIV3YGJ · pith_short_16: C6NGFIIV3YGJAHQZ · pith_short_8: C6NGFIIV

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/C6NGFIIV3YGJAHQZHKWSFRDOEL \
  | 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: 179a62a115de0c901e193aad22c46e22f7925e3a6af823eb04b19b0c3e2d96cc

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "313d0d76fc663b41765eef9be3cff78bb9875ac5fbf8a0be7d7623474c8b03da",
    "cross_cats_sorted": [
      "math.DG",
      "math.MG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2011-05-31T13:39:21Z",
    "title_canon_sha256": "1850b5534db71f45ab423624f479b2c5ae6f94d9ed807370f8423594e801b7d8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1105.6275",
    "kind": "arxiv",
    "version": 1
  }
}