Pith Number

pith:6TOGBMIL

pith:2011:6TOGBMILZ6MPIDMHWGIITOQBIG

not attested not anchored not stored refs pending

Sum of Lyapunov exponents of the Hodge bundle with respect to the Teichmuller geodesic flow

Alex Eskin, Anton Zorich, Maxim Kontsevich

arxiv:1112.5872 v6 · 2011-12-26 · math.DS · 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{6TOGBMILZ6MPIDMHWGIITOQBIG}

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	2026-05-18T02:21:26.928216Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f4dc60b10bcf98f40d87b19089ba01418fe453df5ec19bcac372143c225cc0a1

Aliases

arxiv: 1112.5872 · arxiv_version: 1112.5872v6 · doi: 10.48550/arxiv.1112.5872 · pith_short_12: 6TOGBMILZ6MP · pith_short_16: 6TOGBMILZ6MPIDMH · pith_short_8: 6TOGBMIL

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/6TOGBMILZ6MPIDMHWGIITOQBIG \
  | 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: f4dc60b10bcf98f40d87b19089ba01418fe453df5ec19bcac372143c225cc0a1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7a6b836e471214ffc79b81c9df970830b402512c6f4e60720aa374817f86fb3a",
    "cross_cats_sorted": [
      "math.AG",
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2011-12-26T16:51:52Z",
    "title_canon_sha256": "1016aea22154bf134393ed74c2bf5e0c3a696351a313b5a254384fe2c7d492cc"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1112.5872",
    "kind": "arxiv",
    "version": 6
  }
}