Pith Number

pith:AMPEKQ5F

pith:2011:AMPEKQ5FMNGSXIAQG2LROOFTP7

not attested not anchored not stored refs pending

Lyapunov spectrum of invariant subbundles of the Hodge bundle

Anton Zorich, Carlos Matheus, Giovanni Forni

arxiv:1112.0370 v3 · 2011-12-02 · math.DS

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{AMPEKQ5FMNGSXIAQG2LROOFTP7}

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	2026-05-17T23:53:19.102276Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

031e4543a5634d2ba01036971738b37fe281d15b4f94c75059e1e4cb813e5882

Aliases

arxiv: 1112.0370 · arxiv_version: 1112.0370v3 · doi: 10.48550/arxiv.1112.0370 · pith_short_12: AMPEKQ5FMNGS · pith_short_16: AMPEKQ5FMNGSXIAQ · pith_short_8: AMPEKQ5F

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/AMPEKQ5FMNGSXIAQG2LROOFTP7 \
  | 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: 031e4543a5634d2ba01036971738b37fe281d15b4f94c75059e1e4cb813e5882

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e38339771ab58a0e828d7ef14842c4d3d1cb98e75a8e91327eb1caf1875f5858",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2011-12-02T01:47:48Z",
    "title_canon_sha256": "76948ceabb41abd18ff1afce5dcea3f7b339716eee730cc7c848620b05d3ee9c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1112.0370",
    "kind": "arxiv",
    "version": 3
  }
}