Pith Number

pith:O43RJ6AT

pith:2015:O43RJ6ATP66HLBQGPKYXBAZVYC

not attested not anchored not stored refs pending

On random linear dynamical systems in a Banach space. I. Multiplicative Ergodic Theorem and Krein-Rutmann type Theorems

Yi Wang, Zeng Lian

arxiv:1507.00427 v1 · 2015-07-02 · 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{O43RJ6ATP66HLBQGPKYXBAZVYC}

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	2026-05-18T01:37:24.782571Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

773714f8137fbc7586067ab1708335c0b33ef494a400cbbf3177b0b8c5b607d6

Aliases

arxiv: 1507.00427 · arxiv_version: 1507.00427v1 · doi: 10.48550/arxiv.1507.00427 · pith_short_12: O43RJ6ATP66H · pith_short_16: O43RJ6ATP66HLBQG · pith_short_8: O43RJ6AT

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/O43RJ6ATP66HLBQGPKYXBAZVYC \
  | 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: 773714f8137fbc7586067ab1708335c0b33ef494a400cbbf3177b0b8c5b607d6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "070d204c824eb9d666d332b2f64650e1073fe548c5106aa7299d33877e3ea01f",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2015-07-02T05:07:48Z",
    "title_canon_sha256": "34db005c563d1939fd5ece628ed4e7aef7f515e2d18b83918748e82232d4c566"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1507.00427",
    "kind": "arxiv",
    "version": 1
  }
}