Pith Number

pith:RGW5USSW

pith:2016:RGW5USSWB3BTIRFYTS7PEFEGCV

not attested not anchored not stored refs pending

On the periodic approximation of Lyapunov exponents for semi-invertible cocycles

Lucas Backes

arxiv:1612.04159 v2 · 2016-12-13 · 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{RGW5USSWB3BTIRFYTS7PEFEGCV}

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	2026-05-18T00:37:52.701625Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

89adda4a560ec33444b89cbef214861559f1b7b0c1e891e2fad80e0afd6a0ffa

Aliases

arxiv: 1612.04159 · arxiv_version: 1612.04159v2 · doi: 10.48550/arxiv.1612.04159 · pith_short_12: RGW5USSWB3BT · pith_short_16: RGW5USSWB3BTIRFY · pith_short_8: RGW5USSW

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/RGW5USSWB3BTIRFYTS7PEFEGCV \
  | 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: 89adda4a560ec33444b89cbef214861559f1b7b0c1e891e2fad80e0afd6a0ffa

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3a39094b2eb4fff6b9e7464310dffde9dfc831d2a3d42de77909711917a7f910",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2016-12-13T13:32:52Z",
    "title_canon_sha256": "2145523454a3ec8f162a59c0a811e30c4e64c3d7cf8b6b0bd9612ff6897ee838"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1612.04159",
    "kind": "arxiv",
    "version": 2
  }
}