Pith Number

pith:XLB2EYUB

pith:2015:XLB2EYUB4JAUY5VLX3GKW45ZZ4

not attested not anchored not stored refs pending

Discontinuity of Lyapunov Exponents Near Fiber Bunched Cocycles

Clark Butler

arxiv:1509.04122 v3 · 2015-09-14 · 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{XLB2EYUB4JAUY5VLX3GKW45ZZ4}

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	2026-05-18T01:03:45.234223Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bac3a26281e2414c76abbeccab73b9cf33c8bc3068eb87ac536073b2fa95e0de

Aliases

arxiv: 1509.04122 · arxiv_version: 1509.04122v3 · doi: 10.48550/arxiv.1509.04122 · pith_short_12: XLB2EYUB4JAU · pith_short_16: XLB2EYUB4JAUY5VL · pith_short_8: XLB2EYUB

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/XLB2EYUB4JAUY5VLX3GKW45ZZ4 \
  | 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: bac3a26281e2414c76abbeccab73b9cf33c8bc3068eb87ac536073b2fa95e0de

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3fd790b7b337b95f512cecea6048ac19cab22b92bdf7e9c7691518afa4124ae8",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2015-09-14T14:50:28Z",
    "title_canon_sha256": "7768cb666c9bce5f566f6d5b2aefdf45a2a3729c1f3ec62f8c325197d179432f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1509.04122",
    "kind": "arxiv",
    "version": 3
  }
}