Pith Number

pith:CQKOBWMY

pith:2016:CQKOBWMYOH2Y7B2CW7DFBQKAEG

not attested not anchored not stored refs pending

Lyapunov exponents and related concepts for entire functions

Jianhua Zheng, Walter Bergweiler, Xiao Yao

arxiv:1607.01271 v1 · 2016-07-05 · 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{CQKOBWMYOH2Y7B2CW7DFBQKAEG}

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	2026-05-18T00:18:54.164736Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1414e0d99871f58f8742b7c650c14021b41c3cc697d40c5536c746826bb19567

Aliases

arxiv: 1607.01271 · arxiv_version: 1607.01271v1 · doi: 10.48550/arxiv.1607.01271 · pith_short_12: CQKOBWMYOH2Y · pith_short_16: CQKOBWMYOH2Y7B2C · pith_short_8: CQKOBWMY

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/CQKOBWMYOH2Y7B2CW7DFBQKAEG \
  | 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: 1414e0d99871f58f8742b7c650c14021b41c3cc697d40c5536c746826bb19567

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "116c13b6a4de70d03501c685e9fc99b7a8c6be2623783bcc515a3e4410e77d6f",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2016-07-05T14:37:12Z",
    "title_canon_sha256": "dffaf5f3eabdbe5ceede8131f61dbcdaa105eaa10a0d5dde50023c39435d0315"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1607.01271",
    "kind": "arxiv",
    "version": 1
  }
}