Pith Number

pith:UAT7OGM7

pith:2017:UAT7OGM7NU2CV26FTRQ6UMK6TM

not attested not anchored not stored refs pending

Lyapunov optimization for non-generic one-dimensional expanding Markov maps

Hiroki Takahasi, Mao Shinoda

arxiv:1705.07579 v2 · 2017-05-22 · 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{UAT7OGM7NU2CV26FTRQ6UMK6TM}

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	2026-05-18T00:36:38.477689Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a027f7199f6d342aebc59c61ea315e9b3f80d25be5e5a59682dd8e00cfbd52db

Aliases

arxiv: 1705.07579 · arxiv_version: 1705.07579v2 · doi: 10.48550/arxiv.1705.07579 · pith_short_12: UAT7OGM7NU2C · pith_short_16: UAT7OGM7NU2CV26F · pith_short_8: UAT7OGM7

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/UAT7OGM7NU2CV26FTRQ6UMK6TM \
  | 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: a027f7199f6d342aebc59c61ea315e9b3f80d25be5e5a59682dd8e00cfbd52db

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c99afec74b66920a30f7f2a06e8fd0395123eb53803763075737d79fb7360dd2",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2017-05-22T06:56:49Z",
    "title_canon_sha256": "d10933b1d9d15948288659a2d248efb15c24f416d335e781196859f33474fbb8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1705.07579",
    "kind": "arxiv",
    "version": 2
  }
}