Pith Number

pith:PI7ZL2DT

pith:2021:PI7ZL2DTFE7FT3YUY4W4G2U4GE

not attested not anchored not stored refs pending

On amenability and measure of maximal entropy for semigroups of rational maps: II

Carlos Cabrera, Peter Makienko

arxiv:2109.11601 v5 · 2021-09-23 · math.DS · math.CV

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{PI7ZL2DTFE7FT3YUY4W4G2U4GE}

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.

Cited by

1 paper in Pith

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Receipt and verification

First computed	2026-07-05T06:48:01.157532Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7a3f95e873293e59ef14c72dc36a9c3120584eaac8452e1a5e7e7aacaa154bcb

Aliases

arxiv: 2109.11601 · arxiv_version: 2109.11601v5 · doi: 10.48550/arxiv.2109.11601 · pith_short_12: PI7ZL2DTFE7F · pith_short_16: PI7ZL2DTFE7FT3YU · pith_short_8: PI7ZL2DT

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/PI7ZL2DTFE7FT3YUY4W4G2U4GE \
  | 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: 7a3f95e873293e59ef14c72dc36a9c3120584eaac8452e1a5e7e7aacaa154bcb

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e845afa09aad0ec6fff070a766f770f7cb012f4c91b07895bb1e8cb3068e39c0",
    "cross_cats_sorted": [
      "math.CV"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2021-09-23T19:10:58Z",
    "title_canon_sha256": "c38c238b5c12ed5a904b31aaf86a0480fc080fdace6287b1a9ff35cdd4a06b8d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2109.11601",
    "kind": "arxiv",
    "version": 5
  }
}