Pith Number

pith:JJYE3ZM7

pith:2011:JJYE3ZM7VUPZU7QOVHEA4VZESW

not attested not anchored not stored refs pending

Transversality Family of Expanding Rational Semigroups

Hiroki Sumi, Mariusz Urbanski

arxiv:1109.2380 v6 · 2011-09-12 · math.DS · math.CV · math.GT · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{JJYE3ZM7VUPZU7QOVHEA4VZESW}

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	2026-05-18T02:21:36.821467Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4a704de59fad1f9a7e0ea9c80e5724958a8f56d1a39531b8760a9e7874eacf4b

Aliases

arxiv: 1109.2380 · arxiv_version: 1109.2380v6 · doi: 10.48550/arxiv.1109.2380 · pith_short_12: JJYE3ZM7VUPZ · pith_short_16: JJYE3ZM7VUPZU7QO · pith_short_8: JJYE3ZM7

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/JJYE3ZM7VUPZU7QOVHEA4VZESW \
  | 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: 4a704de59fad1f9a7e0ea9c80e5724958a8f56d1a39531b8760a9e7874eacf4b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "61d2a8ab119d3dc1a31747519223493593c8ec3790832cdcedd083f7fe99ff98",
    "cross_cats_sorted": [
      "math.CV",
      "math.GT",
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2011-09-12T06:12:57Z",
    "title_canon_sha256": "6716846f2db48497f4b1f1d19b63cdcb290f2e825dfe68c25990832cdbb46532"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1109.2380",
    "kind": "arxiv",
    "version": 6
  }
}