Pith Number

pith:CIKFPRWD

pith:2023:CIKFPRWDQDHDX6LEXJSJE2YYOG

not attested not anchored not stored refs pending

Patterson-Sullivan measures for transverse subgroups

Andrew Zimmer, Richard Canary, Tengren Zhang

arxiv:2304.11515 v3 · 2023-04-23 · math.GR · 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{CIKFPRWDQDHDX6LEXJSJE2YYOG}

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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

Finiteness of Bowen-Margulis-Sullivan Measure for Gromov-Patterson-Sullivan Systems

Receipt and verification

First computed	2026-07-05T07:55:20.923568Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

121457c6c380ce3bf964ba64926b1871ae3395c1ad4757af53c8775c35ab4272

Aliases

arxiv: 2304.11515 · arxiv_version: 2304.11515v3 · doi: 10.48550/arxiv.2304.11515 · pith_short_12: CIKFPRWDQDHD · pith_short_16: CIKFPRWDQDHDX6LE · pith_short_8: CIKFPRWD

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/CIKFPRWDQDHDX6LEXJSJE2YYOG \
  | 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: 121457c6c380ce3bf964ba64926b1871ae3395c1ad4757af53c8775c35ab4272

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f0d367b5b70a0a0c15d9025022a87222804806592d7e22bd210213b1ee29a7ed",
    "cross_cats_sorted": [
      "math.DS"
    ],
    "license": "http://creativecommons.org/licenses/by-sa/4.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2023-04-23T01:46:52Z",
    "title_canon_sha256": "762d38528dba4b004a0b2d2ee33294fbf200c52b502728956eeb9a1eb7fa9d57"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2304.11515",
    "kind": "arxiv",
    "version": 3
  }
}