Pith Number

pith:4TWSUWK7

pith:2026:4TWSUWK7R5I5WDJI6XZASGHCXC

not attested not anchored not stored refs pending

Classification of horospherical invariant measures in higher rank: The Full Story

Dongryul M. Kim, Inhyeok Choi

arxiv:2601.22668 v2 · 2026-01-30 · math.DS · math.GR · math.GT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{4TWSUWK7R5I5WDJI6XZASGHCXC}

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	2026-06-04T01:08:40.821688Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e4ed2a595f8f51db0d28f5f20918e2b8af664c1a1829697792fb6b69494603b3

Aliases

arxiv: 2601.22668 · arxiv_version: 2601.22668v2 · doi: 10.48550/arxiv.2601.22668 · pith_short_12: 4TWSUWK7R5I5 · pith_short_16: 4TWSUWK7R5I5WDJI · pith_short_8: 4TWSUWK7

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/4TWSUWK7R5I5WDJI6XZASGHCXC \
  | 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: e4ed2a595f8f51db0d28f5f20918e2b8af664c1a1829697792fb6b69494603b3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3dca7033bb278fe560ca5376b2cb67b2c160d104c460ceda143ca0f394bb22bd",
    "cross_cats_sorted": [
      "math.GR",
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2026-01-30T07:41:50Z",
    "title_canon_sha256": "384738ac6dfa3780fdd19e5d0c1ffe62aa255afd62bff7d585afa5e8de72be43"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2601.22668",
    "kind": "arxiv",
    "version": 2
  }
}