Pith Number

pith:5G2LRFZT

pith:2026:5G2LRFZTO5BJEA4WPP63Q7CPGC

not attested not anchored not stored refs pending

Vertex volumes, lattice-minima tails, and height zeta functions for the standard arithmetic quotient of $\operatorname{PGL}_d$

Sanghoon Kwon, Soonki Hong

arxiv:2607.28433 v1 · 2026-07-30 · math.NT · math.GR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{5G2LRFZTO5BJEA4WPP63Q7CPGC}

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	2026-07-31T01:37:37.609283Z
Builder	pith-number-builder-2026-05-17-v1
Signature	unsigned_v0
Schema	pith-number/v1.0

Canonical hash

e9b4b8973377429203967bfdb87c4f3097456d59f2395d0e1b046e466b38ae79

Aliases

arxiv: 2607.28433 · arxiv_version: 2607.28433v1 · doi: 10.48550/arxiv.2607.28433 · pith_short_12: 5G2LRFZTO5BJ · pith_short_16: 5G2LRFZTO5BJEA4W · pith_short_8: 5G2LRFZT

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/5G2LRFZTO5BJEA4WPP63Q7CPGC \
  | 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: e9b4b8973377429203967bfdb87c4f3097456d59f2395d0e1b046e466b38ae79

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "98c856d3f1fb8ab6c79b480d01ddd5b46eb135ff3324344e297aa9a30bf51341",
    "cross_cats_sorted": [
      "math.GR"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2026-07-30T16:10:10Z",
    "title_canon_sha256": "f2d9c8b647a054a3afc2adcc5c12e3d79208ece3c528a00e6b372fac9f9f7ac6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.28433",
    "kind": "arxiv",
    "version": 1
  }
}