Pith Number

pith:4FESBHVR

pith:2026:4FESBHVRH6YA4WENTJ4GPH445T

not attested not anchored not stored refs pending

Radial Hyperbolic Measures: Shell Geometry, Pyramid Limits, and Gaussian Phase Transitions

Shigeaki Yokota

arxiv:2607.27605 v1 · 2026-07-30 · math.MG · 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{4FESBHVRH6YA4WENTJ4GPH445T}

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	2026-07-31T01:27:10.129581Z
Builder	pith-number-builder-2026-05-17-v1
Signature	unsigned_v0
Schema	pith-number/v1.0

Canonical hash

e149209eb13fb00e588d9a78679f9cecd277ca1af0dfdcf1b8e4951b6306af5a

Aliases

arxiv: 2607.27605 · arxiv_version: 2607.27605v1 · doi: 10.48550/arxiv.2607.27605 · pith_short_12: 4FESBHVRH6YA · pith_short_16: 4FESBHVRH6YA4WEN · pith_short_8: 4FESBHVR

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/4FESBHVRH6YA4WENTJ4GPH445T \
  | 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: e149209eb13fb00e588d9a78679f9cecd277ca1af0dfdcf1b8e4951b6306af5a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f665aad1fdc18541eaae45c80b709279cc4402519f6fcc7a2e60df79b394bda2",
    "cross_cats_sorted": [
      "math.PR"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.MG",
    "submitted_at": "2026-07-30T02:49:56Z",
    "title_canon_sha256": "4a5d8060dac0007d03f7863b8c6e115d4ea3342b037f11457c9ec0103774e36c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.27605",
    "kind": "arxiv",
    "version": 1
  }
}