Pith Number

pith:RA2B7J7X

pith:2023:RA2B7J7XOPF7LMOREYK5YY4DGS

not attested not anchored not stored refs pending

$p$-Means of Convex Bodies: Sharpening Relations and Structural Properties

Florian Grundbacher, Ren\'e Brandenberg

arxiv:2312.17512 v3 · 2023-12-29 · math.MG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{RA2B7J7XOPF7LMOREYK5YY4DGS}

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	2026-06-19T16:09:45.614391Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

88341fa7f773cbf5b1d12615dc6383349a19216a2415e7eb514accb10094dbf1

Aliases

arxiv: 2312.17512 · arxiv_version: 2312.17512v3 · doi: 10.48550/arxiv.2312.17512 · pith_short_12: RA2B7J7XOPF7 · pith_short_16: RA2B7J7XOPF7LMOR · pith_short_8: RA2B7J7X

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/RA2B7J7XOPF7LMOREYK5YY4DGS \
  | 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: 88341fa7f773cbf5b1d12615dc6383349a19216a2415e7eb514accb10094dbf1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2eb9e9ce75d0cfe5f7249f7acf50e3145f0a23d689dd6f67e2fc32cc6ac67f7a",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.MG",
    "submitted_at": "2023-12-29T08:19:00Z",
    "title_canon_sha256": "8bf0ad448ac07907d03caac2c0f514c15358279491c609edf6ef3835ed3be7ae"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2312.17512",
    "kind": "arxiv",
    "version": 3
  }
}