Pith Number

pith:PZMRAJDY

pith:2011:PZMRAJDYMB73ZWLJT3D5Y7C5U6

not attested not anchored not stored refs pending

Brunn-Minkowski and Zhang inequalities for Convolution Bodies

C. Hugo Jimenez, David Alonso-Gutierrez, Rafael Villa

arxiv:1112.4757 v2 · 2011-12-20 · math.FA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{PZMRAJDYMB73ZWLJT3D5Y7C5U6}

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	2026-05-18T03:34:03.425138Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7e59102478607fbcd9699ec7dc7c5da790a4d2413b6e12297ee5c001e60534ee

Aliases

arxiv: 1112.4757 · arxiv_version: 1112.4757v2 · doi: 10.48550/arxiv.1112.4757 · pith_short_12: PZMRAJDYMB73 · pith_short_16: PZMRAJDYMB73ZWLJ · pith_short_8: PZMRAJDY

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/PZMRAJDYMB73ZWLJT3D5Y7C5U6 \
  | 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: 7e59102478607fbcd9699ec7dc7c5da790a4d2413b6e12297ee5c001e60534ee

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0e2f4163f316f8ad45eb4f97ae90e488fec3c13ce4b032554542a9965ddda885",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2011-12-20T16:35:04Z",
    "title_canon_sha256": "1547a421bd8a06e51d7c692b2d385c3fda6e3345f66bfd14cf5f84c53d53906c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1112.4757",
    "kind": "arxiv",
    "version": 2
  }
}