Pith Number

pith:2OLDAQZQ

pith:2015:2OLDAQZQ5D4J6RZT2EHJJGAT2L

not attested not anchored not stored refs pending

Minkowski product of convex sets and product numerical range

Chi-Kwong Li, Diane Christine Pelejo, Kuo-Zhong Wang, Yiu-Tung Poon

arxiv:1505.05382 v1 · 2015-05-19 · 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{2OLDAQZQ5D4J6RZT2EHJJGAT2L}

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	2026-05-18T02:03:56.533029Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d396304330e8f89f4733d10e949813d2cf7f43e00c117b6b69312009c7846dd7

Aliases

arxiv: 1505.05382 · arxiv_version: 1505.05382v1 · doi: 10.48550/arxiv.1505.05382 · pith_short_12: 2OLDAQZQ5D4J · pith_short_16: 2OLDAQZQ5D4J6RZT · pith_short_8: 2OLDAQZQ

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/2OLDAQZQ5D4J6RZT2EHJJGAT2L \
  | 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: d396304330e8f89f4733d10e949813d2cf7f43e00c117b6b69312009c7846dd7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "49a41c7aad35c1be75233046b5e8602a4996e518f298ba05e806666fab8d134a",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.MG",
    "submitted_at": "2015-05-19T04:21:34Z",
    "title_canon_sha256": "7958396d050113c48c833ecf44850aae632d0320d4cf2f20dbc68583a3d3c0d8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1505.05382",
    "kind": "arxiv",
    "version": 1
  }
}