Pith Number

pith:VK5BKFAV

pith:2021:VK5BKFAVUQRVOPQQEPJDZDROSU

not attested not anchored not stored refs pending

Closedness of the orbit-closed $C$-numerical range and submajorization

Jireh Loreaux, Sasmita Patnaik

arxiv:2106.11205 v1 · 2021-06-21 · 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{VK5BKFAVUQRVOPQQEPJDZDROSU}

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	2026-07-05T02:50:57.799761Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

aaba151415a423573e1023d23c8e2e9534758a0f0b899f4b7aeb0d66153690ef

Aliases

arxiv: 2106.11205 · arxiv_version: 2106.11205v1 · doi: 10.48550/arxiv.2106.11205 · pith_short_12: VK5BKFAVUQRV · pith_short_16: VK5BKFAVUQRVOPQQ · pith_short_8: VK5BKFAV

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/VK5BKFAVUQRVOPQQEPJDZDROSU \
  | 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: aaba151415a423573e1023d23c8e2e9534758a0f0b899f4b7aeb0d66153690ef

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "aedd7e92467bc0efe4caed00d648490230806f1f6d753afe62f4694b1453c175",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2021-06-21T15:45:05Z",
    "title_canon_sha256": "7b35f29cb8bb7f924ef65c0cc65686537f1bfb9312d88edb18218face331778a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2106.11205",
    "kind": "arxiv",
    "version": 1
  }
}