Pith Number

pith:S736X5HP

pith:2009:S736X5HPBKGN4V422TOET2A77P

not attested not anchored not stored refs pending

Short proofs of theorems of Mirsky and Horn on diagonals and eigenvalues of matrices

Elliott H. Lieb, Eric A. Carlen

arxiv:0904.0734 v3 · 2009-04-04 · math.FA · math.OA · quant-ph

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{S736X5HPBKGN4V422TOET2A77P}

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	2026-05-18T04:22:11.605080Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

97f7ebf4ef0a8cde579ad4dc49e81ffbfdfc1c72774268509a63d07032df1997

Aliases

arxiv: 0904.0734 · arxiv_version: 0904.0734v3 · doi: 10.48550/arxiv.0904.0734 · pith_short_12: S736X5HPBKGN · pith_short_16: S736X5HPBKGN4V42 · pith_short_8: S736X5HP

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/S736X5HPBKGN4V422TOET2A77P \
  | 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: 97f7ebf4ef0a8cde579ad4dc49e81ffbfdfc1c72774268509a63d07032df1997

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9be3732df3e1c0569ab36376966068cb2ac8abb15c84d1319fdab22057168080",
    "cross_cats_sorted": [
      "math.OA",
      "quant-ph"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2009-04-04T19:04:02Z",
    "title_canon_sha256": "b380b795eb838dde1619b03c1ed7d96d0c0639c81c20ddb3e0550da1a4f376f8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0904.0734",
    "kind": "arxiv",
    "version": 3
  }
}