Pith Number

pith:MDOE5JCV

pith:2013:MDOE5JCVU46L7O6YKGQP7AC7P4

not attested not anchored not stored refs pending

The minimization of matrix logarithms - on a fundamental property of the unitary polar factor

Johannes Lankeit, Patrizio Neff, Yuji Nakatsukasa

arxiv:1308.1122 v1 · 2013-08-05 · math.CA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{MDOE5JCVU46L7O6YKGQP7AC7P4}

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	2026-05-18T03:16:39.775505Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

60dc4ea455a73cbfbbd851a0ff805f7f251c30e62bdf083745d8a0811b1c2604

Aliases

arxiv: 1308.1122 · arxiv_version: 1308.1122v1 · doi: 10.48550/arxiv.1308.1122 · pith_short_12: MDOE5JCVU46L · pith_short_16: MDOE5JCVU46L7O6Y · pith_short_8: MDOE5JCV

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/MDOE5JCVU46L7O6YKGQP7AC7P4 \
  | 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: 60dc4ea455a73cbfbbd851a0ff805f7f251c30e62bdf083745d8a0811b1c2604

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1db500aded0c3d4c30706b6a34bf0a740460ad86a0bb397aa106b44fe475b7ee",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2013-08-05T21:26:38Z",
    "title_canon_sha256": "6c49ab2c92d68cc08485e74540d586c9c814b93014d957bd40346828d948209f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1308.1122",
    "kind": "arxiv",
    "version": 1
  }
}