Pith Number

pith:DHEPHAPZ

pith:2014:DHEPHAPZBGX6ZYS2W4WFASZCOJ

not attested not anchored not stored refs pending

Sinkhorn normal form for unitary matrices

Martin Idel, Michael M. Wolf

arxiv:1408.5728 v3 · 2014-08-25 · math-ph · math.MP · 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{DHEPHAPZBGX6ZYS2W4WFASZCOJ}

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	2026-05-18T01:33:58.678680Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

19c8f381f909afece25ab72c504b22724b237b59cdbaacaa64ad65f6d3dd6882

Aliases

arxiv: 1408.5728 · arxiv_version: 1408.5728v3 · doi: 10.48550/arxiv.1408.5728 · pith_short_12: DHEPHAPZBGX6 · pith_short_16: DHEPHAPZBGX6ZYS2 · pith_short_8: DHEPHAPZ

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/DHEPHAPZBGX6ZYS2W4WFASZCOJ \
  | 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: 19c8f381f909afece25ab72c504b22724b237b59cdbaacaa64ad65f6d3dd6882

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4b7bb955462763afb4fca54e5cebf45791f4609412ef0a411893928adb7bd833",
    "cross_cats_sorted": [
      "math.MP",
      "quant-ph"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2014-08-25T12:06:05Z",
    "title_canon_sha256": "b433cace232fb0c78cb824b714f0ce0f4f4e0b2a1afe4c6b19143781e9929c2c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1408.5728",
    "kind": "arxiv",
    "version": 3
  }
}