Pith Number

pith:S3NVATAI

pith:2016:S3NVATAITMIP2GSBTTLXGWQ2AH

not attested not anchored not stored refs pending

The Birkhoff theorem for unitary matrices of arbitrary dimensions

Alexis De Vos, Lin Chen, Li Yu, Stijn De Baerdemacker

arxiv:1606.08642 v1 · 2016-06-28 · 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{S3NVATAITMIP2GSBTTLXGWQ2AH}

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	2026-05-18T00:58:33.242536Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

96db504c089b10fd1a419cd7735a1a01c5983306a44348a6df098c7fda39d792

Aliases

arxiv: 1606.08642 · arxiv_version: 1606.08642v1 · doi: 10.48550/arxiv.1606.08642 · pith_short_12: S3NVATAITMIP · pith_short_16: S3NVATAITMIP2GSB · pith_short_8: S3NVATAI

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/S3NVATAITMIP2GSBTTLXGWQ2AH \
  | 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: 96db504c089b10fd1a419cd7735a1a01c5983306a44348a6df098c7fda39d792

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "31c4022e247a1985f7a5b380b633e3dc15b0608a0daa957b80934f4b20f520af",
    "cross_cats_sorted": [
      "math.MP",
      "quant-ph"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2016-06-28T10:37:41Z",
    "title_canon_sha256": "b061426f002c742b4bd1bd253f1a9e2ba0db2ad1a658443f9483da2c3e21db41"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1606.08642",
    "kind": "arxiv",
    "version": 1
  }
}