Pith Number

pith:HGZF7EHX

pith:2015:HGZF7EHX5R45KY6TTUZ6MVMQQM

not attested not anchored not stored refs pending

The Birkhoff theorem for unitary matrices of prime dimension

Alexis De Vos, Stijn De Baerdemacker

arxiv:1509.08626 v1 · 2015-09-29 · 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{HGZF7EHX5R45KY6TTUZ6MVMQQM}

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	2026-05-18T01:12:25.192294Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

39b25f90f7ec79d563d39d33e655908331c74743abfe867cb72dd6c86efc61a9

Aliases

arxiv: 1509.08626 · arxiv_version: 1509.08626v1 · doi: 10.48550/arxiv.1509.08626 · pith_short_12: HGZF7EHX5R45 · pith_short_16: HGZF7EHX5R45KY6T · pith_short_8: HGZF7EHX

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/HGZF7EHX5R45KY6TTUZ6MVMQQM \
  | 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: 39b25f90f7ec79d563d39d33e655908331c74743abfe867cb72dd6c86efc61a9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "47b0007c1153473fd5f5bb7c57aaf9b9ca1635c3ce8dd1de24589b5854a59ecd",
    "cross_cats_sorted": [
      "math.MP",
      "quant-ph"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2015-09-29T08:07:57Z",
    "title_canon_sha256": "914870b949186d83bd4dd4261723c7b4c55159178e28cdcfe5edcd97cdfb1e52"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1509.08626",
    "kind": "arxiv",
    "version": 1
  }
}