Pith Number

pith:3JZAMSB7

pith:2015:3JZAMSB75CFLV7RWUKXQS4XPR7

not attested not anchored not stored refs pending

Mutually unbiased bases as minimal Clifford covariant 2-designs

Huangjun Zhu

arxiv:1505.01123 v2 · 2015-05-05 · quant-ph · math-ph · math.MP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{3JZAMSB75CFLV7RWUKXQS4XPR7}

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	2026-05-18T01:37:13.207262Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

da7206483fe88abafe36a2af0972ef8fd755259bbd9c91739d4214caf04fa7a2

Aliases

arxiv: 1505.01123 · arxiv_version: 1505.01123v2 · doi: 10.48550/arxiv.1505.01123 · pith_short_12: 3JZAMSB75CFL · pith_short_16: 3JZAMSB75CFLV7RW · pith_short_8: 3JZAMSB7

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/3JZAMSB75CFLV7RWUKXQS4XPR7 \
  | 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: da7206483fe88abafe36a2af0972ef8fd755259bbd9c91739d4214caf04fa7a2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b2d1f5a4c17e205fc02bd55afc909f9d1379ec9e510339560138d42d108c1f16",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "quant-ph",
    "submitted_at": "2015-05-05T18:51:56Z",
    "title_canon_sha256": "20d90ec7f21f9db6152ffa09089134f9c4199d6468ac5b9d86a2bbcb3a94a009"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1505.01123",
    "kind": "arxiv",
    "version": 2
  }
}