Pith Number

pith:2WIOPQVX

pith:2010:2WIOPQVXICEGKFLJ6F54CH4I5T

not attested not anchored not stored refs pending

Group theoretic formulation of complementarity

J.A. Vaccaro

arxiv:1012.3532 v1 · 2010-12-16 · 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{2WIOPQVXICEGKFLJ6F54CH4I5T}

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	2026-05-18T04:33:06.432162Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d590e7c2b74088651569f17bc11f88ecc8128ac9ba993933d47655d9e36e59be

Aliases

arxiv: 1012.3532 · arxiv_version: 1012.3532v1 · doi: 10.48550/arxiv.1012.3532 · pith_short_12: 2WIOPQVXICEG · pith_short_16: 2WIOPQVXICEGKFLJ · pith_short_8: 2WIOPQVX

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/2WIOPQVXICEGKFLJ6F54CH4I5T \
  | 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: d590e7c2b74088651569f17bc11f88ecc8128ac9ba993933d47655d9e36e59be

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "586be2d26d618ae7f786e42eda171f53b8641f68552a95b6afb1286aea58192b",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "quant-ph",
    "submitted_at": "2010-12-16T08:56:48Z",
    "title_canon_sha256": "73659ab4848025f3f114598f737f2db88d921b0a2c959b7a59d0c657b0e954a7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1012.3532",
    "kind": "arxiv",
    "version": 1
  }
}