Pith Number

pith:32ZR2Q6P

pith:2015:32ZR2Q6P2J3E6EM6VLSSFG5F5O

not attested not anchored not stored refs pending

On some properties of number-phase Wigner function

Maciej Przanowski, Przemyslaw Brzykcy

arxiv:1512.01836 v1 · 2015-12-06 · 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{32ZR2Q6P2J3E6EM6VLSSFG5F5O}

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	2026-05-18T01:25:09.156907Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

deb31d43cfd2764f119eaae5229ba5eb8b157529812157ab4cf26995f3e73644

Aliases

arxiv: 1512.01836 · arxiv_version: 1512.01836v1 · doi: 10.48550/arxiv.1512.01836 · pith_short_12: 32ZR2Q6P2J3E · pith_short_16: 32ZR2Q6P2J3E6EM6 · pith_short_8: 32ZR2Q6P

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/32ZR2Q6P2J3E6EM6VLSSFG5F5O \
  | 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: deb31d43cfd2764f119eaae5229ba5eb8b157529812157ab4cf26995f3e73644

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e94900497f313b772e6644cb6dbf06949b43e91904a5080f2c26adfd4320130d",
    "cross_cats_sorted": [
      "math.MP",
      "quant-ph"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2015-12-06T21:21:39Z",
    "title_canon_sha256": "81aca8e7b2095b6eb064ff65a36425221f68cf4ae3c62f9f69eac00484262d91"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1512.01836",
    "kind": "arxiv",
    "version": 1
  }
}