Pith Number

pith:I3S32C3W

pith:2013:I3S32C3WLJG4QAIPN4ZQZIAJYV

not attested not anchored not stored refs pending

Majorization entropic uncertainty relations

Karol \.Zyczkowski, {\L}ukasz Rudnicki, Zbigniew Pucha{\l}a

arxiv:1304.7755 v3 · 2013-04-29 · quant-ph · cs.IT · math.IT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{I3S32C3WLJG4QAIPN4ZQZIAJYV}

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	2026-05-18T01:26:32.119253Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

46e5bd0b765a4dc8010f6f330ca009c54ba040a0fc92b29d3bd72cd275d662bd

Aliases

arxiv: 1304.7755 · arxiv_version: 1304.7755v3 · doi: 10.48550/arxiv.1304.7755 · pith_short_12: I3S32C3WLJG4 · pith_short_16: I3S32C3WLJG4QAIP · pith_short_8: I3S32C3W

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/I3S32C3WLJG4QAIPN4ZQZIAJYV \
  | 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: 46e5bd0b765a4dc8010f6f330ca009c54ba040a0fc92b29d3bd72cd275d662bd

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "95350a87f2c2d5461c3984e3e29fb461dd284c9c5f47f0298c87dfeea93d4de9",
    "cross_cats_sorted": [
      "cs.IT",
      "math.IT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "quant-ph",
    "submitted_at": "2013-04-29T19:44:42Z",
    "title_canon_sha256": "6dd02eef1a56c0423ae0775429d10443b48b84935bdc0f344df06040f2594740"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1304.7755",
    "kind": "arxiv",
    "version": 3
  }
}