Pith Number

pith:I3UK3TXU

pith:1999:I3UK3TXUB2PIWYO5T6ECNAKLH3

not attested not anchored not stored refs pending

Quantum states and generalized observables: a simple proof of Gleason's theorem

P. Busch (Hull, UK)

arxiv:quant-ph/9909073 v3 · 1999-09-23 · 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{I3UK3TXUB2PIWYO5T6ECNAKLH3}

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	2026-05-18T04:32:09.711284Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

46e8adcef40e9e8b61dd9f8826814b3ece5d45c0d9e47b9aa63000bac3ae214b

Aliases

arxiv: quant-ph/9909073 · arxiv_version: quant-ph/9909073v3 · doi: 10.48550/arxiv.quant-ph/9909073 · pith_short_12: I3UK3TXUB2PI · pith_short_16: I3UK3TXUB2PIWYO5 · pith_short_8: I3UK3TXU

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/I3UK3TXUB2PIWYO5T6ECNAKLH3 \
  | 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: 46e8adcef40e9e8b61dd9f8826814b3ece5d45c0d9e47b9aa63000bac3ae214b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "98e436d60cc15be4798dcce9f67b7c5fd61e683bccb05263b743088fa8adf82a",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "quant-ph",
    "submitted_at": "1999-09-23T13:57:31Z",
    "title_canon_sha256": "e03ed2f8c1ec5f591cc1c31fa28801acc60662ced29b0f1ec5699141ad71f88d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "quant-ph/9909073",
    "kind": "arxiv",
    "version": 3
  }
}