Pith Number

pith:GBJNF27P

pith:2026:GBJNF27PJZPQVGKYQ7EJSXN2AN

not attested not anchored not stored refs pending

Lubkin-Page typicality bounds for Type~II von~Neumann factors

Samuel L. Braunstein, Zhi-Wei Wang

arxiv:2607.01873 v1 · 2026-07-02 · hep-th · gr-qc · 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{GBJNF27PJZPQVGKYQ7EJSXN2AN}

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	2026-07-03T01:17:32.247256Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3052d2ebef4e5f0a995887c8995dba034541cb2e6477b5703548ee4cf4213922

Aliases

arxiv: 2607.01873 · arxiv_version: 2607.01873v1 · doi: 10.48550/arxiv.2607.01873 · pith_short_12: GBJNF27PJZPQ · pith_short_16: GBJNF27PJZPQVGKY · pith_short_8: GBJNF27P

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/GBJNF27PJZPQVGKYQ7EJSXN2AN \
  | 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: 3052d2ebef4e5f0a995887c8995dba034541cb2e6477b5703548ee4cf4213922

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a0cf6ba139b3924aaa1eaa8ff9d361baa9aeb24b7600936d4349b3692d6f1b89",
    "cross_cats_sorted": [
      "gr-qc",
      "math-ph",
      "math.MP",
      "quant-ph"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "hep-th",
    "submitted_at": "2026-07-02T08:27:45Z",
    "title_canon_sha256": "f7d4c455a1a03148f283db1821d6fb0137c3f8fe56650d64ae29617bc7677d4e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.01873",
    "kind": "arxiv",
    "version": 1
  }
}