Pith Number

pith:TO77APMH

pith:2026:TO77APMHAK7CYQTBM4MQ3CHN3L

not attested not anchored not stored refs pending

Note About Koopman-von Neumann Theory and Density Matrix

J. Kluson

arxiv:2606.25085 v1 · 2026-06-23 · 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{TO77APMHAK7CYQTBM4MQ3CHN3L}

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	2026-06-25T00:18:17.337643Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9bbff03d8702be2c426167190d88eddacd6b5e736a30fec5982fef2735236e49

Aliases

arxiv: 2606.25085 · arxiv_version: 2606.25085v1 · doi: 10.48550/arxiv.2606.25085 · pith_short_12: TO77APMHAK7C · pith_short_16: TO77APMHAK7CYQTB · pith_short_8: TO77APMH

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/TO77APMHAK7CYQTBM4MQ3CHN3L \
  | 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: 9bbff03d8702be2c426167190d88eddacd6b5e736a30fec5982fef2735236e49

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6c06438731178cef8539cbd8304f3ca089fdac2f3db620812f89256156c93366",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/publicdomain/zero/1.0/",
    "primary_cat": "quant-ph",
    "submitted_at": "2026-06-23T18:45:17Z",
    "title_canon_sha256": "fe4efccc03957abf0c99874b7a44810f0e2b3fdf887038e6ac7a224a5fc54b25"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.25085",
    "kind": "arxiv",
    "version": 1
  }
}