Pith Number

pith:TWPO4O5Z

pith:2025:TWPO4O5ZYHTCDPS36XCBW7EVPB

not attested not anchored not stored refs pending

Average relative entropy of random states

Lu wei

arxiv:2509.21846 v1 · 2025-09-26 · math-ph · cs.IT · math.IT · 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{TWPO4O5ZYHTCDPS36XCBW7EVPB}

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	2026-05-28T02:04:43.007720Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9d9eee3bb9c1e621be5bf5c41b7c95784c9f8aa108bfecbddce40dfd89429af0

Aliases

arxiv: 2509.21846 · arxiv_version: 2509.21846v1 · doi: 10.48550/arxiv.2509.21846 · pith_short_12: TWPO4O5ZYHTC · pith_short_16: TWPO4O5ZYHTCDPS3 · pith_short_8: TWPO4O5Z

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/TWPO4O5ZYHTCDPS36XCBW7EVPB \
  | 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: 9d9eee3bb9c1e621be5bf5c41b7c95784c9f8aa108bfecbddce40dfd89429af0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1af2bba4854131447da703e6b6820c25f1c22cf9c633f64d6f603a3701a9649a",
    "cross_cats_sorted": [
      "cs.IT",
      "math.IT",
      "math.MP",
      "quant-ph"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2025-09-26T04:15:07Z",
    "title_canon_sha256": "61bd96495a4f03094d52daef9eb6d65ddc123443b3caed743e20b0bf81b7de43"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2509.21846",
    "kind": "arxiv",
    "version": 1
  }
}