Pith Number

pith:LPJ36BTE

pith:2025:LPJ36BTECRZP6DEXP7CBDDGBHV

not attested not anchored not stored refs pending

Single-letter Chain Rule for Quantum Relative Entropy

Giulio Gasbarri, Matt Hoogsteder-Riera

arxiv:2510.16918 v2 · 2025-10-19 · quant-ph · cs.IT · math-ph · math.IT · math.MP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{LPJ36BTECRZP6DEXP7CBDDGBHV}

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	2026-05-26T02:03:58.323998Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5bd3bf06641472ff0c977fc4118cc13d7a9c1b6d23755423648ded6be050c8ad

Aliases

arxiv: 2510.16918 · arxiv_version: 2510.16918v2 · doi: 10.48550/arxiv.2510.16918 · pith_short_12: LPJ36BTECRZP · pith_short_16: LPJ36BTECRZP6DEX · pith_short_8: LPJ36BTE

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/LPJ36BTECRZP6DEXP7CBDDGBHV \
  | 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: 5bd3bf06641472ff0c977fc4118cc13d7a9c1b6d23755423648ded6be050c8ad

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f97ee49fef2586715f6947de050adddc49802cd7ce5f721599564b65a27f8fbc",
    "cross_cats_sorted": [
      "cs.IT",
      "math-ph",
      "math.IT",
      "math.MP"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "quant-ph",
    "submitted_at": "2025-10-19T16:24:58Z",
    "title_canon_sha256": "4d09c39ce22755f03a065c4b8c59817de45cec91646baa20056606f48a5ff642"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2510.16918",
    "kind": "arxiv",
    "version": 2
  }
}