Pith Number

pith:IOPDO7NO

pith:2026:IOPDO7NOD2CBAMZGZMXQKHT2XC

not attested not anchored not stored refs pending

Chain rules for conditional entropies in quantum cryptography: limitations and improvements

Lewis Wooltorton, Omar Fawzi, Peter Brown

arxiv:2605.29787 v1 · 2026-05-28 · 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{IOPDO7NOD2CBAMZGZMXQKHT2XC}

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	2026-05-29T02:05:52.330394Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

439e377dae1e84103326cb2f051e7ab8b5509bcba22db472cb8537e1f9e442a3

Aliases

arxiv: 2605.29787 · arxiv_version: 2605.29787v1 · doi: 10.48550/arxiv.2605.29787 · pith_short_12: IOPDO7NOD2CB · pith_short_16: IOPDO7NOD2CBAMZG · pith_short_8: IOPDO7NO

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/IOPDO7NOD2CBAMZGZMXQKHT2XC \
  | 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: 439e377dae1e84103326cb2f051e7ab8b5509bcba22db472cb8537e1f9e442a3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "191f16a0cf6e9a7d78ff115d3f9d1e85bae31eb67db025f2e4235697738fc2eb",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "quant-ph",
    "submitted_at": "2026-05-28T11:35:27Z",
    "title_canon_sha256": "9d3b5f177528abb4106ca6bad4e90432fa752acbcde29a5cac499a96e7b74ec9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.29787",
    "kind": "arxiv",
    "version": 1
  }
}