Pith Number

pith:PATPALPE

pith:2010:PATPALPEZKI6HXE44MNLMP4MV7

not attested not anchored not stored refs pending

Lazy states: sufficient and necessary condition for zero quantum entropy rates under any coupling to the environment

Alan Aspuru-Guzik, Cesar A. Rodriguez-Rosario, Gen Kimura, Hideki Imai

arxiv:1004.5405 v2 · 2010-04-29 · quant-ph · math-ph · 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{PATPALPEZKI6HXE44MNLMP4MV7}

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	2026-05-18T04:29:53.780202Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7826f02de4ca91e3dc9ce31ab63f8cafd62beefd96e757d8e6ae45fd0b494297

Aliases

arxiv: 1004.5405 · arxiv_version: 1004.5405v2 · doi: 10.48550/arxiv.1004.5405 · pith_short_12: PATPALPEZKI6 · pith_short_16: PATPALPEZKI6HXE4 · pith_short_8: PATPALPE

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/PATPALPEZKI6HXE44MNLMP4MV7 \
  | 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: 7826f02de4ca91e3dc9ce31ab63f8cafd62beefd96e757d8e6ae45fd0b494297

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "11635a86b1097a8eff9813c56ed1d0859133ce36ee71700dfd08f2f9fe28c456",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "quant-ph",
    "submitted_at": "2010-04-29T21:03:13Z",
    "title_canon_sha256": "f7cf12e84346ab491cda5c54491ee285d8163f0d22c39acab357221fadbd0723"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1004.5405",
    "kind": "arxiv",
    "version": 2
  }
}