Pith Number

pith:BJU3XU5S

pith:2020:BJU3XU5SPZ5XBTUMJNLC44KRM4

not attested not anchored not stored refs pending

Entropy, Divergence, and Majorization in Classical and Quantum Thermodynamics

Takahiro Sagawa

arxiv:2007.09974 v3 · 2020-07-20 · quant-ph · cond-mat.stat-mech · 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{BJU3XU5SPZ5XBTUMJNLC44KRM4}

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.

Cited by

2 papers in Pith

Predicting the conditions for observing the Mpemba effect

Receipt and verification

First computed	2026-07-05T01:38:19.668220Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0a69bbd3b27e7b70ce8c4b562e715167155d2a539d6038a38b6c4393633b0bf5

Aliases

arxiv: 2007.09974 · arxiv_version: 2007.09974v3 · doi: 10.48550/arxiv.2007.09974 · pith_short_12: BJU3XU5SPZ5X · pith_short_16: BJU3XU5SPZ5XBTUM · pith_short_8: BJU3XU5S

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/BJU3XU5SPZ5XBTUMJNLC44KRM4 \
  | 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: 0a69bbd3b27e7b70ce8c4b562e715167155d2a539d6038a38b6c4393633b0bf5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "663e82c34c3873b4fd29e93f5710b53ba03fd0e240ab44d9bcef90451bdf4fc0",
    "cross_cats_sorted": [
      "cond-mat.stat-mech",
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "quant-ph",
    "submitted_at": "2020-07-20T09:50:27Z",
    "title_canon_sha256": "f234d0aedd0c667d4caec7b9163d660539a9cdcb7bc073bc539f5fa9e05b9c7b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2007.09974",
    "kind": "arxiv",
    "version": 3
  }
}