Pith Number

pith:PFGKUG6Y

pith:2021:PFGKUG6YWIZYV4DKEEK7QRYG4F

not attested not anchored not stored refs pending

Thermodynamics in new model of loop quantum cosmology

Xiangdong Zhang

arxiv:2111.05660 v1 · 2021-11-10 · gr-qc

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{PFGKUG6YWIZYV4DKEEK7QRYG4F}

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	2026-07-05T03:30:46.819696Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

794caa1bd8b2338af06a2115f84706e1541c4839d8c03477be6eb93badff615b

Aliases

arxiv: 2111.05660 · arxiv_version: 2111.05660v1 · doi: 10.48550/arxiv.2111.05660 · pith_short_12: PFGKUG6YWIZY · pith_short_16: PFGKUG6YWIZYV4DK · pith_short_8: PFGKUG6Y

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/PFGKUG6YWIZYV4DKEEK7QRYG4F \
  | 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: 794caa1bd8b2338af06a2115f84706e1541c4839d8c03477be6eb93badff615b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "cc7fcd6b55b1a4d68ef5cf8c8b7adf153118374e8ec250bf4bad1c78cdb0d0ea",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "gr-qc",
    "submitted_at": "2021-11-10T11:57:50Z",
    "title_canon_sha256": "44544a02f122793bbc89a88b21200e3e30b1643d5470bb5fbe261f474746f19f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2111.05660",
    "kind": "arxiv",
    "version": 1
  }
}