Pith Number

pith:3J4THLUG

pith:2021:3J4THLUGZ2A7D7KQ3NT5AITKJ6

not attested not anchored not stored refs pending

Solid/Liquid Phase Transition and Heat Engine in Asymptotically Flat Schwarzschild Black Hole via the R\'enyi Extended Phase Space Approach

Chatchai Promsiri, Ekapong Hirunsirisawat, Watchara Liewrian

arxiv:2106.02406 v2 · 2021-06-04 · hep-th · 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{3J4THLUGZ2A7D7KQ3NT5AITKJ6}

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

1 paper in Pith

Modified Cosmology from Mass-to-Horizon Relation: Background Evolution

Receipt and verification

First computed	2026-07-05T03:12:06.969036Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

da7933ae86ce81f1fd50db67d0226a4fbeabc3a0ad1a1869834b446332ada4bb

Aliases

arxiv: 2106.02406 · arxiv_version: 2106.02406v2 · doi: 10.48550/arxiv.2106.02406 · pith_short_12: 3J4THLUGZ2A7 · pith_short_16: 3J4THLUGZ2A7D7KQ · pith_short_8: 3J4THLUG

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/3J4THLUGZ2A7D7KQ3NT5AITKJ6 \
  | 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: da7933ae86ce81f1fd50db67d0226a4fbeabc3a0ad1a1869834b446332ada4bb

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c7f82f59d602c7485a7c769503a3922270a2ace29eb6866abc0042f3c733859b",
    "cross_cats_sorted": [
      "gr-qc"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "hep-th",
    "submitted_at": "2021-06-04T10:47:59Z",
    "title_canon_sha256": "1a9532e42cc69849d8ae0a00188a0eca6eacbd57e99ba020f35c3bfb99fcf454"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2106.02406",
    "kind": "arxiv",
    "version": 2
  }
}