Pith Number

pith:UPI6EFCY

pith:2026:UPI6EFCY35AT7PYGJV3WNNIVLK

not attested not anchored not stored refs pending

Comment on "Specific heat of an ideal Bose gas above the Bose condensation temperature," [Am. J. Phys. 72(9), 1193--1194 (2004)]

Frank Wang

Einstein's formula for the specific heat of an ideal Bose gas above condensation temperature differs from the 2004 version and corrects errors in the English translation.

arxiv:2604.18180 v3 · 2026-04-20 · physics.hist-ph

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\usepackage{pith}
\pithnumber{UPI6EFCY35AT7PYGJV3WNNIVLK}

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Record completeness

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2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

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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.

Claims

C1strongest claim

Einstein's formula for the specific heat of an ideal Bose gas above the condensation temperature differs from the one published in the American Journal of Physics in 2004, and the English translation contains numerical errors that the paper corrects.

C2weakest assumption

That the English translation faithfully represents Einstein's original 1925 calculations and that the 2004 formula provides a meaningful independent benchmark for comparison.

C3one line summary

Corrects numerical errors in Einstein's 1925 specific-heat calculations for an ideal Bose gas above condensation temperature and compares his formula to a 2004 alternative while summarizing the theory's acceptance.

Receipt and verification

First computed	2026-06-09T02:07:26.666726Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a3d1e21458df413fbf064d7766b5155aaf619e3747efad456e3df84bfe2d2228

Aliases

arxiv: 2604.18180 · arxiv_version: 2604.18180v3 · doi: 10.48550/arxiv.2604.18180 · pith_short_12: UPI6EFCY35AT · pith_short_16: UPI6EFCY35AT7PYG · pith_short_8: UPI6EFCY

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/UPI6EFCY35AT7PYGJV3WNNIVLK \
  | 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: a3d1e21458df413fbf064d7766b5155aaf619e3747efad456e3df84bfe2d2228

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1a3ed40ef1ff00dfe77dd62020a82ea1733072367a6fe6075b1ab77f7f6bf438",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "physics.hist-ph",
    "submitted_at": "2026-04-20T12:36:22Z",
    "title_canon_sha256": "6eb6344ef6fb7d289e27d0cf87dcea0a634e791007385f643c4b145046cb43fb"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2604.18180",
    "kind": "arxiv",
    "version": 3
  }
}