Pith Number

pith:TQY6HRJY

pith:2009:TQY6HRJYAU3QOVW3UR7YWZ3RFD

not attested not anchored not stored refs pending

Energy average formula of photon gas rederived by using the generalized Hermann-Feynman theorem

Hong-yi Fan

arxiv:0907.4267 v1 · 2009-07-24 · quant-ph

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{TQY6HRJYAU3QOVW3UR7YWZ3RFD}

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	2026-05-18T02:12:53.916156Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9c31e3c53805370756dba47f8b677128efed3de0fac4ccf03157bc4f8a17b798

Aliases

arxiv: 0907.4267 · arxiv_version: 0907.4267v1 · doi: 10.48550/arxiv.0907.4267 · pith_short_12: TQY6HRJYAU3Q · pith_short_16: TQY6HRJYAU3QOVW3 · pith_short_8: TQY6HRJY

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/TQY6HRJYAU3QOVW3UR7YWZ3RFD \
  | 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: 9c31e3c53805370756dba47f8b677128efed3de0fac4ccf03157bc4f8a17b798

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a0806348a7c45102484e86382219d97527c937347b8e3adf98d168c0f7d1ddce",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "quant-ph",
    "submitted_at": "2009-07-24T11:47:22Z",
    "title_canon_sha256": "01f2df0db84ec4c8441727ee14a0bfdf5e5b7d62077a07bf585d8e9e5e600c6c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0907.4267",
    "kind": "arxiv",
    "version": 1
  }
}