Pith Number

pith:MWBK52JX

pith:2012:MWBK52JXCHKTDGE37RZ63BLKLO

not attested not anchored not stored refs pending

On the Hellmann-Feynman theorem for statistical averages

Francisco M. Fern\'andez

arxiv:1211.5958 v1 · 2012-11-26 · 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{MWBK52JXCHKTDGE37RZ63BLKLO}

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	2026-05-18T03:39:53.724063Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6582aee93711d531989bfc73ed856a5b8bd835ee54785a7cc684860fef8e14ed

Aliases

arxiv: 1211.5958 · arxiv_version: 1211.5958v1 · doi: 10.48550/arxiv.1211.5958 · pith_short_12: MWBK52JXCHKT · pith_short_16: MWBK52JXCHKTDGE3 · pith_short_8: MWBK52JX

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/MWBK52JXCHKTDGE37RZ63BLKLO \
  | 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: 6582aee93711d531989bfc73ed856a5b8bd835ee54785a7cc684860fef8e14ed

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "98d9bcf1e8490352f8e195fe0c8a9939a5cc4286f5dcba8ca365c184b83031f8",
    "cross_cats_sorted": [
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2012-11-26T14:11:56Z",
    "title_canon_sha256": "d52f8fef8ab15ffc3588382303873460ee0fbeb47a50fb6474c445b9ba88abb0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1211.5958",
    "kind": "arxiv",
    "version": 1
  }
}