Pith Number

pith:64B574DZ

pith:2026:64B574DZ7QNSWGTGHIUJVIH4SG

not attested not anchored not stored refs pending

Sum rules and a second order Feynman-Hellman theorem for abstract operators with applications

Joachim Stubbe

arxiv:2605.24694 v1 · 2026-05-23 · math.SP · 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{64B574DZ7QNSWGTGHIUJVIH4SG}

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	2026-05-26T01:03:53.665161Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f703dff079fc1b2b1a663a289aa0fc9195215fc51a40a5552852604591928547

Aliases

arxiv: 2605.24694 · arxiv_version: 2605.24694v1 · doi: 10.48550/arxiv.2605.24694 · pith_short_12: 64B574DZ7QNS · pith_short_16: 64B574DZ7QNSWGTG · pith_short_8: 64B574DZ

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/64B574DZ7QNSWGTGHIUJVIH4SG \
  | 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: f703dff079fc1b2b1a663a289aa0fc9195215fc51a40a5552852604591928547

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c123538f19764004acadb9a6a41e092560911b567f06a80f5e722ca1e0fb5aed",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.SP",
    "submitted_at": "2026-05-23T18:14:09Z",
    "title_canon_sha256": "58ab7f325f901345edd16dab8975c35b8951990b750b4a2835b1bfb208a476a2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.24694",
    "kind": "arxiv",
    "version": 1
  }
}