Pith Number

pith:7VOIU4SK

pith:2025:7VOIU4SKM56TJOCLM5NW4KERX7

not attested not anchored not stored refs pending

Generalized product formulas for Whittaker's functions and a novel class of index transforms

Semyon Yakubovich

arxiv:2506.05013 v2 · 2025-06-05 · math.CA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{7VOIU4SKM56TJOCLM5NW4KERX7}

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	2026-07-05T11:17:24.823044Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fd5c8a724a677d34b84b675b6e2891bfcb0357d8094a4cd8f5c65631f43df7e3

Aliases

arxiv: 2506.05013 · arxiv_version: 2506.05013v2 · doi: 10.48550/arxiv.2506.05013 · pith_short_12: 7VOIU4SKM56T · pith_short_16: 7VOIU4SKM56TJOCL · pith_short_8: 7VOIU4SK

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/7VOIU4SKM56TJOCLM5NW4KERX7 \
  | 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: fd5c8a724a677d34b84b675b6e2891bfcb0357d8094a4cd8f5c65631f43df7e3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "24d855f27ef42777a9f995c40254d988bdc79a92d4d8c94b9f1cdb06b7293155",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/publicdomain/zero/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2025-06-05T13:22:10Z",
    "title_canon_sha256": "39cf043ad1fb34cbc422654e7b837e0826c1533be715d9e73d076fae0c5dd591"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2506.05013",
    "kind": "arxiv",
    "version": 2
  }
}