Pith Number

pith:MHQJLPJU

pith:2022:MHQJLPJU3TYCJASJVVCWIA5T3R

not attested not anchored not stored refs pending

On Infinite Series of Bessel functions of the First Kind: $\sum_\nu J_{N\nu+p}(x), \sum_\nu (-1)^\nu J_{N\nu+p}(x)$

Robert Hovden, Suk Hyun Sung

arxiv:2211.01148 v1 · 2022-11-01 · math-ph · math.CA · 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{MHQJLPJU3TYCJASJVVCWIA5T3R}

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	2026-07-05T05:12:55.388419Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

61e095bd34dcf0248249ad456403b3dc687ff486b75d5441df792f8e981aee66

Aliases

arxiv: 2211.01148 · arxiv_version: 2211.01148v1 · doi: 10.48550/arxiv.2211.01148 · pith_short_12: MHQJLPJU3TYC · pith_short_16: MHQJLPJU3TYCJASJ · pith_short_8: MHQJLPJU

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/MHQJLPJU3TYCJASJVVCWIA5T3R \
  | 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: 61e095bd34dcf0248249ad456403b3dc687ff486b75d5441df792f8e981aee66

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c56e2ae27a01cb99f655690ea6409cec782f69a8fdc36a1f78928c1d399ba608",
    "cross_cats_sorted": [
      "math.CA",
      "math.MP"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2022-11-01T17:29:58Z",
    "title_canon_sha256": "c0821e389a543fc008886848e60278b232e4ba6beff6604425c2c6a056c17d22"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2211.01148",
    "kind": "arxiv",
    "version": 1
  }
}