Pith Number

pith:3EW4C3P6

pith:2018:3EW4C3P6MMFHUVXGDY2ZJJRTLB

not attested not anchored not stored refs pending

Two classical properties of the Bessel quotient $I_{\nu+1}/I_\nu$ and their implications in pde's

Nicola Garofalo

arxiv:1810.09756 v1 · 2018-10-23 · math.AP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{3EW4C3P6MMFHUVXGDY2ZJJRTLB}

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	2026-05-18T00:02:29.480690Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d92dc16dfe630a7a56e61e3594a63358791578a246bfd55d38c32464a27a0fcd

Aliases

arxiv: 1810.09756 · arxiv_version: 1810.09756v1 · doi: 10.48550/arxiv.1810.09756 · pith_short_12: 3EW4C3P6MMFH · pith_short_16: 3EW4C3P6MMFHUVXG · pith_short_8: 3EW4C3P6

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/3EW4C3P6MMFHUVXGDY2ZJJRTLB \
  | 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: d92dc16dfe630a7a56e61e3594a63358791578a246bfd55d38c32464a27a0fcd

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e27fd86b394a38ca58ef3698e6cbc6bd9f0f67859942c7bf8912b3833947b496",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2018-10-23T10:15:11Z",
    "title_canon_sha256": "1a710be9530d668a2b2a969cc78cf63a001bb4b193b9022cde631595a14acb62"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1810.09756",
    "kind": "arxiv",
    "version": 1
  }
}