Pith Number

pith:A7BJRE7X

pith:2026:A7BJRE7XKDPPCE7MFA5T7OLTWL

not attested not anchored not stored refs pending

The logarithmic $p$-Laplacian on hyperbolic spaces

Jorge J. Betancor, Lourdes Rodr\'{\i}guez-Mesa

arxiv:2608.01079 v1 · 2026-08-02 · 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{A7BJRE7XKDPPCE7MFA5T7OLTWL}

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	2026-08-04T01:56:29.350437Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

07c29893f750def113ec283b3fb973b2ebc7d65bfa51c63fdb9c814ba7acb8e6

Aliases

arxiv: 2608.01079 · arxiv_version: 2608.01079v1 · doi: 10.48550/arxiv.2608.01079 · pith_short_12: A7BJRE7XKDPP · pith_short_16: A7BJRE7XKDPPCE7M · pith_short_8: A7BJRE7X

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/A7BJRE7XKDPPCE7MFA5T7OLTWL \
  | 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: 07c29893f750def113ec283b3fb973b2ebc7d65bfa51c63fdb9c814ba7acb8e6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "dd3d5f23847ed6b1c6f87e047015fb0bf640fde8510d3918c772b019d57c13c6",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2026-08-02T08:26:05Z",
    "title_canon_sha256": "1c3bac0fab0e257a148cd1853c7ea80f964fb7a3ea224c7b045cae40301f4114"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2608.01079",
    "kind": "arxiv",
    "version": 1
  }
}