Pith Number

pith:BDGZ4KSQ

pith:2013:BDGZ4KSQWRCJMEMWCWEKZFQGJC

not attested not anchored not stored refs pending

Square functions and spectral multipliers for Bessel operators in UMD spaces

Alejandro J. Castro, Jorge J. Betancor, Lourdes Rodriguez-Mesa

arxiv:1303.3159 v1 · 2013-03-13 · 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{BDGZ4KSQWRCJMEMWCWEKZFQGJC}

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	2026-05-18T01:12:43.918826Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

08cd9e2a50b4449611961588ac960648a385f627c5352320527276fea0467c7e

Aliases

arxiv: 1303.3159 · arxiv_version: 1303.3159v1 · doi: 10.48550/arxiv.1303.3159 · pith_short_12: BDGZ4KSQWRCJ · pith_short_16: BDGZ4KSQWRCJMEMW · pith_short_8: BDGZ4KSQ

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/BDGZ4KSQWRCJMEMWCWEKZFQGJC \
  | 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: 08cd9e2a50b4449611961588ac960648a385f627c5352320527276fea0467c7e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a9131beae213510c6f16399edb7989d0ce9cada44526b47ca2fa542ef1de8a12",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2013-03-13T13:46:10Z",
    "title_canon_sha256": "8998d353682badce1a9561837ef9d0b6ae678b4ae8a23c0189cb05c611d800e5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1303.3159",
    "kind": "arxiv",
    "version": 1
  }
}