Pith Number

pith:GZ3LIPJS

pith:2011:GZ3LIPJSTDZYXD2IM2X5Q4V4NR

not attested not anchored not stored refs pending

Sharp Lower bound estimates for vector-valued and matrix-valued multipliers in $L^p$

Alexander Volberg, Nicholas Boros

arxiv:1110.5405 v1 · 2011-10-25 · math.CA · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{GZ3LIPJSTDZYXD2IM2X5Q4V4NR}

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	2026-05-18T04:10:22.960635Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3676b43d3298f38b8f4866afd872bc6c68016e4a7bbd2915a49a58c95cdcd603

Aliases

arxiv: 1110.5405 · arxiv_version: 1110.5405v1 · doi: 10.48550/arxiv.1110.5405 · pith_short_12: GZ3LIPJSTDZY · pith_short_16: GZ3LIPJSTDZYXD2I · pith_short_8: GZ3LIPJS

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/GZ3LIPJSTDZYXD2IM2X5Q4V4NR \
  | 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: 3676b43d3298f38b8f4866afd872bc6c68016e4a7bbd2915a49a58c95cdcd603

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "02cb7cebe2b339ae788232a250fb2f4cf6ba092af73e309b60cc9063bf992f59",
    "cross_cats_sorted": [
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2011-10-25T04:14:46Z",
    "title_canon_sha256": "d0a2709a846d1923f72526462c0a7136174c2627b75132ec98a1902c94bec0ca"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1110.5405",
    "kind": "arxiv",
    "version": 1
  }
}