Pith Number

pith:IVFR6D7M

pith:2015:IVFR6D7MCZUWWHIPN3NUP4NPAR

not attested not anchored not stored refs pending

Bloom's Inequality: Commutators in a Two-Weight Setting

Brett D. Wick, Irina Holmes, Michael T. Lacey

arxiv:1505.07947 v2 · 2015-05-29 · 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{IVFR6D7MCZUWWHIPN3NUP4NPAR}

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	2026-05-18T01:13:09.706978Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

454b1f0fec16696b1d0f6edb47f1af044f8c9726d518b8896c8c72fea9c4a7bb

Aliases

arxiv: 1505.07947 · arxiv_version: 1505.07947v2 · doi: 10.48550/arxiv.1505.07947 · pith_short_12: IVFR6D7MCZUW · pith_short_16: IVFR6D7MCZUWWHIP · pith_short_8: IVFR6D7M

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/IVFR6D7MCZUWWHIPN3NUP4NPAR \
  | 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: 454b1f0fec16696b1d0f6edb47f1af044f8c9726d518b8896c8c72fea9c4a7bb

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "20286bf848bd1687908d583496b4df2c4336871c91334df93aa21e88c996d5d8",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2015-05-29T07:26:59Z",
    "title_canon_sha256": "d6a90e35535676976a7b7ce5936029a7fda9469bead5ee1f027cf3c32cee3486"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1505.07947",
    "kind": "arxiv",
    "version": 2
  }
}