Pith Number

pith:7T6FARW4

pith:2019:7T6FARW4WZDJZBIDPMYCNGK3K7

not attested not anchored not stored refs pending

Two-weight estimates for sparse square functions and the separated bump conjecture

Spyridon Kakaroumpas

arxiv:1908.02867 v3 · 2019-08-07 · 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{7T6FARW4WZDJZBIDPMYCNGK3K7}

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	2026-07-05T00:35:19.411014Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fcfc5046dcb6469c85037b3026995b57f72bc14f4c9cd8cce2740276fb79e43d

Aliases

arxiv: 1908.02867 · arxiv_version: 1908.02867v3 · doi: 10.48550/arxiv.1908.02867 · pith_short_12: 7T6FARW4WZDJ · pith_short_16: 7T6FARW4WZDJZBID · pith_short_8: 7T6FARW4

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/7T6FARW4WZDJZBIDPMYCNGK3K7 \
  | 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: fcfc5046dcb6469c85037b3026995b57f72bc14f4c9cd8cce2740276fb79e43d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9b58ad0bf3f2a2d28d7c96a83977ba60e91df8fa85c200d99d904f34e00844f2",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2019-08-07T23:07:40Z",
    "title_canon_sha256": "30087166b4b8eb0f6a5f5f892f835b32e0913f7e7fa74fc84cb90f2f8c5d0d93"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1908.02867",
    "kind": "arxiv",
    "version": 3
  }
}