Pith Number

pith:HXIX5BX6

pith:2015:HXIX5BX6ZUA5MOYIUSWK3SRRJC

not attested not anchored not stored refs pending

Certain Multi(sub)linear square functions

Loukas Grafakos, Qingying Xue, Sha He

arxiv:1504.03424 v1 · 2015-04-14 · 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{HXIX5BX6ZUA5MOYIUSWK3SRRJC}

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	2026-05-18T02:18:52.224451Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3dd17e86fecd01d63b08a4acadca314895e66f9c133fc2b4a47d3bfb3333f45c

Aliases

arxiv: 1504.03424 · arxiv_version: 1504.03424v1 · doi: 10.48550/arxiv.1504.03424 · pith_short_12: HXIX5BX6ZUA5 · pith_short_16: HXIX5BX6ZUA5MOYI · pith_short_8: HXIX5BX6

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/HXIX5BX6ZUA5MOYIUSWK3SRRJC \
  | 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: 3dd17e86fecd01d63b08a4acadca314895e66f9c133fc2b4a47d3bfb3333f45c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fdae02bd20cc72e4e362f3317446431481a63562a27dc85b09a5b404a04c627c",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2015-04-14T05:47:53Z",
    "title_canon_sha256": "f3a6d1881cc79bd5707e733e2fc71d91e0e42748c5448b69116d4ce6f137acf9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1504.03424",
    "kind": "arxiv",
    "version": 1
  }
}