Pith Number

pith:HBZJOI4J

pith:2016:HBZJOI4JYWN6NOSDFK55TJKKHQ

not attested not anchored not stored refs pending

Endpoint Mapping properties of the Littlewood-Paley square function

Odysseas Bakas

arxiv:1612.09573 v1 · 2016-12-30 · 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{HBZJOI4JYWN6NOSDFK55TJKKHQ}

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	2026-05-18T00:53:41.189938Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3872972389c59be6ba432abbd9a54a3c17f0b5a90b9a7444a1733e680a4faccd

Aliases

arxiv: 1612.09573 · arxiv_version: 1612.09573v1 · doi: 10.48550/arxiv.1612.09573 · pith_short_12: HBZJOI4JYWN6 · pith_short_16: HBZJOI4JYWN6NOSD · pith_short_8: HBZJOI4J

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/HBZJOI4JYWN6NOSDFK55TJKKHQ \
  | 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: 3872972389c59be6ba432abbd9a54a3c17f0b5a90b9a7444a1733e680a4faccd

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "02cbb8ecfb4c08d0878647ce6abe9cd432020467aaaae546e6a8ebcbc785f538",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2016-12-30T19:48:36Z",
    "title_canon_sha256": "59e6351ca74d0324e1b8e350dddcc5383e83be5f682645ec79a2add828ab2e9f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1612.09573",
    "kind": "arxiv",
    "version": 1
  }
}