Pith Number

pith:GA3UKU5H

pith:2014:GA3UKU5H3OCEVTLBMZT7GIJCR4

not attested not anchored not stored refs pending

An Hardy estimate for commutators of pseudo-differential operators

Ha Duy Hung, Luong Dang Ky

arxiv:1406.7393 v3 · 2014-06-28 · 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{GA3UKU5H3OCEVTLBMZT7GIJCR4}

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	2026-05-18T02:19:16.751148Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

30374553a7db844acd616667f321228f088f771cf2cbc96c4cc5fcbbf7fbc1cc

Aliases

arxiv: 1406.7393 · arxiv_version: 1406.7393v3 · doi: 10.48550/arxiv.1406.7393 · pith_short_12: GA3UKU5H3OCE · pith_short_16: GA3UKU5H3OCEVTLB · pith_short_8: GA3UKU5H

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/GA3UKU5H3OCEVTLBMZT7GIJCR4 \
  | 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: 30374553a7db844acd616667f321228f088f771cf2cbc96c4cc5fcbbf7fbc1cc

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b9e495c750b9d9a7ab235f44d51e3000fa2624c41dfefc6e5ffaf5b43d4250c2",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2014-06-28T12:42:29Z",
    "title_canon_sha256": "c5c58eeebe01bbd691661a6005638dec0f4905fd184b2086f0b12ed4157b7434"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1406.7393",
    "kind": "arxiv",
    "version": 3
  }
}