Pith Number

pith:ZZUIHRN3

pith:2015:ZZUIHRN35NUVTPZBBMUO6NHOXC

not attested not anchored not stored refs pending

Hardy's inequality for fractional powers of the sublaplacian on the Heisenberg group

L. Roncal, S. Thangavelu

arxiv:1508.00714 v2 · 2015-08-04 · math.CA · math.AP · math.FA

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{ZZUIHRN35NUVTPZBBMUO6NHOXC}

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	2026-05-18T01:11:05.171278Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ce6883c5bbeb6959bf210b28ef34eeb882bd2a2a7491e34a5912075cc949c41e

Aliases

arxiv: 1508.00714 · arxiv_version: 1508.00714v2 · doi: 10.48550/arxiv.1508.00714 · pith_short_12: ZZUIHRN35NUV · pith_short_16: ZZUIHRN35NUVTPZB · pith_short_8: ZZUIHRN3

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/ZZUIHRN35NUVTPZBBMUO6NHOXC \
  | 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: ce6883c5bbeb6959bf210b28ef34eeb882bd2a2a7491e34a5912075cc949c41e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "49c4db6c78f67de9cf5891ab8dea7f7fe16b442cd7c5231bad4e8b91ec68ab6b",
    "cross_cats_sorted": [
      "math.AP",
      "math.FA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2015-08-04T09:32:39Z",
    "title_canon_sha256": "f33a1be3bb3d01427a3800d0ac70954ce3320fe49c2c4e1ac196326eb70b4c28"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1508.00714",
    "kind": "arxiv",
    "version": 2
  }
}