Pith Number

pith:KPCBUKKV

pith:2011:KPCBUKKV3XLGQNDVHJPMZCPWBR

not attested not anchored not stored refs pending

Revisiting Riesz transforms on Heisenberg groups

P.K.Sanjay, S.Thangavelu

arxiv:1110.3236 v1 · 2011-10-14 · 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{KPCBUKKV3XLGQNDVHJPMZCPWBR}

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	2026-05-18T04:10:57.710452Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

53c41a2955ddd66834753a5ecc89f60c7cdad471b0bac4da6063a51a3928c5e1

Aliases

arxiv: 1110.3236 · arxiv_version: 1110.3236v1 · doi: 10.48550/arxiv.1110.3236 · pith_short_12: KPCBUKKV3XLG · pith_short_16: KPCBUKKV3XLGQNDV · pith_short_8: KPCBUKKV

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/KPCBUKKV3XLGQNDVHJPMZCPWBR \
  | 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: 53c41a2955ddd66834753a5ecc89f60c7cdad471b0bac4da6063a51a3928c5e1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d78c11a3cff18fa2b50235369d4b81f39e807c20df8d7b13a64a78aa9b1a74bd",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2011-10-14T15:09:02Z",
    "title_canon_sha256": "61e57eb88da21700c32c9f8e7db5d13f56f8024a82da317d575260de724bfa9c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1110.3236",
    "kind": "arxiv",
    "version": 1
  }
}