Pith Number

pith:ACBIKO4D

pith:2010:ACBIKO4DRB2MHMYLDHAQISEVGQ

not attested not anchored not stored refs pending

The optimal constant in the $L^2$ Folland-Stein inequality on the quaternionic Heisenberg group

Dimiter Vassilev, Ivan Minchev, Stefan Ivanov

arxiv:1009.2978 v2 · 2010-09-15 · math.AP · math.DG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{ACBIKO4DRB2MHMYLDHAQISEVGQ}

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	2026-05-18T04:40:08.096866Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0082853b838874c3b30b19c1044895340dd729dd3924f57d771d09484fab81d4

Aliases

arxiv: 1009.2978 · arxiv_version: 1009.2978v2 · doi: 10.48550/arxiv.1009.2978 · pith_short_12: ACBIKO4DRB2M · pith_short_16: ACBIKO4DRB2MHMYL · pith_short_8: ACBIKO4D

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/ACBIKO4DRB2MHMYLDHAQISEVGQ \
  | 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: 0082853b838874c3b30b19c1044895340dd729dd3924f57d771d09484fab81d4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fd4fdd247ba2ac8fc3903987bf23ff6a11a4138ab994cb9db87d84ea57d7c711",
    "cross_cats_sorted": [
      "math.DG"
    ],
    "license": "http://creativecommons.org/licenses/publicdomain/",
    "primary_cat": "math.AP",
    "submitted_at": "2010-09-15T17:56:45Z",
    "title_canon_sha256": "07470d634df897217c8d27a420bce4c3c3d7b0675e85f8eaf93d878531ad8030"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1009.2978",
    "kind": "arxiv",
    "version": 2
  }
}