Pith Number

pith:SS6PH5RT

pith:2018:SS6PH5RTDYNW5HU6XVVGQYH7ZB

not attested not anchored not stored refs pending

Attainability of the best Sobolev constant in a ball

Norisuke Ioku

arxiv:1807.00127 v2 · 2018-06-30 · math.FA · math.AP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{SS6PH5RTDYNW5HU6XVVGQYH7ZB}

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	2026-05-18T00:11:46.432052Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

94bcf3f6331e1b6e9e9ebd6a6860ffc86f2871acf1cb914f6bb41b918786f662

Aliases

arxiv: 1807.00127 · arxiv_version: 1807.00127v2 · doi: 10.48550/arxiv.1807.00127 · pith_short_12: SS6PH5RTDYNW · pith_short_16: SS6PH5RTDYNW5HU6 · pith_short_8: SS6PH5RT

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/SS6PH5RTDYNW5HU6XVVGQYH7ZB \
  | 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: 94bcf3f6331e1b6e9e9ebd6a6860ffc86f2871acf1cb914f6bb41b918786f662

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fa14d44998b34c4e68756458ea18c368df52b45fddae1693325ec86dfb9f7221",
    "cross_cats_sorted": [
      "math.AP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2018-06-30T05:47:54Z",
    "title_canon_sha256": "92c438e2f401dc8d7f715fc90b20f48ff7032efe80c3bafb59dd1c6a7f3bde8e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1807.00127",
    "kind": "arxiv",
    "version": 2
  }
}