Pith Number

pith:VH623RCO

pith:2012:VH623RCOJL7SBKF3K6IVWAHC42

not attested not anchored not stored refs pending

Remainder terms in the fractional Sobolev inequality

Rupert L. Frank, Shibing Chen, Tobias Weth

arxiv:1205.5666 v1 · 2012-05-25 · 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{VH623RCOJL7SBKF3K6IVWAHC42}

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	2026-05-18T03:54:50.634592Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a9fdadc44e4aff20a8bb57915b00e2e68bd45556e440f1143dad4d7f656f29a9

Aliases

arxiv: 1205.5666 · arxiv_version: 1205.5666v1 · doi: 10.48550/arxiv.1205.5666 · pith_short_12: VH623RCOJL7S · pith_short_16: VH623RCOJL7SBKF3 · pith_short_8: VH623RCO

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/VH623RCOJL7SBKF3K6IVWAHC42 \
  | 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: a9fdadc44e4aff20a8bb57915b00e2e68bd45556e440f1143dad4d7f656f29a9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fb3ab8e3fc8219fa48b27db3eb21613db71bd7c0e3f4dd60e1090324a3e0deb2",
    "cross_cats_sorted": [
      "math.FA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2012-05-25T11:45:26Z",
    "title_canon_sha256": "dde7fabec7e7a278ec42e099c51d943a894b8471c65e7ce193195334e7e7b250"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1205.5666",
    "kind": "arxiv",
    "version": 1
  }
}