Pith Number

pith:USAFZ3ZX

pith:2026:USAFZ3ZXFZQEXHRLTRF22XBJX5

not attested not anchored not stored refs pending

Sobolev extensions, interpolation inequalities and consequences

Pekka Koskela, Riddhi Mishra, Rupert L. Frank

arxiv:2606.17738 v1 · 2026-06-16 · 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{USAFZ3ZXFZQEXHRLTRF22XBJX5}

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	2026-06-19T16:10:20.713117Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a4805cef372e604b9e2b9c4bad5c29bf6dada59273c0b0bf0dca10d7ae4547a6

Aliases

arxiv: 2606.17738 · arxiv_version: 2606.17738v1 · doi: 10.48550/arxiv.2606.17738 · pith_short_12: USAFZ3ZXFZQE · pith_short_16: USAFZ3ZXFZQEXHRL · pith_short_8: USAFZ3ZX

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/USAFZ3ZXFZQEXHRLTRF22XBJX5 \
  | 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: a4805cef372e604b9e2b9c4bad5c29bf6dada59273c0b0bf0dca10d7ae4547a6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8a4f2d1bd3ac41c16e3b6e6030fc232da1a38df4ea28da598ccdc36d70464be5",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2026-06-16T09:57:35Z",
    "title_canon_sha256": "04c27cf0c62eb9dd6c4c32df8dc5aa3ed6345fc15e0f1cbb76a69a1473926da7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.17738",
    "kind": "arxiv",
    "version": 1
  }
}