Pith Number

pith:6LLTPEKW

pith:2016:6LLTPEKWNP4NQNVAMNLOZVIDZB

not attested not anchored not stored refs pending

Optimal sampling recovery of mixed order Sobolev embeddings via discrete Littlewood-Paley type characterizations

Glenn Byrenheid, Tino Ullrich

arxiv:1603.04809 v6 · 2016-03-15 · math.NA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{6LLTPEKWNP4NQNVAMNLOZVIDZB}

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	2026-05-18T00:49:47.108161Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f2d73791566bf8d836a06356ecd503c8614a2b0806f38f37ba12f5114b3d85b8

Aliases

arxiv: 1603.04809 · arxiv_version: 1603.04809v6 · doi: 10.48550/arxiv.1603.04809 · pith_short_12: 6LLTPEKWNP4N · pith_short_16: 6LLTPEKWNP4NQNVA · pith_short_8: 6LLTPEKW

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/6LLTPEKWNP4NQNVAMNLOZVIDZB \
  | 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: f2d73791566bf8d836a06356ecd503c8614a2b0806f38f37ba12f5114b3d85b8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "dfefdaf5a6d003dc6e5562fa0dc1108cc1270469d6bd5c20291c71255e34a7e3",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NA",
    "submitted_at": "2016-03-15T18:43:57Z",
    "title_canon_sha256": "c5c8493281cb2b35ebc6901fe06f772cf6bc1bda8e5985423477ed3add0299a0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1603.04809",
    "kind": "arxiv",
    "version": 6
  }
}