Pith Number

pith:4QCWJQET

pith:2011:4QCWJQETZWFBZNOZ5ISAHVGFZ6

not attested not anchored not stored refs pending

On strict inclusion relations between approximation and interpolation spaces

J. M. Almira

arxiv:1103.1330 v1 · 2011-03-07 · math.CA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{4QCWJQETZWFBZNOZ5ISAHVGFZ6}

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	2026-05-18T04:27:16.647440Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e40564c093cd8a1cb5d9ea2403d4c5cf9fa7395fa800c26640c9fc1640988bd9

Aliases

arxiv: 1103.1330 · arxiv_version: 1103.1330v1 · doi: 10.48550/arxiv.1103.1330 · pith_short_12: 4QCWJQETZWFB · pith_short_16: 4QCWJQETZWFBZNOZ · pith_short_8: 4QCWJQET

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/4QCWJQETZWFBZNOZ5ISAHVGFZ6 \
  | 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: e40564c093cd8a1cb5d9ea2403d4c5cf9fa7395fa800c26640c9fc1640988bd9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0a4a99267ed33cee5ecfe998b7a46bc27170b767ad1ada78db9f68149c4b7d2c",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2011-03-07T18:52:28Z",
    "title_canon_sha256": "13272deb7cf58891eff3bf6d9bacbc93872b7bc9382c258d47125489a7ff837e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1103.1330",
    "kind": "arxiv",
    "version": 1
  }
}