Pith Number

pith:QJ2FMTCQ

pith:2017:QJ2FMTCQUOAVR4JKYX5PDDZ7P3

not attested not anchored not stored refs pending

Gossez's approximation theorems in the Musielak-Orlicz-Sobolev spaces

Ahmed Youssfi, Iwona Chlebicka, Piotr Gwiazda, Youssef Ahmida

arxiv:1711.06145 v2 · 2017-11-16 · 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{QJ2FMTCQUOAVR4JKYX5PDDZ7P3}

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	2026-05-17T23:46:30.916801Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8274564c50a38158f12ac5faf18f3f7eee591f4a9610ff01b44d277f23ec50a5

Aliases

arxiv: 1711.06145 · arxiv_version: 1711.06145v2 · doi: 10.48550/arxiv.1711.06145 · pith_short_12: QJ2FMTCQUOAV · pith_short_16: QJ2FMTCQUOAVR4JK · pith_short_8: QJ2FMTCQ

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/QJ2FMTCQUOAVR4JKYX5PDDZ7P3 \
  | 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: 8274564c50a38158f12ac5faf18f3f7eee591f4a9610ff01b44d277f23ec50a5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2c0d87ccee7138b1c25cb2d9d794f0f0c7d096ea74a1bf14b5ed36c862af04de",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2017-11-16T15:38:37Z",
    "title_canon_sha256": "f27038a3f419762d59ca8557f2267d03dcceaa1b5a609a0758a30ad5a46dd039"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1711.06145",
    "kind": "arxiv",
    "version": 2
  }
}