Pith Number

pith:T6DIURD6

pith:2025:T6DIURD6ZR4DA2BWYEHKVVKOEZ

not attested not anchored not stored refs pending

Optimal Sobolev embeddings for generalized Lorentz-Zygmund spaces

Ladislav Dr\'a\v{z}n\'y, Paola Cavaliere

arxiv:2508.14777 v3 · 2025-08-20 · 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{T6DIURD6ZR4DA2BWYEHKVVKOEZ}

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	2026-05-25T02:02:08.640166Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9f868a447ecc78306836c10eaad54e2662f5fa34567d4f0703329b5c4929d1e4

Aliases

arxiv: 2508.14777 · arxiv_version: 2508.14777v3 · doi: 10.48550/arxiv.2508.14777 · pith_short_12: T6DIURD6ZR4D · pith_short_16: T6DIURD6ZR4DA2BW · pith_short_8: T6DIURD6

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/T6DIURD6ZR4DA2BWYEHKVVKOEZ \
  | 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: 9f868a447ecc78306836c10eaad54e2662f5fa34567d4f0703329b5c4929d1e4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2bd0685e1123c62e4886ea598c5d5f4e62d879dd91c8ef19c86d789f2ed1a1cc",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2025-08-20T15:24:10Z",
    "title_canon_sha256": "7c4db6e927d5bc2dcd29e70180113d072613c33cd5359047429658d849e3f6b9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2508.14777",
    "kind": "arxiv",
    "version": 3
  }
}