Pith Number

pith:M7BESOY6

pith:2017:M7BESOY6ZG4IUTQZ73GGDRRMIN

not attested not anchored not stored refs pending

Hausdorff operators on the Sobolev spaces $W^{k,1}$

Guoping Zhao, Weichao Guo

arxiv:1710.10603 v2 · 2017-10-29 · 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{M7BESOY6ZG4IUTQZ73GGDRRMIN}

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	2026-05-18T00:21:50.856796Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

67c2493b1ec9b88a4e19fecc61c62c4349f7d5c8050a915efa49f7d115653f08

Aliases

arxiv: 1710.10603 · arxiv_version: 1710.10603v2 · doi: 10.48550/arxiv.1710.10603 · pith_short_12: M7BESOY6ZG4I · pith_short_16: M7BESOY6ZG4IUTQZ · pith_short_8: M7BESOY6

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/M7BESOY6ZG4IUTQZ73GGDRRMIN \
  | 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: 67c2493b1ec9b88a4e19fecc61c62c4349f7d5c8050a915efa49f7d115653f08

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b91690a79c3a1279df56eb21214c97a9013c79b1e872d19575995667f469e553",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2017-10-29T12:26:36Z",
    "title_canon_sha256": "1868d13096acffc9403847b0fdd64ef980a9e3124105fe1a27886c8fddeb9df3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1710.10603",
    "kind": "arxiv",
    "version": 2
  }
}