Pith Number

pith:Z3G477YG

pith:2018:Z3G477YGZPL4IEA3LSHHSNFC2J

not attested not anchored not stored refs pending

Sobolev extension via reflections

Pekka Koskela, ZhengZhu

arxiv:1812.09037 v2 · 2018-12-21 · 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{Z3G477YGZPL4IEA3LSHHSNFC2J}

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.

Cited by

1 paper in Pith

Extension operators on Sobolev spaces with decreasing integrability

Receipt and verification

First computed	2026-07-05T01:03:18.522771Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cecdcfff06cbd7c4101b5c8e7934a2d265a5b47db70f0d7c6f24e5d62067ea25

Aliases

arxiv: 1812.09037 · arxiv_version: 1812.09037v2 · doi: 10.48550/arxiv.1812.09037 · pith_short_12: Z3G477YGZPL4 · pith_short_16: Z3G477YGZPL4IEA3 · pith_short_8: Z3G477YG

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/Z3G477YGZPL4IEA3LSHHSNFC2J \
  | 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: cecdcfff06cbd7c4101b5c8e7934a2d265a5b47db70f0d7c6f24e5d62067ea25

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f31b7a3a0baf6d9379f7f38f84f5d7ee4f0f005d0853653e87d7c1a5162a61f2",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2018-12-21T10:38:17Z",
    "title_canon_sha256": "021b9308596b9d4ae7357ad043e2b3c9ce606884d7b96837da9ab107882305bf"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1812.09037",
    "kind": "arxiv",
    "version": 2
  }
}