Pith Number

pith:6GJZOGNW

pith:2018:6GJZOGNWYYZ72GBU7OYELDVR4P

not attested not anchored not stored refs pending

Radial extensions in fractional Sobolev spaces

Haim Brezis, Itai Shafrir, Petru Mironescu

arxiv:1803.00241 v1 · 2018-03-01 · 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{6GJZOGNWYYZ72GBU7OYELDVR4P}

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	2026-05-18T00:22:12.881902Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f1939719b6c633fd1834fbb0458eb1e3c6af87b004f3d4d5d16fc9a8341f450c

Aliases

arxiv: 1803.00241 · arxiv_version: 1803.00241v1 · doi: 10.48550/arxiv.1803.00241 · pith_short_12: 6GJZOGNWYYZ7 · pith_short_16: 6GJZOGNWYYZ72GBU · pith_short_8: 6GJZOGNW

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/6GJZOGNWYYZ72GBU7OYELDVR4P \
  | 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: f1939719b6c633fd1834fbb0458eb1e3c6af87b004f3d4d5d16fc9a8341f450c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c7851ee318cdb708d5c94c71c3c7ca27347ba59ceb68f501fc56719dd51508c5",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2018-03-01T08:12:28Z",
    "title_canon_sha256": "a1aab00a2e08f832544001d9df6ae96ffa8e180ad1c0ab0e792d4be05f4f6a27"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1803.00241",
    "kind": "arxiv",
    "version": 1
  }
}