Pith Number

pith:XAAYZ5NA

pith:2016:XAAYZ5NAQ56AQQP3OKXRCNA7I3

not attested not anchored not stored refs pending

Distances between classes in $W^{1,1}(\Omega;{\mathbb S}^1)$

Haim Brezis, Itai Shafrir, Petru Mironescu

arxiv:1606.01526 v3 · 2016-06-05 · 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{XAAYZ5NAQ56AQQP3OKXRCNA7I3}

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	2026-05-18T00:27:03.028872Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b8018cf5a0877c0841fb72af11341f46e76af08e603e5b8b08ae570404850a51

Aliases

arxiv: 1606.01526 · arxiv_version: 1606.01526v3 · doi: 10.48550/arxiv.1606.01526 · pith_short_12: XAAYZ5NAQ56A · pith_short_16: XAAYZ5NAQ56AQQP3 · pith_short_8: XAAYZ5NA

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/XAAYZ5NAQ56AQQP3OKXRCNA7I3 \
  | 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: b8018cf5a0877c0841fb72af11341f46e76af08e603e5b8b08ae570404850a51

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "99d2e3a7732de0ea10651d658d423e19adefd73d6de96aeee0d0b55bc195f2c9",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2016-06-05T15:32:56Z",
    "title_canon_sha256": "fd0bdf5cb349525ec9967686ac34df5babf274523de88c4c1cedcea1c688d44c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1606.01526",
    "kind": "arxiv",
    "version": 3
  }
}