Pith Number

pith:YGUCXJGW

pith:2016:YGUCXJGWKNHPXGBBKST2FMT7H7

not attested not anchored not stored refs pending

Distances between homotopy classes of $W^{s,p}({\mathbb S}^N;{\mathbb S}^N)$

Haim Brezis, Itai Shafrir, Petru Mironescu

arxiv:1606.04687 v1 · 2016-06-15 · 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{YGUCXJGWKNHPXGBBKST2FMT7H7}

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	2026-05-18T01:12:24.580603Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c1a82ba4d6534efb982154a7a2b27f3ff30ea2cc4c277d1d40dafa544bcc1150

Aliases

arxiv: 1606.04687 · arxiv_version: 1606.04687v1 · doi: 10.48550/arxiv.1606.04687 · pith_short_12: YGUCXJGWKNHP · pith_short_16: YGUCXJGWKNHPXGBB · pith_short_8: YGUCXJGW

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/YGUCXJGWKNHPXGBBKST2FMT7H7 \
  | 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: c1a82ba4d6534efb982154a7a2b27f3ff30ea2cc4c277d1d40dafa544bcc1150

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4711450b8560e29ba8cad6abb20439a255747d0a6d3ef815cbfb56411c331955",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2016-06-15T09:06:56Z",
    "title_canon_sha256": "9d30757846e9de7a663178fe82d0b2fc52354c3c592ffec1a1f216ffc115700c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1606.04687",
    "kind": "arxiv",
    "version": 1
  }
}