Pith Number

pith:AJCR2EPH

pith:2016:AJCR2EPHU5X2VEFBZA5EBJB4EP

not attested not anchored not stored refs pending

Variations on a proof of a borderline Bourgain-Brezis Sobolev embedding theorem

Jean Van Schaftingen, Po-Lam Yung, Sagun Chanillo

arxiv:1612.02888 v1 · 2016-12-09 · math.CA · math.AP

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{AJCR2EPHU5X2VEFBZA5EBJB4EP}

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	2026-05-18T00:41:07.646099Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

02451d11e7a76faa90a1c83a40a43c23d4f958914285455f2b6621e1c8223f4e

Aliases

arxiv: 1612.02888 · arxiv_version: 1612.02888v1 · doi: 10.48550/arxiv.1612.02888 · pith_short_12: AJCR2EPHU5X2 · pith_short_16: AJCR2EPHU5X2VEFB · pith_short_8: AJCR2EPH

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/AJCR2EPHU5X2VEFBZA5EBJB4EP \
  | 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: 02451d11e7a76faa90a1c83a40a43c23d4f958914285455f2b6621e1c8223f4e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b3cff542ba1e48682e9e18035c590f3e409270072143ceed93f64ac95975e090",
    "cross_cats_sorted": [
      "math.AP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2016-12-09T01:43:43Z",
    "title_canon_sha256": "2f32c833be59b231a94694d0efffe693197ce0000d8dc02b8edb7d99e96aa4b5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1612.02888",
    "kind": "arxiv",
    "version": 1
  }
}