Pith Number

pith:OCBC6JG7

pith:2015:OCBC6JG7XYUOUTCCDWZBMLALHV

not attested not anchored not stored refs pending

Sobolev-Trace inequalities of order four

Antonio Ache, Sun-Yung Alice Chang

arxiv:1509.06069 v1 · 2015-09-20 · math.AP · math.DG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{OCBC6JG7XYUOUTCCDWZBMLALHV}

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	2026-05-18T00:32:44.851446Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

70822f24dfbe28ea4c421db2162c0b3d73168b72e9c193fa4555502b991ddec7

Aliases

arxiv: 1509.06069 · arxiv_version: 1509.06069v1 · doi: 10.48550/arxiv.1509.06069 · pith_short_12: OCBC6JG7XYUO · pith_short_16: OCBC6JG7XYUOUTCC · pith_short_8: OCBC6JG7

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/OCBC6JG7XYUOUTCCDWZBMLALHV \
  | 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: 70822f24dfbe28ea4c421db2162c0b3d73168b72e9c193fa4555502b991ddec7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "24e686043c603397fb64d0e1c437f348085d347516b69e37957e23b18eb87a46",
    "cross_cats_sorted": [
      "math.DG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2015-09-20T22:48:26Z",
    "title_canon_sha256": "459078ab08c19eae79273d786f805fb6ce5ab7e11a1e2cfc32d1d0d4a51fdc3e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1509.06069",
    "kind": "arxiv",
    "version": 1
  }
}