Pith Number

pith:C3B4ZZ2A

pith:2010:C3B4ZZ2AGLT2QVVHNLXBK7BVFG

not attested not anchored not stored refs pending

Optimal boundary holes for the Sobolev trace constant

Julian Fernandez Bonder, Leandro Del Pezzo, Wladimir Neves

arxiv:1011.2731 v1 · 2010-11-11 · 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{C3B4ZZ2AGLT2QVVHNLXBK7BVFG}

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	2026-05-18T03:07:11.237635Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

16c3cce74032e7a856a76aee157c3529b2424a98ea378a3034cbd34559aba793

Aliases

arxiv: 1011.2731 · arxiv_version: 1011.2731v1 · doi: 10.48550/arxiv.1011.2731 · pith_short_12: C3B4ZZ2AGLT2 · pith_short_16: C3B4ZZ2AGLT2QVVH · pith_short_8: C3B4ZZ2A

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/C3B4ZZ2AGLT2QVVHNLXBK7BVFG \
  | 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: 16c3cce74032e7a856a76aee157c3529b2424a98ea378a3034cbd34559aba793

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9beedb677d5ce6b6703e6657ec91aacf4cb4509a013132ebd67e0e35cc5e2e89",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2010-11-11T18:19:08Z",
    "title_canon_sha256": "b8509f22c2072172665ebb19e367b05ac1f9283d86e95919ee96fd9db9e3d3e0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1011.2731",
    "kind": "arxiv",
    "version": 1
  }
}