Pith Number

pith:FH6BCVD7

pith:2014:FH6BCVD7VQCMDBIIPK33DQESRX

not attested not anchored not stored refs pending

The Paneitz-Sobolev constant of a closed Riemannian manifold and an application to the nonlocal $\mathbf{Q}$-curvature flow

Xuezhang Chen

arxiv:1405.4412 v2 · 2014-05-17 · math.DG · 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{FH6BCVD7VQCMDBIIPK33DQESRX}

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	2026-05-18T02:51:32.848123Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

29fc11547fac04c185087ab7b1c0928dc3d6a14d19f064d893dec523cb2422a1

Aliases

arxiv: 1405.4412 · arxiv_version: 1405.4412v2 · doi: 10.48550/arxiv.1405.4412 · pith_short_12: FH6BCVD7VQCM · pith_short_16: FH6BCVD7VQCMDBII · pith_short_8: FH6BCVD7

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/FH6BCVD7VQCMDBIIPK33DQESRX \
  | 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: 29fc11547fac04c185087ab7b1c0928dc3d6a14d19f064d893dec523cb2422a1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "590c58048b53fb26a5d96c35be4c07401a6d647a1528e5a1ca7631b4e28f6b8d",
    "cross_cats_sorted": [
      "math.AP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2014-05-17T15:41:38Z",
    "title_canon_sha256": "c588dcbdd8db6f6ead0d457692478b6c0f87f06738d04581a14f0e2c1a9510b3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1405.4412",
    "kind": "arxiv",
    "version": 2
  }
}