Pith Number

pith:HKKPTFGS

pith:2018:HKKPTFGSMOOK6HHP7KVAYPYVZW

not attested not anchored not stored refs pending

Best constants for two families of higher order critical Sobolev embeddings

Daniel Spector, Itai Shafrir

arxiv:1804.07025 v1 · 2018-04-19 · 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{HKKPTFGSMOOK6HHP7KVAYPYVZW}

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	2026-05-18T00:18:04.541306Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3a94f994d2639caf1ceffaaa0c3f15cdb6746afca40f73da3fceff9fe008c469

Aliases

arxiv: 1804.07025 · arxiv_version: 1804.07025v1 · doi: 10.48550/arxiv.1804.07025 · pith_short_12: HKKPTFGSMOOK · pith_short_16: HKKPTFGSMOOK6HHP · pith_short_8: HKKPTFGS

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/HKKPTFGSMOOK6HHP7KVAYPYVZW \
  | 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: 3a94f994d2639caf1ceffaaa0c3f15cdb6746afca40f73da3fceff9fe008c469

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "998a77e498589bb9d309a3380b8b335502dbf65a0254b7f01a41244f1840a9fc",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2018-04-19T07:46:36Z",
    "title_canon_sha256": "73f48b2e7dfe41f06af188f06e0ff867577e4efa82b99e69185cae77c2bc8d7d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1804.07025",
    "kind": "arxiv",
    "version": 1
  }
}