Pith Number

pith:YDPHE52L

pith:2012:YDPHE52LTHR3C7IXIIAAKNMOS6

not attested not anchored not stored refs pending

A characterization of Sobolev spaces on the sphere and an extension of Stolarsky's invariance principle to arbitrary smoothness

J. Brauchart, J. Dick

arxiv:1203.5157 v1 · 2012-03-23 · math.NA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{YDPHE52LTHR3C7IXIIAAKNMOS6}

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	2026-05-18T02:59:06.586811Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c0de72774b99e3b17d17420005358e979c06e08010b49037510d82deb17ce835

Aliases

arxiv: 1203.5157 · arxiv_version: 1203.5157v1 · doi: 10.48550/arxiv.1203.5157 · pith_short_12: YDPHE52LTHR3 · pith_short_16: YDPHE52LTHR3C7IX · pith_short_8: YDPHE52L

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/YDPHE52LTHR3C7IXIIAAKNMOS6 \
  | 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: c0de72774b99e3b17d17420005358e979c06e08010b49037510d82deb17ce835

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b7199f19f3cb430a4ac2240e48483b13162a98e3bd4c0be7f41c95d98969867f",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NA",
    "submitted_at": "2012-03-23T02:30:21Z",
    "title_canon_sha256": "6faad7fe0602dcafc4f1116464ca1f92438cef4021b94093d75994d9089d69fe"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1203.5157",
    "kind": "arxiv",
    "version": 1
  }
}