Pith Number

pith:TIU5XIVJ

pith:2017:TIU5XIVJCSXST4D3D2GNBVHJ6D

not attested not anchored not stored refs pending

Approximation numbers of Sobolev and Gevrey type embeddings on the sphere and on the ball -- Preasymptotics, asymptotics, and tractability

Heping Wang, Jia Chen

arxiv:1701.03545 v1 · 2017-01-13 · math.CA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{TIU5XIVJCSXST4D3D2GNBVHJ6D}

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	2026-05-18T00:52:54.563374Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9a29dba2a914af29f07b1e8cd0d4e9f0d2282129b624e6f79c3a4fa79ba8285f

Aliases

arxiv: 1701.03545 · arxiv_version: 1701.03545v1 · doi: 10.48550/arxiv.1701.03545 · pith_short_12: TIU5XIVJCSXS · pith_short_16: TIU5XIVJCSXST4D3 · pith_short_8: TIU5XIVJ

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/TIU5XIVJCSXST4D3D2GNBVHJ6D \
  | 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: 9a29dba2a914af29f07b1e8cd0d4e9f0d2282129b624e6f79c3a4fa79ba8285f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d8820e0e310f6c7914b7f3f953e7a97e976e96ced5a1e0ef3c433a06ef6d48a6",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2017-01-13T02:04:49Z",
    "title_canon_sha256": "27e3bcf6338cd5b169474b6d4060b014fb18336d3e0954ed2dd2f9c4c9e83cd6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1701.03545",
    "kind": "arxiv",
    "version": 1
  }
}