Pith Number

pith:FAUZPJB2

pith:2013:FAUZPJB2L64MEGM2MCA75VBNMG

not attested not anchored not stored refs pending

Approximation of mixed order Sobolev functions on the $d$-torus -- Asymptotics, preasymptotics and $d$-dependence

Thomas Kuehn, Tino Ullrich, Winfried Sickel

arxiv:1312.6386 v1 · 2013-12-22 · 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{FAUZPJB2L64MEGM2MCA75VBNMG}

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	2026-05-18T03:03:58.449235Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

282997a43a5fb8c2199a6081fed42d61964adf5231845d2f06d57f123c1a559f

Aliases

arxiv: 1312.6386 · arxiv_version: 1312.6386v1 · doi: 10.48550/arxiv.1312.6386 · pith_short_12: FAUZPJB2L64M · pith_short_16: FAUZPJB2L64MEGM2 · pith_short_8: FAUZPJB2

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/FAUZPJB2L64MEGM2MCA75VBNMG \
  | 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: 282997a43a5fb8c2199a6081fed42d61964adf5231845d2f06d57f123c1a559f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6d3738dbbfe6cb7e28850e5ebe45fec90154fbfdb2d8b03e73e4cc0b15d15844",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NA",
    "submitted_at": "2013-12-22T14:20:57Z",
    "title_canon_sha256": "0f4d7d96508044cd2e75203fbec2d4c08c3904160b92a631188155f46448ce9c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1312.6386",
    "kind": "arxiv",
    "version": 1
  }
}