Pith Number

pith:JTME4UZF

pith:2015:JTME4UZF6XJXO5LOV32QSLTXTA

not attested not anchored not stored refs pending

Counting via entropy: new preasymptotics for the approximation numbers of Sobolev embeddings

Sebastian Mayer, Thomas K\"uhn, Tino Ullrich

arxiv:1505.00631 v3 · 2015-05-04 · 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{JTME4UZF6XJXO5LOV32QSLTXTA}

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	2026-05-18T01:04:50.603825Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4cd84e5325f5d377756eaef5092e7798300d8a072af3e32993a25846cfbf7a6f

Aliases

arxiv: 1505.00631 · arxiv_version: 1505.00631v3 · doi: 10.48550/arxiv.1505.00631 · pith_short_12: JTME4UZF6XJX · pith_short_16: JTME4UZF6XJXO5LO · pith_short_8: JTME4UZF

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/JTME4UZF6XJXO5LOV32QSLTXTA \
  | 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: 4cd84e5325f5d377756eaef5092e7798300d8a072af3e32993a25846cfbf7a6f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bacce7235b561dd9665b128e19e91c40efc789309bc6c2988331b0289caeeacf",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NA",
    "submitted_at": "2015-05-04T13:41:05Z",
    "title_canon_sha256": "95b3c0b92e91a952c33a099577d56bb28dd27d0251d8ce376756771131b17af2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1505.00631",
    "kind": "arxiv",
    "version": 3
  }
}