Pith Number

pith:XXMG3BQ4

pith:2019:XXMG3BQ4RA3DTQOXGWRFKCLNYX

not attested not anchored not stored refs pending

Function values are enough for $L_2$-approximation

David Krieg, Mario Ullrich

arxiv:1905.02516 v5 · 2019-05-07 · math.NA · cs.NA · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{XXMG3BQ4RA3DTQOXGWRFKCLNYX}

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.

Cited by

1 paper in Pith

Some lower bounds for optimal sampling recovery of functions with mixed smoothness

Receipt and verification

First computed	2026-07-05T09:19:49.297940Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bdd86d861c883639c1d735a255096dc5fd7a843ed381b4fd57b554c89479d00d

Aliases

arxiv: 1905.02516 · arxiv_version: 1905.02516v5 · doi: 10.48550/arxiv.1905.02516 · pith_short_12: XXMG3BQ4RA3D · pith_short_16: XXMG3BQ4RA3DTQOX · pith_short_8: XXMG3BQ4

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/XXMG3BQ4RA3DTQOXGWRFKCLNYX \
  | 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: bdd86d861c883639c1d735a255096dc5fd7a843ed381b4fd57b554c89479d00d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e660ab9078d4c474c1d1a3c8da97629e9582c978c5a3e2ece18aea31f7898954",
    "cross_cats_sorted": [
      "cs.NA",
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NA",
    "submitted_at": "2019-05-07T12:58:27Z",
    "title_canon_sha256": "504cdee1fffec5b621ff00818d3b39c1f1b5eec9d1600ae1447c4de0dfd64db9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1905.02516",
    "kind": "arxiv",
    "version": 5
  }
}