Pith Number

pith:ZTXA4ZNK

pith:2014:ZTXA4ZNKLQPR4RJZWA7E3UMPJH

not attested not anchored not stored refs pending

On "Upper error bounds for quadrature formulas on function classes" by K. K. Frolov

Mario Ullrich

arxiv:1404.5457 v1 · 2014-04-22 · 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{ZTXA4ZNKLQPR4RJZWA7E3UMPJH}

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	2026-05-18T00:41:58.688375Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ccee0e65aa5c1f1e4539b03e4dd18f49eeea89f73b412007368425f7f9dc01c5

Aliases

arxiv: 1404.5457 · arxiv_version: 1404.5457v1 · doi: 10.48550/arxiv.1404.5457 · pith_short_12: ZTXA4ZNKLQPR · pith_short_16: ZTXA4ZNKLQPR4RJZ · pith_short_8: ZTXA4ZNK

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/ZTXA4ZNKLQPR4RJZWA7E3UMPJH \
  | 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: ccee0e65aa5c1f1e4539b03e4dd18f49eeea89f73b412007368425f7f9dc01c5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1dc2c9c5edff909d287748d327707191a1321ab76704f21f67002218dd4c0fda",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NA",
    "submitted_at": "2014-04-22T11:24:22Z",
    "title_canon_sha256": "f6e7bdcb9f68512962b79996eac69c79b9a54083be417448b93bc3f5a1f6d53b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1404.5457",
    "kind": "arxiv",
    "version": 1
  }
}