Pith Number

pith:PHAFS4QM

pith:2015:PHAFS4QM4FRXJKFJJIPKHOKHN5

not attested not anchored not stored refs pending

Discrete Hybrid Polyharmonic Cubature Formulas with weight on the disc. with error bounds

H. Render, O. Kounchev

arxiv:1509.00060 v1 · 2015-08-31 · math.NA · 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{PHAFS4QM4FRXJKFJJIPKHOKHN5}

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	2026-05-18T01:34:30.714809Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

79c059720ce16374a8a94a1ea3b9476f511515a6c7d28803357f215d45240fee

Aliases

arxiv: 1509.00060 · arxiv_version: 1509.00060v1 · doi: 10.48550/arxiv.1509.00060 · pith_short_12: PHAFS4QM4FRX · pith_short_16: PHAFS4QM4FRXJKFJ · pith_short_8: PHAFS4QM

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/PHAFS4QM4FRXJKFJJIPKHOKHN5 \
  | 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: 79c059720ce16374a8a94a1ea3b9476f511515a6c7d28803357f215d45240fee

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "81ddc5421b220528798ad95064b9d3e3980dceab91369303592f62fe000e35fa",
    "cross_cats_sorted": [
      "math.CA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NA",
    "submitted_at": "2015-08-31T20:44:46Z",
    "title_canon_sha256": "4d2ab371daaae077623bfe67bcf88f787e70239a088684f6985f21e22163ba3c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1509.00060",
    "kind": "arxiv",
    "version": 1
  }
}