Pith Number

pith:4OTYWNPF

pith:2016:4OTYWNPFUB5SYHYHQ746XW2DLQ

not attested not anchored not stored refs pending

A Matrix-free Preconditioner for the Helmholtz Equation based on the Fast Multipole Method

David Keyes, Huda Ibeid, Rio Yokota

arxiv:1608.02461 v1 · 2016-08-08 · math.NA · cs.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{4OTYWNPFUB5SYHYHQ746XW2DLQ}

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	2026-05-18T01:09:40.148713Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e3a78b35e5a07b2c1f0787f9ebdb435c39d2bcf7f2466f9c2ec944b079fcc9da

Aliases

arxiv: 1608.02461 · arxiv_version: 1608.02461v1 · doi: 10.48550/arxiv.1608.02461 · pith_short_12: 4OTYWNPFUB5S · pith_short_16: 4OTYWNPFUB5SYHYH · pith_short_8: 4OTYWNPF

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/4OTYWNPFUB5SYHYHQ746XW2DLQ \
  | 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: e3a78b35e5a07b2c1f0787f9ebdb435c39d2bcf7f2466f9c2ec944b079fcc9da

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a501600f3bc845b0572849650808fe214f1c2866874d64e2e784689b08b0cd22",
    "cross_cats_sorted": [
      "cs.NA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NA",
    "submitted_at": "2016-08-08T14:48:25Z",
    "title_canon_sha256": "418ae2154889cea53c17f73efe4c7c73792283d8b37cc38dfa1e094c8396ea81"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1608.02461",
    "kind": "arxiv",
    "version": 1
  }
}