Pith Number

pith:HPX4CLE2

pith:2019:HPX4CLE2H3AS5S4Y2ZXHJVLIVY

not attested not anchored not stored refs pending

A sharp relative-error bound for the Helmholtz $h$-FEM at high frequency

David Lafontaine, Euan A. Spence, Jared Wunsch

arxiv:1911.11093 v4 · 2019-11-25 · 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{HPX4CLE2H3AS5S4Y2ZXHJVLIVY}

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	2026-07-05T03:28:57.851164Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3befc12c9a3ec12ecb98d66e74d568ae293c370ba98e9889de1814c4a606b550

Aliases

arxiv: 1911.11093 · arxiv_version: 1911.11093v4 · doi: 10.48550/arxiv.1911.11093 · pith_short_12: HPX4CLE2H3AS · pith_short_16: HPX4CLE2H3AS5S4Y · pith_short_8: HPX4CLE2

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/HPX4CLE2H3AS5S4Y2ZXHJVLIVY \
  | 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: 3befc12c9a3ec12ecb98d66e74d568ae293c370ba98e9889de1814c4a606b550

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "956aefd0465c8b5b0689b1686b778f2c77a21b7fa8d632c434b50aa988e2bbcc",
    "cross_cats_sorted": [
      "cs.NA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NA",
    "submitted_at": "2019-11-25T17:48:05Z",
    "title_canon_sha256": "3c09d234fd4ac4c050e86ce290425941072389fe34e1038013533a715742b72f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1911.11093",
    "kind": "arxiv",
    "version": 4
  }
}