Pith Number

pith:ZRPTOHQ7

pith:2021:ZRPTOHQ7UAWG6KFYJBVCZOQLCV

not attested not anchored not stored refs pending

Wavenumber explicit convergence of a multiscale generalized finite element method for heterogeneous Helmholtz problems

Christian Alber, Chupeng Ma, Robert Scheichl

arxiv:2112.10544 v2 · 2021-12-20 · 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{ZRPTOHQ7UAWG6KFYJBVCZOQLCV}

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

Singularity Formation: Synergy in Theoretical, Numerical and Machine Learning Approaches

Receipt and verification

First computed	2026-07-05T04:57:23.796300Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cc5f371e1fa02c6f28b8486a2cba0b15645c4c85d03593548ad0806ad94acf5d

Aliases

arxiv: 2112.10544 · arxiv_version: 2112.10544v2 · doi: 10.48550/arxiv.2112.10544 · pith_short_12: ZRPTOHQ7UAWG · pith_short_16: ZRPTOHQ7UAWG6KFY · pith_short_8: ZRPTOHQ7

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/ZRPTOHQ7UAWG6KFYJBVCZOQLCV \
  | 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: cc5f371e1fa02c6f28b8486a2cba0b15645c4c85d03593548ad0806ad94acf5d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6b9fc40fe1fd2051d3a77146df07f1b365a2bbed0ba56e42a1d0969e4e896e81",
    "cross_cats_sorted": [
      "cs.NA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NA",
    "submitted_at": "2021-12-20T14:09:36Z",
    "title_canon_sha256": "badcf425c8935053b95d9f0136c88cd9ec621f2f681b91122a2abfa6f0996fb0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2112.10544",
    "kind": "arxiv",
    "version": 2
  }
}