Pith Number

pith:VGR5RLAX

pith:2022:VGR5RLAXO3EJPKHFLWKYTVK6K5

not attested not anchored not stored refs pending

Multigrid for two-sided fractional differential equations discretized by finite volume elements on graded meshes

Ken Trotti, Marco Donatelli, Mariarosa Mazza, Rolf Krause

arxiv:2209.08841 v1 · 2022-09-19 · 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{VGR5RLAXO3EJPKHFLWKYTVK6K5}

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	2026-07-05T04:58:46.778462Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a9a3d8ac1776c897a8e55d9589d55e5769666bbc628846c116852450b19ad8e1

Aliases

arxiv: 2209.08841 · arxiv_version: 2209.08841v1 · doi: 10.48550/arxiv.2209.08841 · pith_short_12: VGR5RLAXO3EJ · pith_short_16: VGR5RLAXO3EJPKHF · pith_short_8: VGR5RLAX

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/VGR5RLAXO3EJPKHFLWKYTVK6K5 \
  | 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: a9a3d8ac1776c897a8e55d9589d55e5769666bbc628846c116852450b19ad8e1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "58cf8ad911bf2c546e8b632235654208b3ccce349cce6f3c5ba2868aec0f2493",
    "cross_cats_sorted": [
      "cs.NA"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.NA",
    "submitted_at": "2022-09-19T08:40:01Z",
    "title_canon_sha256": "21c8c98788caf3b651591ab56170dc035c597525289a75f0e18e7daa0e3baba4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2209.08841",
    "kind": "arxiv",
    "version": 1
  }
}