Pith Number

pith:4TURIHIY

pith:2019:4TURIHIYHXFB6VGIL2VBIMKMTM

not attested not anchored not stored refs pending

Modifying AMG coarse spaces with weak approximation property to exhibit approximation in energy norm

Panayot S. Vassilevski, Xiaozhe Hu

arxiv:1906.08186 v1 · 2019-06-19 · 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{4TURIHIYHXFB6VGIL2VBIMKMTM}

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	2026-05-17T23:42:54.381364Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e4e9141d183dca1f54c85eaa14314c9b1f8a030f5a925e089707a781ff2f1f84

Aliases

arxiv: 1906.08186 · arxiv_version: 1906.08186v1 · doi: 10.48550/arxiv.1906.08186 · pith_short_12: 4TURIHIYHXFB · pith_short_16: 4TURIHIYHXFB6VGI · pith_short_8: 4TURIHIY

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/4TURIHIYHXFB6VGIL2VBIMKMTM \
  | 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: e4e9141d183dca1f54c85eaa14314c9b1f8a030f5a925e089707a781ff2f1f84

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1de3a3e3d7c9a3de6f9b0343c0ecded422daa13c0417b771f29f779b89fb4dd9",
    "cross_cats_sorted": [
      "cs.NA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NA",
    "submitted_at": "2019-06-19T15:59:20Z",
    "title_canon_sha256": "1adb951e7354c0c197f539970f84fb1a4e68abd7f9db73592fff4527735a4d58"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1906.08186",
    "kind": "arxiv",
    "version": 1
  }
}