Pith Number

pith:ZHIQZ2S5

pith:2021:ZHIQZ2S5RQOA3IDMLFG36BC7WF

not attested not anchored not stored refs pending

A priori and a posteriori error estimates for the Deep Ritz method applied to the Laplace and Stokes problem

Piotr Minakowski, Thomas Richter

arxiv:2107.11035 v4 · 2021-07-23 · 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{ZHIQZ2S5RQOA3IDMLFG36BC7WF}

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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

Reliable Error Estimation for PINNs: Lower and Upper A Posteriori Bounds

Receipt and verification

First computed	2026-07-05T05:08:50.114146Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c9d10cea5d8c1c0da06c594dbf045fb149029ca57f616554eccc89ed4cfcfc7a

Aliases

arxiv: 2107.11035 · arxiv_version: 2107.11035v4 · doi: 10.48550/arxiv.2107.11035 · pith_short_12: ZHIQZ2S5RQOA · pith_short_16: ZHIQZ2S5RQOA3IDM · pith_short_8: ZHIQZ2S5

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/ZHIQZ2S5RQOA3IDMLFG36BC7WF \
  | 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: c9d10cea5d8c1c0da06c594dbf045fb149029ca57f616554eccc89ed4cfcfc7a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "63bfb65ba49236b2124c072179943ba0d4c4de0233780315a71c251c9fbcbe38",
    "cross_cats_sorted": [
      "cs.NA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NA",
    "submitted_at": "2021-07-23T05:37:54Z",
    "title_canon_sha256": "ae8d31d88092a21020baf002ad7ec8b490cf1d3698270bd23ffa39760af80ee6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2107.11035",
    "kind": "arxiv",
    "version": 4
  }
}