Pith Number

pith:H4FUPTIP

pith:2021:H4FUPTIPXTROHDRXXTGF7DI3K7

not attested not anchored not stored refs pending

HiDeNN-PGD: reduced-order hierarchical deep learning neural networks

(2) Northwestern University, 3), (3) Visiting student, Beijing, China, Department of Mechanical Engineering, Evanston, Lei Zhang (1, Northwestern University), Shaoqiang Tang (1), USA, Wing Kam Liu (2) ((1) Peking University, Ye Lu (2)

arxiv:2105.06363 v1 · 2021-05-13 · math.NA · cs.LG · 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{H4FUPTIPXTROHDRXXTGF7DI3K7}

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	2026-07-05T03:47:19.403784Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3f0b47cd0fbce2e38e37bccc5f8d1b57e669eec4076754d4d2bdd53fa66a4bfc

Aliases

arxiv: 2105.06363 · arxiv_version: 2105.06363v1 · doi: 10.48550/arxiv.2105.06363 · pith_short_12: H4FUPTIPXTRO · pith_short_16: H4FUPTIPXTROHDRX · pith_short_8: H4FUPTIP

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/H4FUPTIPXTROHDRXXTGF7DI3K7 \
  | 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: 3f0b47cd0fbce2e38e37bccc5f8d1b57e669eec4076754d4d2bdd53fa66a4bfc

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bc90b95d58013184208686c029dcb45acbfd9e31cbb0baf2863e04149f19b651",
    "cross_cats_sorted": [
      "cs.LG",
      "cs.NA"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.NA",
    "submitted_at": "2021-05-13T15:42:59Z",
    "title_canon_sha256": "af4db7f867d69c26d9a8dddd7d43d39e1986673e2909ea081c7bb8b0edbe1b1c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2105.06363",
    "kind": "arxiv",
    "version": 1
  }
}