Pith Number

pith:USNL3OAX

pith:2023:USNL3OAX5DDRYVQWZB4KI776HI

not attested not anchored not stored refs pending

Higher-order multi-scale deep Ritz method for multi-scale problems of authentic composite materials

Hao Dong, Jiale Linghu, JunZhi Cui, Yufeng Nie

arxiv:2307.15256 v2 · 2023-07-28 · 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{USNL3OAX5DDRYVQWZB4KI776HI}

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	2026-07-05T06:40:16.029120Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a49abdb817e8c71c5616c878a47ffe3a128e37b0f7848dc88428380393a59045

Aliases

arxiv: 2307.15256 · arxiv_version: 2307.15256v2 · doi: 10.48550/arxiv.2307.15256 · pith_short_12: USNL3OAX5DDR · pith_short_16: USNL3OAX5DDRYVQW · pith_short_8: USNL3OAX

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/USNL3OAX5DDRYVQWZB4KI776HI \
  | 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: a49abdb817e8c71c5616c878a47ffe3a128e37b0f7848dc88428380393a59045

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b9eb74cb958944782da1edf00a2206aa014887a1c8d315b16a25c3a5fb9c3785",
    "cross_cats_sorted": [
      "cs.NA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NA",
    "submitted_at": "2023-07-28T01:44:10Z",
    "title_canon_sha256": "193dbce1552366e95df5bc9be41506ce9cbafb63354dd02d0d2394914dcb98d6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2307.15256",
    "kind": "arxiv",
    "version": 2
  }
}