Pith Number

pith:N2QBB3WF

pith:2026:N2QBB3WFJTZ6L2ZXHJ6MIVOQPA

not attested not anchored not stored refs pending

A new strategy for physics-informed neural networks based on hierarchical collocation point refinement

Dukhwan Shin, Eunjung Lee, Minjae Choi, Youngsoo Yang

arxiv:2607.14665 v1 · 2026-07-16 · 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{N2QBB3WFJTZ6L2ZXHJ6MIVOQPA}

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	2026-07-17T01:21:23.941791Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6ea010eec54cf3e5eb373a7cc455d07801c114b297960e4e27ef9f13ca46c011

Aliases

arxiv: 2607.14665 · arxiv_version: 2607.14665v1 · doi: 10.48550/arxiv.2607.14665 · pith_short_12: N2QBB3WFJTZ6 · pith_short_16: N2QBB3WFJTZ6L2ZX · pith_short_8: N2QBB3WF

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/N2QBB3WFJTZ6L2ZXHJ6MIVOQPA \
  | 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: 6ea010eec54cf3e5eb373a7cc455d07801c114b297960e4e27ef9f13ca46c011

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c3e5ad6e1c1c2d0cc45f79e9aff1f474bf55a9ef3bd5dc3ea4e693420ec2a2da",
    "cross_cats_sorted": [
      "cs.NA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NA",
    "submitted_at": "2026-07-16T07:31:42Z",
    "title_canon_sha256": "f95b92b07ceea38c630ab5189e1438cf277d9a68a92f22d561a84375ec8354aa"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.14665",
    "kind": "arxiv",
    "version": 1
  }
}