Pith Number

pith:25ZIPZM5

pith:2026:25ZIPZM5PAB6XJNPJ2YVPRYCKU

not attested not anchored not stored refs pending

MATLAB-Based Layerwise Self-Adaptive Physics-Informed Neural Network in Applications to Multidimensional Coupled Burgers' Equations with High Reynolds Numbers

Harish P. Bhatt, Jingsai Liang, Xi Chen

arxiv:2606.12348 v1 · 2026-06-10 · 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{25ZIPZM5PAB6XJNPJ2YVPRYCKU}

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	2026-06-11T01:11:03.288363Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d77287e59d7803eba5af4eb157c702553decdb8ccd0cf8314d2af869e92024bd

Aliases

arxiv: 2606.12348 · arxiv_version: 2606.12348v1 · doi: 10.48550/arxiv.2606.12348 · pith_short_12: 25ZIPZM5PAB6 · pith_short_16: 25ZIPZM5PAB6XJNP · pith_short_8: 25ZIPZM5

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/25ZIPZM5PAB6XJNPJ2YVPRYCKU \
  | 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: d77287e59d7803eba5af4eb157c702553decdb8ccd0cf8314d2af869e92024bd

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "689fb93dc79696c3056ed405b08bf0487962d876ef94b8562254d6dfa25846e1",
    "cross_cats_sorted": [
      "cs.NA"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.NA",
    "submitted_at": "2026-06-10T17:21:02Z",
    "title_canon_sha256": "9787a6f641de69d5a88eb85cb934783d6e1e506fc4675a8dba9b25ac6776e704"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.12348",
    "kind": "arxiv",
    "version": 1
  }
}