Pith Number

pith:YK5WL723

pith:2025:YK5WL723C7TA6DYC6FY7MMPZB7

not attested not anchored not stored refs pending

Layer Separation Deep Learning Model with Auxiliary Variables for Partial Differential Equations

Yaru Liu, Yiqi Gu

arxiv:2507.12766 v1 · 2025-07-17 · cs.LG

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{YK5WL723C7TA6DYC6FY7MMPZB7}

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	2026-07-05T11:38:38.748977Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c2bb65ff5b17e60f0f02f171f631f90fe185b4d008dd09f5a373bcc85fa03071

Aliases

arxiv: 2507.12766 · arxiv_version: 2507.12766v1 · doi: 10.48550/arxiv.2507.12766 · pith_short_12: YK5WL723C7TA · pith_short_16: YK5WL723C7TA6DYC · pith_short_8: YK5WL723

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/YK5WL723C7TA6DYC6FY7MMPZB7 \
  | 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: c2bb65ff5b17e60f0f02f171f631f90fe185b4d008dd09f5a373bcc85fa03071

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "cfb3b0648df1611f06867ec82acba85aa89c3dd8d64cbc1cd7e643295bb4bad6",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2025-07-17T03:43:18Z",
    "title_canon_sha256": "6bf4638a3fa8740f69c73aa663eda13b645060174b08b9847dafda1de0a60974"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2507.12766",
    "kind": "arxiv",
    "version": 1
  }
}