Pith Number

pith:HFPUUNGE

pith:2026:HFPUUNGEVM3SPFRX7USDB452XN

not attested not anchored not stored refs pending

Hierarchical rank-evolving representation for physics-informed neural networks

Kun Li, Liang Li, Ruoyang Su, Xi-Le Zhao

arxiv:2608.09483 v1 · 2026-08-10 · cs.LG · cs.NA · math.NA · physics.comp-ph

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{HFPUUNGEVM3SPFRX7USDB452XN}

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	2026-08-11T02:24:19.004805Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

395f4a34c4ab37279637fd2430f3babb60b982e73c289eeb319b2ea2f0d3fa55

Aliases

arxiv: 2608.09483 · arxiv_version: 2608.09483v1 · doi: 10.48550/arxiv.2608.09483 · pith_short_12: HFPUUNGEVM3S · pith_short_16: HFPUUNGEVM3SPFRX · pith_short_8: HFPUUNGE

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/HFPUUNGEVM3SPFRX7USDB452XN \
  | 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: 395f4a34c4ab37279637fd2430f3babb60b982e73c289eeb319b2ea2f0d3fa55

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "52c7a70a44f8f64853a7d88019f5819b5ee5a12b0391b0257c9a727d7030f7af",
    "cross_cats_sorted": [
      "cs.NA",
      "math.NA",
      "physics.comp-ph"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2026-08-10T11:48:43Z",
    "title_canon_sha256": "910bc3a73d1f040b85b1b3d3384129c392425938756ff890eebe4a65b5bfdd0b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2608.09483",
    "kind": "arxiv",
    "version": 1
  }
}