Pith Number

pith:PCZGSQ2A

pith:2025:PCZGSQ2A7LVYTOEFLHFC2JMAQV

not attested not anchored not stored refs pending

Hierarchical Dimensionless Learning (Hi-{\pi}): A physics-data hybrid-driven approach for discovering dimensionless parameter combinations

Haitao Lin, Mingkun Xia, Weiwei Zhang

arxiv:2507.18332 v1 · 2025-07-24 · physics.flu-dyn · cs.LG · physics.data-an

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{PCZGSQ2A7LVYTOEFLHFC2JMAQV}

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	2026-07-05T11:42:46.228389Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

78b2694340faeb89b88559ca2d2580855585e7ba935d4510cfddfb159524e888

Aliases

arxiv: 2507.18332 · arxiv_version: 2507.18332v1 · doi: 10.48550/arxiv.2507.18332 · pith_short_12: PCZGSQ2A7LVY · pith_short_16: PCZGSQ2A7LVYTOEF · pith_short_8: PCZGSQ2A

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/PCZGSQ2A7LVYTOEFLHFC2JMAQV \
  | 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: 78b2694340faeb89b88559ca2d2580855585e7ba935d4510cfddfb159524e888

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "85e69c2140e008bb5016edd20ed4f433769ab811ddec5e66e000825d4f650e84",
    "cross_cats_sorted": [
      "cs.LG",
      "physics.data-an"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "physics.flu-dyn",
    "submitted_at": "2025-07-24T11:59:10Z",
    "title_canon_sha256": "a7c03dec8058f7ef8d99eca43dd1cddfbee3947e22c041d45a496a2127768d70"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2507.18332",
    "kind": "arxiv",
    "version": 1
  }
}