Pith Number

pith:SWY4F54J

pith:2026:SWY4F54JUYWKW6UHJ2CH7DLBJH

not attested not anchored not stored refs pending

A Statistical Formulation Gap for Nonlinear Multiscale Physics-Informed Learning

Ronald Katende

arxiv:2607.15702 v1 · 2026-07-17 · math.NA · cs.LG · cs.NA · math.AP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{SWY4F54JUYWKW6UHJ2CH7DLBJH}

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	2026-07-20T01:19:05.103368Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

95b1c2f789a62cab7a874e847f8d6149c930532502c685a552d917bb1e2513ff

Aliases

arxiv: 2607.15702 · arxiv_version: 2607.15702v1 · doi: 10.48550/arxiv.2607.15702 · pith_short_12: SWY4F54JUYWK · pith_short_16: SWY4F54JUYWKW6UH · pith_short_8: SWY4F54J

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/SWY4F54JUYWKW6UHJ2CH7DLBJH \
  | 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: 95b1c2f789a62cab7a874e847f8d6149c930532502c685a552d917bb1e2513ff

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c6259947b859b4e4e88688fff93826bf128e271dc478d87680e6daefde826d5b",
    "cross_cats_sorted": [
      "cs.LG",
      "cs.NA",
      "math.AP"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.NA",
    "submitted_at": "2026-07-17T07:26:29Z",
    "title_canon_sha256": "bfc5e7339a16ed2a27a0fd06d8aff25708abf6b4c66d9bbeaced835a64539005"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.15702",
    "kind": "arxiv",
    "version": 1
  }
}