Pith Number

pith:4L3JUU4T

pith:2026:4L3JUU4TLUEOGRRNS5AF5BYBEZ

not attested not anchored not stored refs pending

Tropical Geometry as a Restricted Architecture for Physics-Informed Neural Networks: Applications in Nonlinear Fluid-Structure Examples

Alonso Andapia-Viveros, Carla Valencia-Negrete, Cristhian Garay-Lopez, Marco Favela-Rodriguez

arxiv:2607.00237 v1 · 2026-06-30 · math.AP · math.AC

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{4L3JUU4TLUEOGRRNS5AF5BYBEZ}

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	2026-07-02T00:18:40.505949Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e2f69a53935d08e3462d97405e8701264d8a470d78eed8fc74b2406f9b26ecdd

Aliases

arxiv: 2607.00237 · arxiv_version: 2607.00237v1 · doi: 10.48550/arxiv.2607.00237 · pith_short_12: 4L3JUU4TLUEO · pith_short_16: 4L3JUU4TLUEOGRRN · pith_short_8: 4L3JUU4T

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/4L3JUU4TLUEOGRRNS5AF5BYBEZ \
  | 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: e2f69a53935d08e3462d97405e8701264d8a470d78eed8fc74b2406f9b26ecdd

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e7ca235418fc84224fef0cd9bf7f863142247025926a93a56290e4ceafd7897f",
    "cross_cats_sorted": [
      "math.AC"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2026-06-30T22:29:05Z",
    "title_canon_sha256": "7780b221be0a318712f813e79052abe37bb8460284ab3644ed8d1e74755e7914"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.00237",
    "kind": "arxiv",
    "version": 1
  }
}