Pith Number

pith:J5IPIXZJ

pith:2026:J5IPIXZJ3IBLRO7WP5QI5BCDHR

not attested not anchored not stored refs pending

Extended pseudo-spectral physics-informed neural networks for phase-field models

Andreas Munch, Callum Marsh, Radek Erban

arxiv:2606.24660 v1 · 2026-06-23 · q-bio.QM · cs.LG · cs.NA · math.NA · physics.bio-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{J5IPIXZJ3IBLRO7WP5QI5BCDHR}

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	2026-06-24T01:15:38.522846Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4f50f45f29da02b8bbf67f608e84433c705d49a03cad4eb222c0f8f0bbe16935

Aliases

arxiv: 2606.24660 · arxiv_version: 2606.24660v1 · doi: 10.48550/arxiv.2606.24660 · pith_short_12: J5IPIXZJ3IBL · pith_short_16: J5IPIXZJ3IBLRO7W · pith_short_8: J5IPIXZJ

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/J5IPIXZJ3IBLRO7WP5QI5BCDHR \
  | 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: 4f50f45f29da02b8bbf67f608e84433c705d49a03cad4eb222c0f8f0bbe16935

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "10c67b30b686b47c03b90ab2fbfd8da36b23853e778ff17e9b5d639c83fa636d",
    "cross_cats_sorted": [
      "cs.LG",
      "cs.NA",
      "math.NA",
      "physics.bio-ph"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "q-bio.QM",
    "submitted_at": "2026-06-23T14:51:58Z",
    "title_canon_sha256": "69a1f7d6f22887906966bf1e673d4f50fbbce594562471a98ee641489fc062a7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.24660",
    "kind": "arxiv",
    "version": 1
  }
}