Pith Number

pith:OJ3Q55A6

pith:2025:OJ3Q55A6IKSAOVDJ7TV2MPPFSV

not attested not anchored not stored refs pending

HYCO: Hybrid-Cooperative Learning for Data-Driven PDE Modeling

Enrique Zuazua, Lorenzo Liverani

arxiv:2509.14123 v2 · 2025-09-17 · math.OC · cs.NA · math.AP · math.NA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{OJ3Q55A6IKSAOVDJ7TV2MPPFSV}

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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.

Cited by

3 papers in Pith

The Coercivity Gap in Neural PDE Solvers: Parameter Escape and Functional Convergence

HYCO: A Formalism for Hybrid-Cooperative PDE Modelling

Receipt and verification

First computed	2026-07-27T01:19:50.053568Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

72770ef41e42a4075469fceba63de59566a694a9ec300e783d8a00fcfbef5be8

Aliases

arxiv: 2509.14123 · arxiv_version: 2509.14123v2 · doi: 10.48550/arxiv.2509.14123 · pith_short_12: OJ3Q55A6IKSA · pith_short_16: OJ3Q55A6IKSAOVDJ · pith_short_8: OJ3Q55A6

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/OJ3Q55A6IKSAOVDJ7TV2MPPFSV \
  | 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: 72770ef41e42a4075469fceba63de59566a694a9ec300e783d8a00fcfbef5be8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0cbb9988b67fe77ffa7c13937b3a40c07926a10776cf27117c68ad392675f3f3",
    "cross_cats_sorted": [
      "cs.NA",
      "math.AP",
      "math.NA"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2025-09-17T16:02:24Z",
    "title_canon_sha256": "11887908d9726aecc4ef3fcbf31c28531592c370154b4e467a01d35a63220348"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2509.14123",
    "kind": "arxiv",
    "version": 2
  }
}