Pith Number

pith:62OOEDM2

pith:2025:62OOEDM2HDEFD3XTG7D6H4LCV5

not attested not anchored not stored refs pending

Efficient Training of Physics-enhanced Neural ODEs via Direct Collocation and Nonlinear Programming

Bernhard Bachmann, Linus Langenkamp, Philip Hannebohm

arxiv:2505.03552 v2 · 2025-05-06 · cs.LG · math.DS · math.OC

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{62OOEDM2HDEFD3XTG7D6H4LCV5}

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	2026-07-05T11:49:09.825701Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f69ce20d9a38c851eef337c7e3f162af5f512f7b55c6164e857cdfb9ba0da9a2

Aliases

arxiv: 2505.03552 · arxiv_version: 2505.03552v2 · doi: 10.48550/arxiv.2505.03552 · pith_short_12: 62OOEDM2HDEF · pith_short_16: 62OOEDM2HDEFD3XT · pith_short_8: 62OOEDM2

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/62OOEDM2HDEFD3XTG7D6H4LCV5 \
  | 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: f69ce20d9a38c851eef337c7e3f162af5f512f7b55c6164e857cdfb9ba0da9a2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8260005cf9672b8b397adc991a9e5817449c7f6fc7ab86db6f33fb4df837d111",
    "cross_cats_sorted": [
      "math.DS",
      "math.OC"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2025-05-06T14:04:46Z",
    "title_canon_sha256": "8e1ede93b35cb3e943d7506a1354ce7eb96993fd37b676c973978cc05ad6e396"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2505.03552",
    "kind": "arxiv",
    "version": 2
  }
}