Pith Number

pith:DFM7I2GH

pith:2026:DFM7I2GHFQWL7NPIMUE5FZTYSU

not attested not anchored not stored refs pending

Exact ensemble controllability for neural differential equations via neural interpolation

Control, Department of Mathematics, Erlangen, Germany), Lehrstuhl f\"ur Dynamics, Machine Learning, Martin Gugat (Friedrich-Alexander-Universit\"at Erlangen-N\"urnberg (FAU), Numerics

arxiv:2607.21112 v1 · 2026-07-23 · 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{DFM7I2GHFQWL7NPIMUE5FZTYSU}

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	2026-07-24T01:23:52.577679Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1959f468c72c2cbfb5e86509d2e67895239df88a18b73045a1d71d4a1441479e

Aliases

arxiv: 2607.21112 · arxiv_version: 2607.21112v1 · doi: 10.48550/arxiv.2607.21112 · pith_short_12: DFM7I2GHFQWL · pith_short_16: DFM7I2GHFQWL7NPI · pith_short_8: DFM7I2GH

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/DFM7I2GHFQWL7NPIMUE5FZTYSU \
  | 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: 1959f468c72c2cbfb5e86509d2e67895239df88a18b73045a1d71d4a1441479e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a4d3168b815afbc0acefef515ef27f343f09bb685b17fd2b9675d3d29c862137",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2026-07-23T09:41:13Z",
    "title_canon_sha256": "313d3c1dd55c67f22958ee7c2590b0441bbbfe25f7db8f045e08d12ca55ad11b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.21112",
    "kind": "arxiv",
    "version": 1
  }
}