Pith Number

pith:I273S3OE

pith:2026:I273S3OEWQJ42FKHCI32RLAI7Q

not attested not anchored not stored refs pending

1-Lipschitz Neural Networks on Hadamard Manifolds

Ben Adcock, Brynjulf Owren, Carola-Bibiane Sch\"onlieb, Davide Murari, Elena Celledoni, Marta Ghirardelli

arxiv:2607.19335 v1 · 2026-07-21 · math.NA · cs.LG · cs.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{I273S3OEWQJ42FKHCI32RLAI7Q}

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	2026-07-22T01:24:37.683393Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

46bfb96dc4b413cd15471237a8ac08fc1d1989f8d35ed2eb16b637546c41b6c8

Aliases

arxiv: 2607.19335 · arxiv_version: 2607.19335v1 · doi: 10.48550/arxiv.2607.19335 · pith_short_12: I273S3OEWQJ4 · pith_short_16: I273S3OEWQJ42FKH · pith_short_8: I273S3OE

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/I273S3OEWQJ42FKHCI32RLAI7Q \
  | 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: 46bfb96dc4b413cd15471237a8ac08fc1d1989f8d35ed2eb16b637546c41b6c8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d74a42c5466698e4a225b3c6fd1794b102ca5f4333b9b463c5f5f3a7a4cb6b25",
    "cross_cats_sorted": [
      "cs.LG",
      "cs.NA"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.NA",
    "submitted_at": "2026-07-21T17:54:34Z",
    "title_canon_sha256": "4d702051303c381081ff2e1ba6decf550023e53d9e73e7b191bd8a23b5a23d2c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.19335",
    "kind": "arxiv",
    "version": 1
  }
}