Pith Number

pith:3WIVMAK2

pith:2026:3WIVMAK257IZ35TNWDNK3UEIQS

not attested not anchored not stored refs pending

Tubular Neighbourhoods of Pfaffian Sets and Applications to Neural Networks

Martin Lotz, Paul Lezeau

arxiv:2607.08370 v1 · 2026-07-09 · math.AG · cs.LG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{3WIVMAK257IZ35TNWDNK3UEIQS}

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	2026-07-10T01:19:48.334283Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

dd9156015aefd19df66db0daadd088849dc4110d064df8281cb07996a5f38738

Aliases

arxiv: 2607.08370 · arxiv_version: 2607.08370v1 · doi: 10.48550/arxiv.2607.08370 · pith_short_12: 3WIVMAK257IZ · pith_short_16: 3WIVMAK257IZ35TN · pith_short_8: 3WIVMAK2

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/3WIVMAK257IZ35TNWDNK3UEIQS \
  | 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: dd9156015aefd19df66db0daadd088849dc4110d064df8281cb07996a5f38738

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "39ab51818b96a9d033b3cdb8ce936f37ddbc1c6c03b9a5668d6bf88361b8cde3",
    "cross_cats_sorted": [
      "cs.LG"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2026-07-09T11:37:56Z",
    "title_canon_sha256": "4de6c8c4f5c3ec9d5d0cfedce5e59e358b452d8dcc2a00af12dbe5615f0279f3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.08370",
    "kind": "arxiv",
    "version": 1
  }
}