Pith Number

pith:CD3HLOFM

pith:2026:CD3HLOFM4M4VFCZQJNZL64UOJX

not attested not anchored not stored refs pending

Multi-Headed Transformer Architectures as Time-dependent Wasserstein Gradient Flows

Alex Massucco, Carola-Bibiane Sch\"onlieb, Christoff Brune, Leonardo Del Grande, Marcello Carioni

arxiv:2605.18870 v1 · 2026-05-15 · cs.LG · math.AP · math.FA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{CD3HLOFM4M4VFCZQJNZL64UOJX}

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	2026-05-20T00:06:29.595920Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

10f675b8ace339528b304b72bf728e4de9838ef3bcb42348a0c2b68dcc3e1322

Aliases

arxiv: 2605.18870 · arxiv_version: 2605.18870v1 · doi: 10.48550/arxiv.2605.18870 · pith_short_12: CD3HLOFM4M4V · pith_short_16: CD3HLOFM4M4VFCZQ · pith_short_8: CD3HLOFM

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/CD3HLOFM4M4VFCZQJNZL64UOJX \
  | 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: 10f675b8ace339528b304b72bf728e4de9838ef3bcb42348a0c2b68dcc3e1322

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f3cb7851e05d26284e1e4c858ba4911744fe5d05e63dc6533512cb3414ff5053",
    "cross_cats_sorted": [
      "math.AP",
      "math.FA"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2026-05-15T15:32:18Z",
    "title_canon_sha256": "2c20fc3825ecd7f4dde040a210f81d45f86ae20bebc183dd0104c41ea371b032"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.18870",
    "kind": "arxiv",
    "version": 1
  }
}