Pith Number

pith:TUAFA7BM

pith:2026:TUAFA7BMGKSMTXLE3ZE57O4IOB

not attested not anchored not stored refs pending

Multimodal Alignment Through Joint Kernel Entropic Gromov--Wasserstein Optimal Transport

Naichen Shi, Yilun Zhu, Yixuan Florence Wu

arxiv:2608.04234 v1 · 2026-08-04 · math.ST · cs.LG · stat.ML · stat.TH

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{TUAFA7BMGKSMTXLE3ZE57O4IOB}

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	2026-08-06T01:31:43.406451Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9d00507c2c32a4c9dd64de49dfbb887062b587d8cfd2d3a28151877f23476d84

Aliases

arxiv: 2608.04234 · arxiv_version: 2608.04234v1 · doi: 10.48550/arxiv.2608.04234 · pith_short_12: TUAFA7BMGKSM · pith_short_16: TUAFA7BMGKSMTXLE · pith_short_8: TUAFA7BM

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/TUAFA7BMGKSMTXLE3ZE57O4IOB \
  | 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: 9d00507c2c32a4c9dd64de49dfbb887062b587d8cfd2d3a28151877f23476d84

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ac490b798e48a27e2f5fd14ee3d2df7d37b9486ddd48b7285f69b9c66bb3488f",
    "cross_cats_sorted": [
      "cs.LG",
      "stat.ML",
      "stat.TH"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.ST",
    "submitted_at": "2026-08-04T21:21:09Z",
    "title_canon_sha256": "04655bcc9fe1ab0907db7ae46438e2eaebd38523c8d2e3f738586a6b8be8e160"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2608.04234",
    "kind": "arxiv",
    "version": 1
  }
}