Pith Number

pith:XJTO3ZWX

pith:2026:XJTO3ZWXDKBSW3BJLQSFZQRRA2

not attested not anchored not stored refs pending

Wasserstein Residuals: Learning Gradient Flows from Population Dynamics

Daniel Waxman, Dmitry Batenkov, Eli Bingham, Markus Heinonen, Ricardo Baptista, Tim Cooijmans, Yair Shenfeld

arxiv:2607.04738 v1 · 2026-07-06 · stat.ML · cs.AI · 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{XJTO3ZWXDKBSW3BJLQSFZQRRA2}

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	2026-07-07T02:20:00.776507Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ba66ede6d71a832b6c295c245cc23106a6688fa4196ff32bdebbc71882a07211

Aliases

arxiv: 2607.04738 · arxiv_version: 2607.04738v1 · doi: 10.48550/arxiv.2607.04738 · pith_short_12: XJTO3ZWXDKBS · pith_short_16: XJTO3ZWXDKBSW3BJ · pith_short_8: XJTO3ZWX

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/XJTO3ZWXDKBSW3BJLQSFZQRRA2 \
  | 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: ba66ede6d71a832b6c295c245cc23106a6688fa4196ff32bdebbc71882a07211

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "54e4f1e23f029fa0077a02e6d8b27db3a803e4ff46e9e6684b84a29c4ba1bff1",
    "cross_cats_sorted": [
      "cs.AI",
      "cs.LG"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "stat.ML",
    "submitted_at": "2026-07-06T07:20:30Z",
    "title_canon_sha256": "568fe838575fb5d84372b10ddbdc5fc2b0351e920e00a02b97431e339a670cf2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.04738",
    "kind": "arxiv",
    "version": 1
  }
}