Pith Number

pith:VF2IZIJ4

pith:2026:VF2IZIJ4K45NNN6WL5MZRONHJW

not attested not anchored not stored refs pending

Limit Points of Reflow with Minibatch Optimal Transport

Antonin Chambolle, Johannes Hertrich

arxiv:2608.07042 v1 · 2026-08-07 · math.PR · cs.LG · cs.NA · math.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{VF2IZIJ4K45NNN6WL5MZRONHJW}

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	2026-08-10T01:12:57.985638Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a9748ca13c573ad6b7d65f5998b9a74d92196696a7072c76238e14a42a3f2b90

Aliases

arxiv: 2608.07042 · arxiv_version: 2608.07042v1 · doi: 10.48550/arxiv.2608.07042 · pith_short_12: VF2IZIJ4K45N · pith_short_16: VF2IZIJ4K45NNN6W · pith_short_8: VF2IZIJ4

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/VF2IZIJ4K45NNN6WL5MZRONHJW \
  | 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: a9748ca13c573ad6b7d65f5998b9a74d92196696a7072c76238e14a42a3f2b90

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b24f005e9b5e1d9e3da5d3d9e382b77f4c341f20890216a0df88b5e629f5982c",
    "cross_cats_sorted": [
      "cs.LG",
      "cs.NA",
      "math.NA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2026-08-07T09:51:33Z",
    "title_canon_sha256": "b3da6c7c8194bf9bbeb687a31b99dfacee90afa4ff96bf2d974d6fcc5c02c2bf"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2608.07042",
    "kind": "arxiv",
    "version": 1
  }
}