Pith Number

pith:ARMMCWZ4

pith:2024:ARMMCWZ4TWF4ABVF3RSQSL4TUP

not attested not anchored not stored refs pending

Sum-of-Squares Programming for Ma-Trudinger-Wang Regularity of Optimal Transport Maps

Abhishek Halder, Gabriel Khan, Georgiy A. Bondar, Sachin Shivakumar

arxiv:2412.13372 v1 · 2024-12-17 · math.OC · cs.AI · cs.LG · math.DG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{ARMMCWZ4TWF4ABVF3RSQSL4TUP}

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	2026-07-05T09:52:19.884320Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0458c15b3c9d8bc006a5dc65092f93a3d736392f9006a28b395e7a5ded052fcd

Aliases

arxiv: 2412.13372 · arxiv_version: 2412.13372v1 · doi: 10.48550/arxiv.2412.13372 · pith_short_12: ARMMCWZ4TWF4 · pith_short_16: ARMMCWZ4TWF4ABVF · pith_short_8: ARMMCWZ4

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/ARMMCWZ4TWF4ABVF3RSQSL4TUP \
  | 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: 0458c15b3c9d8bc006a5dc65092f93a3d736392f9006a28b395e7a5ded052fcd

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8ada331cf79d106095dab97106d933c38153d7fe1178f67fd6197a528e21bc01",
    "cross_cats_sorted": [
      "cs.AI",
      "cs.LG",
      "math.DG"
    ],
    "license": "http://creativecommons.org/licenses/by-nc-sa/4.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2024-12-17T23:10:03Z",
    "title_canon_sha256": "1297cc02992d3de11447dd9eff80e041ac081ec082ce6c8f9e7cfda47a941669"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2412.13372",
    "kind": "arxiv",
    "version": 1
  }
}