Pith Number

pith:R7VS3VFC

pith:2025:R7VS3VFC7XZAI27Q5CFFTARWIS

not attested not anchored not stored refs pending

Weak Optimal Transport: When is the Dual Potential Convex?

Filip Pramenkovi\'c

arxiv:2507.07200 v2 · 2025-07-09 · math.PR · math.OC

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{R7VS3VFC7XZAI27Q5CFFTARWIS}

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	2026-07-05T11:37:25.552660Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8feb2dd4a2fdf2046bf0e88a598236448cb5db86afcdd8c4518c979aa086c8ae

Aliases

arxiv: 2507.07200 · arxiv_version: 2507.07200v2 · doi: 10.48550/arxiv.2507.07200 · pith_short_12: R7VS3VFC7XZA · pith_short_16: R7VS3VFC7XZAI27Q · pith_short_8: R7VS3VFC

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/R7VS3VFC7XZAI27Q5CFFTARWIS \
  | 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: 8feb2dd4a2fdf2046bf0e88a598236448cb5db86afcdd8c4518c979aa086c8ae

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "13e754b54ed627c58b0f1da959a9dc15e7f2119ba74a9c348b9539cb42672afb",
    "cross_cats_sorted": [
      "math.OC"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2025-07-09T18:14:58Z",
    "title_canon_sha256": "4b52c4b6c9fdf0b83c2b6fad3aa17fd934911ee19e156885d0ca91db6c24dd48"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2507.07200",
    "kind": "arxiv",
    "version": 2
  }
}