Pith Number

pith:YJ3FORXC

pith:2026:YJ3FORXCMDDG5B4RVCMGFTZEIQ

not attested not anchored not stored refs pending

Global $W^{2,p}$ Regularity in Optimal Transport

Shibing Chen, Xianduo Wang, Yuanyuan Li

arxiv:2607.24666 v1 · 2026-07-27 · math.AP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{YJ3FORXCMDDG5B4RVCMGFTZEIQ}

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	2026-07-28T02:24:21.576887Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c2765746e260c66e8791a89862cf24443b764b55e0189b8ade7a451d70075cc5

Aliases

arxiv: 2607.24666 · arxiv_version: 2607.24666v1 · doi: 10.48550/arxiv.2607.24666 · pith_short_12: YJ3FORXCMDDG · pith_short_16: YJ3FORXCMDDG5B4R · pith_short_8: YJ3FORXC

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/YJ3FORXCMDDG5B4RVCMGFTZEIQ \
  | 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: c2765746e260c66e8791a89862cf24443b764b55e0189b8ade7a451d70075cc5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f9fd4b115a9f329c7f096f3e657f9a9f0109838aaba7d44a4cd8fbd6ce59a0eb",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2026-07-27T17:08:26Z",
    "title_canon_sha256": "3d5d1cb27bdb1dd863bd6d3894bad6da3d19f8998c3c7d63d209fee729edf1f3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.24666",
    "kind": "arxiv",
    "version": 1
  }
}