Pith Number

pith:PK22UZC5

pith:2025:PK22UZC5RIYO2LVPPGCGCXPCIQ

not attested not anchored not stored refs pending

Quadratic-form Optimal Transport

Ruodu Wang, Zhenyuan Zhang

arxiv:2501.04658 v5 · 2025-01-08 · 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{PK22UZC5RIYO2LVPPGCGCXPCIQ}

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	2026-06-08T01:03:42.869891Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7ab5aa645d8a30ed2eaf7984615de24425f93e4caac1632a89c3f98966a56677

Aliases

arxiv: 2501.04658 · arxiv_version: 2501.04658v5 · doi: 10.48550/arxiv.2501.04658 · pith_short_12: PK22UZC5RIYO · pith_short_16: PK22UZC5RIYO2LVP · pith_short_8: PK22UZC5

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/PK22UZC5RIYO2LVPPGCGCXPCIQ \
  | 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: 7ab5aa645d8a30ed2eaf7984615de24425f93e4caac1632a89c3f98966a56677

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5e721e757a1c3bea6d3e8e94fc8c35274734c9d44a1020d52bf81f2f803b42f3",
    "cross_cats_sorted": [
      "math.OC"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2025-01-08T18:13:35Z",
    "title_canon_sha256": "e1301716a5005b3ce53edc024f057aa88163c29698030c85025312ae707de5df"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2501.04658",
    "kind": "arxiv",
    "version": 5
  }
}