Pith Number

pith:HPMOQVIR

pith:2022:HPMOQVIR6YPOCXWD57QKUT6P5M

not attested not anchored not stored refs pending

Discrete Optimal Transport with Independent Marginals is #P-Hard

Bahar Ta\c{s}kesen, Daniel Kuhn, Karthik Natarajan, Soroosh Shafieezadeh-Abadeh

arxiv:2203.01161 v2 · 2022-03-02 · math.OC · cs.CC · cs.LG · stat.ML

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{HPMOQVIR6YPOCXWD57QKUT6P5M}

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	2026-07-05T05:06:30.455899Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3bd8e85511f61ee15ec3efe0aa4fcfeb2eb98ceed7aba1e5cc2788ab0e85cc35

Aliases

arxiv: 2203.01161 · arxiv_version: 2203.01161v2 · doi: 10.48550/arxiv.2203.01161 · pith_short_12: HPMOQVIR6YPO · pith_short_16: HPMOQVIR6YPOCXWD · pith_short_8: HPMOQVIR

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/HPMOQVIR6YPOCXWD57QKUT6P5M \
  | 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: 3bd8e85511f61ee15ec3efe0aa4fcfeb2eb98ceed7aba1e5cc2788ab0e85cc35

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bf61207edc9e5b65a4d925502770bbe6f26584b0d09938ed8edaa402342a9d20",
    "cross_cats_sorted": [
      "cs.CC",
      "cs.LG",
      "stat.ML"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2022-03-02T15:04:37Z",
    "title_canon_sha256": "3f0cc16ef1701732176abe8a6bc7565883cc92f14c9e27bd4280cc21693fb8d0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2203.01161",
    "kind": "arxiv",
    "version": 2
  }
}