Pith Number

pith:NIX54YEP

pith:2021:NIX54YEPO5U4QTBHTBX26EVJOV

not attested not anchored not stored refs pending

On the Wasserstein Distance Between $k$-Step Probability Measures on Finite Graphs

Arushi Mantri, Quinn Perian, Sophia Benjamin

arxiv:2110.10363 v1 · 2021-10-20 · math.CO · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{NIX54YEPO5U4QTBHTBX26EVJOV}

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	2026-07-05T03:24:16.362375Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6a2fde608f7769c84c27986faf12a97565f2af309e0bd7d3eb50cffba42f74ca

Aliases

arxiv: 2110.10363 · arxiv_version: 2110.10363v1 · doi: 10.48550/arxiv.2110.10363 · pith_short_12: NIX54YEPO5U4 · pith_short_16: NIX54YEPO5U4QTBH · pith_short_8: NIX54YEP

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/NIX54YEPO5U4QTBHTBX26EVJOV \
  | 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: 6a2fde608f7769c84c27986faf12a97565f2af309e0bd7d3eb50cffba42f74ca

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "78bb5867e561d3913610a90628c80f0a0aee833a847b1a6df9cca6a502ecd56e",
    "cross_cats_sorted": [
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2021-10-20T03:44:03Z",
    "title_canon_sha256": "679573d64d4d813c134e3a563290075165452fe00ca6e932f78f3054772cee66"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2110.10363",
    "kind": "arxiv",
    "version": 1
  }
}