Pith Number

pith:5GSQKAMY

pith:2026:5GSQKAMYWLDBIMGJYEJKJGR5V5

not attested not anchored not stored refs pending

A Discrete Cumulative Distribution Transform via Optimal Transport

Aryan Saxena, Gustavo Rohde, Harbir Antil

arxiv:2606.12131 v1 · 2026-06-10 · math.ST · math.OC · stat.TH

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{5GSQKAMYWLDBIMGJYEJKJGR5V5}

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	2026-06-11T01:10:49.992768Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e9a5050198b2c61430c9c112a49a3daf4ed6727caa0821cbbd6d05453a72b6c5

Aliases

arxiv: 2606.12131 · arxiv_version: 2606.12131v1 · doi: 10.48550/arxiv.2606.12131 · pith_short_12: 5GSQKAMYWLDB · pith_short_16: 5GSQKAMYWLDBIMGJ · pith_short_8: 5GSQKAMY

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/5GSQKAMYWLDBIMGJYEJKJGR5V5 \
  | 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: e9a5050198b2c61430c9c112a49a3daf4ed6727caa0821cbbd6d05453a72b6c5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b786cff8820a8f13d8eaa91d1f7784a57ec7c516a2a280b81e92b8213c2262aa",
    "cross_cats_sorted": [
      "math.OC",
      "stat.TH"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.ST",
    "submitted_at": "2026-06-10T14:25:52Z",
    "title_canon_sha256": "4d33c7e997e58d73241b33a4e5e8b3421efbcd62a2cfeff0080c8687ecfff3ea"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.12131",
    "kind": "arxiv",
    "version": 1
  }
}