Pith Number

pith:XD7FSFEM

pith:2026:XD7FSFEM5INQWRD72UFVW5HHSY

not attested not anchored not stored refs pending

Learning sufficient low-dimensional structures through conditional optimal transport

Efstathia Bura, Kaiqiang Alan Zeng

arxiv:2607.18861 v1 · 2026-07-21 · math.ST · stat.ME · 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{XD7FSFEM5INQWRD72UFVW5HHSY}

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	2026-07-22T01:23:16.350833Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b8fe59148cea1b0b447fd50b5b74e796305bf279e5c3f379ccc59b317c7d81fa

Aliases

arxiv: 2607.18861 · arxiv_version: 2607.18861v1 · doi: 10.48550/arxiv.2607.18861 · pith_short_12: XD7FSFEM5INQ · pith_short_16: XD7FSFEM5INQWRD7 · pith_short_8: XD7FSFEM

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/XD7FSFEM5INQWRD72UFVW5HHSY \
  | 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: b8fe59148cea1b0b447fd50b5b74e796305bf279e5c3f379ccc59b317c7d81fa

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "61a8fdb7b2590c40b5bf73cb4fe6664d09131820f41d160da450dab0f160bf5e",
    "cross_cats_sorted": [
      "stat.ME",
      "stat.TH"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.ST",
    "submitted_at": "2026-07-21T08:51:44Z",
    "title_canon_sha256": "7805bb0ee47adb8e8c441525adac719d96b7407d5ec64942cfc16040052ec266"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.18861",
    "kind": "arxiv",
    "version": 1
  }
}