Pith Number

pith:2PR7UVZI

pith:2026:2PR7UVZIWM6C3JLESC4PDQZ5GJ

not attested not anchored not stored refs pending

A Theory on Flow Matching with Neural Networks

Han Liu, Jianqing Fan, Qishuo Yin, Yihan He, Yuan Cao

arxiv:2606.10089 v1 · 2026-06-08 · cs.LG · cs.AI

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{2PR7UVZIWM6C3JLESC4PDQZ5GJ}

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	2026-06-10T00:08:48.690565Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d3e3fa5728b33c2da56490b8f1c33d326449680af0aaedf1d054b92b88a0ce00

Aliases

arxiv: 2606.10089 · arxiv_version: 2606.10089v1 · doi: 10.48550/arxiv.2606.10089 · pith_short_12: 2PR7UVZIWM6C · pith_short_16: 2PR7UVZIWM6C3JLE · pith_short_8: 2PR7UVZI

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/2PR7UVZIWM6C3JLESC4PDQZ5GJ \
  | 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: d3e3fa5728b33c2da56490b8f1c33d326449680af0aaedf1d054b92b88a0ce00

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c624e7cddd65f57d66cdf449ff981439ccbd558719e4936c4f031834c51cf497",
    "cross_cats_sorted": [
      "cs.AI"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2026-06-08T19:16:32Z",
    "title_canon_sha256": "8ace797e1434727930392dbee0635bd6e0c39e644937f32f86332d2bebed62a3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.10089",
    "kind": "arxiv",
    "version": 1
  }
}