Pith Number

pith:SK4UNTNI

pith:2026:SK4UNTNIUKECTSSB2QYYMTSVCH

not attested not anchored not stored refs pending

Provably Learning Diffusion Models under the Manifold Hypothesis: Collapse and Refine

Andi Han, Huanjian Zhou, Kenji Fukumizu, Mingyuan Bai, Qixin Zhang, Taiji Suzuki, Wei Huang

arxiv:2605.20235 v1 · 2026-05-16 · 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{SK4UNTNIUKECTSSB2QYYMTSVCH}

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	2026-05-21T00:04:22.086913Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

92b946cda8a28829ca41d431864e5511d1d4df64a6b2402da39f5317ac328544

Aliases

arxiv: 2605.20235 · arxiv_version: 2605.20235v1 · doi: 10.48550/arxiv.2605.20235 · pith_short_12: SK4UNTNIUKEC · pith_short_16: SK4UNTNIUKECTSSB · pith_short_8: SK4UNTNI

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/SK4UNTNIUKECTSSB2QYYMTSVCH \
  | 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: 92b946cda8a28829ca41d431864e5511d1d4df64a6b2402da39f5317ac328544

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "50982a5d2b91b6b5e5d2cab7119bd5318840145c67b381423f8d958f5fc15687",
    "cross_cats_sorted": [
      "cs.AI"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2026-05-16T16:51:10Z",
    "title_canon_sha256": "02e78addd8950902b856167495143361861152ba4480726f21b7ac8fd20cb6d5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.20235",
    "kind": "arxiv",
    "version": 1
  }
}