Pith Number

pith:PV5N7DNT

pith:2026:PV5N7DNTF4VSCKI5FRLKSMSVJA

not attested not anchored not stored refs pending

When Do LLMs Reason? A Dynamical Systems View via Entropy Phase Transitions

Haoqing Wang, Wei Xia, Yehui Tang, Zhi-Hong Deng

arxiv:2605.22873 v1 · 2026-05-20 · cs.LG · cs.AI · cs.CL

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{PV5N7DNTF4VSCKI5FRLKSMSVJA}

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	2026-05-25T02:01:28.049625Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7d7adf8db32f2b21291d2c56a93255480da1bf6ac897a12d9fd295b32e4f44fa

Aliases

arxiv: 2605.22873 · arxiv_version: 2605.22873v1 · doi: 10.48550/arxiv.2605.22873 · pith_short_12: PV5N7DNTF4VS · pith_short_16: PV5N7DNTF4VSCKI5 · pith_short_8: PV5N7DNT

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/PV5N7DNTF4VSCKI5FRLKSMSVJA \
  | 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: 7d7adf8db32f2b21291d2c56a93255480da1bf6ac897a12d9fd295b32e4f44fa

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c412a2bc1b7d1ce4f738b97d84bb64c3cc535f683feb3c992f0953d06abead14",
    "cross_cats_sorted": [
      "cs.AI",
      "cs.CL"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2026-05-20T03:15:46Z",
    "title_canon_sha256": "e139517294f5b6f57d17e9d94e8da2ca11013e33762d129b18d976c5e5598da9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.22873",
    "kind": "arxiv",
    "version": 1
  }
}