Pith Number

pith:T2JDCCJL

pith:2026:T2JDCCJLYHLASWIVK6IUR4FZJH

not attested not anchored not stored refs pending

Cliff Tokens: Identifying Single-Token Failure Triggers in LLM Mathematical Reasoning

Jaeyong Ko, Pilsung Kang, Yukyung Lee

arxiv:2606.25524 v1 · 2026-06-24 · 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{T2JDCCJLYHLASWIVK6IUR4FZJH}

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	2026-06-25T01:18:07.828062Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9e9231092bc1d6095915579148f0b949ea28b79739d7f826043feec4a0264bda

Aliases

arxiv: 2606.25524 · arxiv_version: 2606.25524v1 · doi: 10.48550/arxiv.2606.25524 · pith_short_12: T2JDCCJLYHLA · pith_short_16: T2JDCCJLYHLASWIV · pith_short_8: T2JDCCJL

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/T2JDCCJLYHLASWIVK6IUR4FZJH \
  | 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: 9e9231092bc1d6095915579148f0b949ea28b79739d7f826043feec4a0264bda

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "311dab5cae06d881329a24a378a2489dc0f6be926d6f269f51909119a97e55d6",
    "cross_cats_sorted": [
      "cs.CL"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.AI",
    "submitted_at": "2026-06-24T08:03:24Z",
    "title_canon_sha256": "7188e536520d886a10b65f5c44dbf3544ae06cbe47b2069d148a6d8eea986300"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.25524",
    "kind": "arxiv",
    "version": 1
  }
}