Pith Number

pith:EZ2XCRJS

pith:2025:EZ2XCRJSIBLT5CVEWKQEJ2BWBP

not attested not anchored not stored refs pending

MDPO: Multi-Granularity Direct Preference Optimization for Mathematical Reasoning

Yunze Lin

arxiv:2506.15706 v1 · 2025-05-30 · 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{EZ2XCRJSIBLT5CVEWKQEJ2BWBP}

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	2026-07-05T11:23:50.737055Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

267571453240573e8aa4b2a044e8360bf61f4594d8648958205bb3d9c17f1ab0

Aliases

arxiv: 2506.15706 · arxiv_version: 2506.15706v1 · doi: 10.48550/arxiv.2506.15706 · pith_short_12: EZ2XCRJSIBLT · pith_short_16: EZ2XCRJSIBLT5CVE · pith_short_8: EZ2XCRJS

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/EZ2XCRJSIBLT5CVEWKQEJ2BWBP \
  | 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: 267571453240573e8aa4b2a044e8360bf61f4594d8648958205bb3d9c17f1ab0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "561a87d10060d341195318a94dcc4e8907b521a3a9aa630c1a6639a941a509ed",
    "cross_cats_sorted": [
      "cs.AI"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2025-05-30T08:42:14Z",
    "title_canon_sha256": "5ceffa782a9e855d8b577d0af99e06bcde2830ad01560556a82315dbb59d819a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2506.15706",
    "kind": "arxiv",
    "version": 1
  }
}