Re-verify RLM note vs arXiv:2512.24601v3 — verified clean, date refreshed

[OpenCnid]

Re-verification: density-chain.md vs pinned source

Source: arXiv:2512.24601v3 — Recursive Language Models (Alex L. Zhang, Tim Kraska, Omar Khattab; MIT CSAIL). Pin resolves at source (arXiv API + abs page); v3 confirmed as the latest version (v1 2025-12-31, v2 2026-01-28, v3 2026-05-11). Studied fresh this session from the arXiv v3 PDF and the arXiv HTML rendering; the PDF was treated as session material and is not committed.

Result: verified clean against arXiv:2512.24601v3 on 2026-07-20; refreshed verification date only.

Discrepancy ledger

None. Every quantitative claim, benchmark name, coefficient, and locator matches the source.

Checked and confirmed against the source:

Claim	Note	Source	Locator
Headline medians (GPT-5)	26% / 130% / 13%	26% / 130% / 13%	Abstract
Input scale	>1 order of magnitude	"more than an order of magnitude"	Abstract
RLM-Qwen3-8B gain	median 28% (Abstract) / 28.3% (§1)	"median of 28%" / "median of 28.3%"	Abstract; §1
OOLONG-Pairs (GPT-5)	0.1 → d1 58.0 → d2 65.5 → d3 76.0	0.1 / 58.0 / 65.5 / 76.0	Table 1
OOLONG-Pairs (Qwen3-Coder d1)	23.1	23.1	Table 1; Obs. 1
BrowseComp-Plus (GPT-5)	0.0 → d1 91.3 @ $0.99±$1.22; d2 92.0	0.0 / 91.3 ($0.99±$1.22) / 92.0	Table 1; Obs. 1
Extrapolated ingestion	$1.50–2.75 vs $0.99; ≥29%	$1.50–$2.75; $0.99; "over 29%"	Obs. 1
OOLONG gain (d1)	+28.4% GPT-5 / +33.3% Qwen3-Coder	28.4% / 33.3%	Obs. 1
CodeQA	GPT-5 base 24.0; d2 66.0; Qwen3-Coder best d0 66.0	24.0 / 66.0 / 66.0	Table 1; Obs. 2
Claude Code (+offloading)	CodeQA 62.0; BC+ 84.0; OOLONG 48.0; OP 6.5	62.0 / 84.0 / 48.0 / 6.5	Table 1
LONGCOT-MINI (GPT-5.2)	38.7 → 50.6 → 65.6 (+69.5%); LOGIC/CHESS 99.0	38.7 / 50.6 / 65.6; +69.5%; 99.0/99.0	Table 2; Obs. 5
Training	1,000 rejection-FT trajectories (LongBenchPro); median +28.3%; >3× faster	matches	§3.2; §1; Obs. 6
Length generalization	RLVR MRCRv2 64k/2-needle → 1M/8-needle	matches	Obs. 6; Fig. 3
Cost profile	median RLM cheaper; average dearer (outliers)	matches	Obs. 4
Syntax errors	RLM(Qwen3-Coder) ≫ RLM(GPT-5); propagate at depth	matches	§5; Fig. 4
Code	github.com/alexzhang13/rlm	matches	Abstract
License	CC BY 4.0	CC BY 4.0	arXiv record

Also confirmed: authors/affiliations (all MIT CSAIL), venue, three design choices (symbolic handle / Final variable / symbolic recursion), Ω(|P|)/Ω(|P|²) framing, task-complexity taxonomy (S-NIAH / BrowseComp-Plus 1K docs / OOLONG / OOLONG-Pairs / CodeQA), model roots and depths 0–3, and the §7 limitations (guardrails, exploding sub-call costs, blocking implementation).

Note on arXiv metadata

The arXiv API <summary> field currently reads "up to two orders of magnitude" and "28.3% on average", which differs from the v3 PDF/HTML ("more than an order of magnitude" and "median of 28%"). The note pins and follows the v3 PDF, so the note is correct as written — flagging only so a future reviewer isn't misled by the metadata abstract.

Changes

• verified_against_source: 2026-07-18 → 2026-07-20 (frontmatter + provenance block + index.json)
• index.json updated: 2026-07-18 → 2026-07-20
• No changes to tiers, Key results, entity ledger, or Our take — the one-way rule had nothing to correct this round.

🤖 Generated with Claude Code