Reasoning Models - Vendor Capability Matrix
Chapter 5 of Loop Engineering argues the prefrontal cortex layer runs two loops: a deliberation loop (reasoning models) and a critical-thinking loop (metacognition). This matrix tracks the deliberation-loop side: which vendors expose what, and where the architecturally-relevant deltas sit.
Refreshed quarterly; next review 2026-09. Verified 2026-06. The reasoning-model surface changes faster than print can keep up - treat any row older than six months as a snapshot and consult the linked vendor docs.
The matrix
| Model family | Visible chain | Thinking budget control | Cost vs flagship non-reasoning | Faithfulness caveat | Materiality fit | Verified |
|---|---|---|---|---|---|---|
| OpenAI o-series o1, o3, o4 lineage |
Summary only (the full internal chain is hidden by API design). | reasoning.effort parameter (low / medium / high) and reasoning-token budget. |
Higher per-call cost; reasoning tokens billed separately. | Vendor does not publish a formal faithfulness claim for the visible summary; treat as a presentation layer. | Medium to high stakes. | 2026-06 |
| DeepSeek R-series R1, R1-Distill |
Full visible chain in the API and chat surfaces. | Implicit via prompt-side controls; full chain is always emitted. | Open weights; self-hosted cost dominates. | Chain is what the model produced; published in the R1 paper alongside training recipe. | Medium to high stakes; research and audit-heavy contexts. | 2026-06 |
| Anthropic Claude extended thinking Sonnet / Opus extended thinking |
Visible thinking blocks in API and chat (when enabled). | Thinking-budget tokens are an explicit parameter on the request. | Higher cost when extended thinking is enabled; off by default. | Vendor-published explicit caveat: visible thinking is not guaranteed to be a faithful trace of the model's actual computation. See launch post. | Medium to high stakes; verifiability-sensitive work. | 2026-06 |
| Google Gemini thinking modes Flash Thinking, 2.5 Thinking lineage |
Visible thinking summaries in surfaces; API surface varies by model and tier. | Per-model "thinking config" controls; consult Gemini API docs for current parameters. | Varies by tier; thinking variants are typically billed above non-thinking flagships. | Treat visible thinking as presentation-layer unless Google publishes a formal faithfulness claim. | Medium stakes; product-integration contexts. | 2026-06 |
| OpenAI GPT-5 reasoning modes unified reasoning-capable family |
Summary only; full chain hidden by API design (consistent with the o-series convention). | Effort dial and per-call reasoning budget; surface details consolidating across OpenAI's reasoning offerings. | Tier-dependent; reasoning calls billed at the higher tier. | No formal faithfulness claim published for the visible summary. | Medium to high stakes. | 2026-06 |
What the columns mean
- Visible chain - does the API or chat surface return the actual reasoning steps the model generated, or just a summary the vendor prepared from them? Architecturally relevant because the visible chain is what the critical-thinking loop has to work with.
- Thinking budget control - can the caller bound how much reasoning is done? Materiality calibration depends on being able to dial this.
- Cost vs flagship non-reasoning - reasoning calls are not free. Materiality budgets get burned on the wrong tier without explicit dial-down.
- Faithfulness caveat - is the visible chain guaranteed to reflect what the model actually did? Anthropic is the only major vendor that has published an explicit "no" so far; others are silent, which means "treat as presentation layer until shown otherwise."
- Materiality fit - recommended materiality-dial range for this model class, given cost and caveat profile.
The faithfulness caveat in plain text
The visible thinking trace is what the model emitted as thinking; it is not necessarily what the model actually used to produce the answer. This matters when you are auditing the reasoning to decide whether to trust the result. A visible chain that looks rigorous can still be window-dressing on a different underlying computation. Anthropic's extended thinking launch says this explicitly. Other vendors' silence on this point is not the same as saying their visible thinking is faithful.
Architectural implication: the critical-thinking loop in the prefrontal layer (the metacognitive frameworks) is what makes reasoning models defensible. The visible chain is evidence, not proof.
What this matrix does not cover
- Per-task benchmark performance - benchmark leaderboards age too fast for a quarterly refresh; consult Chatbot Arena, LiveCodeBench, and the vendors' own technical reports for current numbers.
- Latency - reasoning latency varies by load, region, and tier; this matrix tracks capability shape, not throughput.
- Fine-tuning availability - some reasoning families allow fine-tuning, some do not; consult the relevant vendor doc.
- Open-weights status - DeepSeek R-series is open-weights; the rest of the families in this matrix are closed-weights as of the verified date.
Correction policy
If a vendor surface changes materially before the next quarterly refresh, please flag it via the errata page. Substantive corrections that change a "visible chain" or "faithfulness caveat" cell will be reflected here within two weeks.