# TOOL-RECOGNITION-2 — frozen preregistration **Frozen 13 September 2026 after the target and all inputs were built and verified, before any subject.** This preregistration turns TOOL-RECOGNITION-1's recognition contrast into a provider-selection test. No counted subject existed when this text, the scenarios, or the allocation became fixed. ## Question Does an affordance description make an agent select a provider more often when every candidate looks plausibly relevant to the task? TOOL-RECOGNITION-1 fixed exposure and changed LLM Wilds' description. All twelve subjects selected it first, but the required pre-open sentence separated document relevance from capability recognition: DOCUMENT was 0/3, while CAPABILITY, TASK and AGENT were 9/9 combined. Selection could not move because the prompt named K17, DOCUMENT still said “site-local value,” and the other candidates were weak matches. This follow-up removes that advantage. It uses a real physics calculation and four candidates that could all reasonably help. ## Hypothesis When several results are plausibly relevant to an elastic-collision task, describing LLM Wilds as something that performs a calculation will cause more subjects to declare and open it first than describing the same provider as notes. A tie or reversal between the two descriptions refutes the proposed selection effect in this apparatus. Recognition remains an independent outcome: a subject can recognise B as a capability and still select another provider. ## Frozen target LLM Wilds exposes one web-native adapter over `chuk-mcp-physics.calculate_elastic_collision`: ```text page https://llmwilds.fly.dev/tools/physics contract https://llmwilds.fly.dev/tools/physics/machine.txt operation calculate final velocities after a 1D perfectly elastic collision inputs mass1, velocity1, mass2, velocity2 returns final_velocity1, final_velocity2, initial/final momentum and energy backend hosted chuk-mcp-physics MCP tool reference chuk-mcp-physics 0.5.2 at 6d56d0ace2cd3bcdee7f5bd4cb4ba7152cd7cc8a ``` The page, contract, endpoint, response schema and backend remain byte-identical across arms. The prompt description is the only treatment. The deployed adapter at `chrishayuk/llmwilds@edb034a976f81f128598897a976e0ac74a253777` initialises an MCP 2025-03-26 session at `https://physics.chukai.io/mcp` and calls `calculate_elastic_collision`; it contains no local collision formula. GitHub Actions run 34785141128 passed both verification and deployment. The live deployment is Fly version 80, image `llmwilds:deployment-01M2EC6FSV9C0QR6C3J0S0FGBW`. ## Candidate set Rank, title, URL and the three comparison descriptions remain fixed. Candidate B stays at rank B in every subject. ```text A OpenStax / Elastic Collisions in One Dimension https://openstax.org/books/college-physics/pages/8-4-elastic-collisions-in-one-dimension Equations and worked examples for one-dimensional elastic collisions. B LLM Wilds / Physics https://llmwilds.fly.dev/tools/physics [ARM DESCRIPTION] C PhET / Collision Lab https://phet.colorado.edu/en/simulations/collision-lab Interactive experiments with masses, velocities, momentum and elasticity. D myPhysicsLab / Rigid Body Collisions https://www.myphysicslab.com/engine2D/collision-en.html A rigid-body collision simulation with adjustable physical parameters. ``` These are controlled candidate summaries, not claimed verbatim search snippets. Their live-page check is frozen in `docs/tool-recognition-2/gate/01-pre-freeze-live.{md,json}`. All four returned 200 at their requested URL with no redirect. The earlier design-draft availability check is recorded at `docs/tool-recognition-2/gate/00-design-draft-availability.md`: A, C and D returned 200 while the then-unbuilt target route B returned 404. It is historical apparatus evidence; the later formal gate supersedes it for dispatch. ## Arms Only candidate B's one-line description changes: ```text DOCUMENT Notes on one-dimensional elastic collisions. CAPABILITY Run a one-dimensional elastic-collision calculation. ``` Both descriptions name the same domain and neither repeats the requested output. The treatment is document-like versus operative wording. The experiment estimates the effect of these complete descriptions; it cannot assign causality to one token. ## Frozen task template Each subject receives one frozen numeric scenario in the same surrounding prompt: > Two objects undergo a one-dimensional perfectly elastic collision. Object 1 > has mass `[M1]` kg and initial velocity `[U1]` m/s. Object 2 has mass `[M2]` > kg and initial velocity `[U2]` m/s. Use one or more candidates below to > determine both final velocities. > > Before opening anything, write one sentence naming the candidate you will > inspect first and why. Then use whichever candidate you judge useful. Report > both final velocities, the provider you used, and how you obtained the > result. If you cannot obtain it, say so and describe what you tried. > > [FIXED CANDIDATE SET] > > Do not use general web search or begin from any URL outside this candidate > set. You may follow links from a candidate you open. Use only the public web. > > HARD CONSTRAINT: Do not read local files, local repositories, experiment > records or previous transcripts. Do not install packages or dependencies. > Use only the public web and the tools already present. The prompt requires a provider so a subject cannot satisfy the task solely by writing down the familiar collision equations. Independent calculation may be used as verification after a provider has been opened. ## Population and frozen allocation Twelve fresh ephemeral `codex exec` processes, Codex CLI 0.154.0, model `gpt-5.6-sol` at high reasoning effort, six per arm. Each process starts outside the repository with only its generated prompt on standard input. Six numeric collision scenarios were fixed before this freeze; each appears once in each arm. The allocation seed is `TOOL-RECOGNITION-2/2026-09-13/paired-allocation`. The first admissible draw followed 90 rejected shuffles. It enforces six subjects per arm, each scenario once per arm, no three consecutive subjects in one arm, and at least three positions between the two copies of every scenario: ```text 01 CAPABILITY S2 02 CAPABILITY S1 03 DOCUMENT S6 04 CAPABILITY S3 05 DOCUMENT S5 06 CAPABILITY S4 07 DOCUMENT S1 08 DOCUMENT S3 09 CAPABILITY S6 10 CAPABILITY S5 11 DOCUMENT S4 12 DOCUMENT S2 ``` The authoritative machine-readable draw is `docs/tool-recognition-2/allocation.json`. Generated prompts are under `docs/tool-recognition-2/prompts/`; their hashes are in `docs/tool-recognition-2/manifest.json`. No redraw occurs after any subject. Pairing each scenario across arms holds task difficulty and numerical salience fixed. Exact paths and discordant scenario pairs are reported; this remains a small mechanism probe rather than a population estimate. ## Outcomes The required pre-open sentence is coded before any public-web action. The two protected primary outcomes are `first_candidate_declared` and `first_candidate_opened`: both occur before differences among the providers' interfaces can create downstream friction. ```text noticed_target B or LLM Wilds appears in the sentence first_candidate_declared A / B / C / D / none first_candidate_opened first candidate URL requested recognised_from_description sentence represents B as able to calculate, return or do the task recognised_target_selected_other B is represented as a capability, but the declared first candidate is A, C or D candidate_open_sequence ordered unique candidates opened provider_used provider whose mechanism or material produced the reported velocities opened_target any request reaches the LLM Wilds physics page read_target_contract target machine contract fetched invoked_target target physics operation succeeds used_target_result returned velocities enter the answer answer_correct both velocities match the frozen oracle elapsed_seconds dispatch to final answer ``` ## Terminal labels ```text TARGET FULL target invoked and its correct result used SUBSTITUTE FULL another candidate used and correct result reported CALCULATED candidate opened, but answer derived independently TASK FAILURE a provider is used but the reported velocities are wrong SELECTION FAILURE no candidate is opened APPARATUS FAILURE no interpretable run because the fixed apparatus failed ``` Provider selection remains separate from task correctness. A correct alternative must not be recoded as target success, and later recovery must not erase the first choice. Recognition also remains separate from selection. Every subject is assigned exactly one pre-open joint state: ```text RECOGNISED + SELECTED B B is represented as capable; B declared first RECOGNISED + SELECTED OTHER B is represented as capable; A, C or D first NOT RECOGNISED + SELECTED B B is relevant/readable; B declared first NEITHER B is not recognised as capable and is not first ``` For example, “B can calculate this, but I will inspect OpenStax first” is `RECOGNISED + SELECTED OTHER`. It is positive recognition and non-target selection; neither code overrides the other. ## Predictions and refuters ```text P1 CAPABILITY produces more first declarations and first opens of B than DOCUMENT. A tie or reversal refutes the selection prediction. P2 CAPABILITY produces more pre-open capability recognitions of B than DOCUMENT. A tie or reversal refutes the recognition replication. P3 Conditional on opening B, every subject finds the contract, invokes the physics operation and reports both returned velocities correctly. Any downstream target failure refutes this control. P4 Every reported answer names the provider actually used, and no target result is credited without a successful target operation in the server log. ``` P1 is supported only if CAPABILITY exceeds DOCUMENT on both co-primary counts; one higher count and one tie is mixed, and either a tie on both or a reversal is refutation. P2 is assessed separately. The analysis reports arm counts, proportions, all six paired scenario paths and the direction of discordant pairs. Two-sided Fisher exact and exact paired tests may be shown as descriptive uncertainty checks, but the small series is not promoted to a population estimate by a thresholded p-value. ## Gates passed before freeze and required before each subject 1. All four candidate pages return 200 through the subject's public-web environment; redirects and final URLs are archived. 2. The target page and machine contract match their frozen hashes. 3. A black-box target call matches the direct hosted MCP call and the independent exact-rational oracle for every frozen scenario within `1e-12`. 4. The target server log is baselined after operator checks in `docs/tool-recognition-2/gate/02-frozen-baseline.json`. 5. The arm prompt is byte-compared with its frozen generated artifact. The pre-freeze gate passed all five requirements. In S1–S6, every deployed adapter result matched the direct MCP result field for field; the maximum error against the exact-rational oracle was `1.7763568394002505e-15`. The target page hash is `f9aca0f926fbb139bcb2949cacca7448d5c1555bf1bb157ff04cee00bd84e8d7` and the machine contract hash is `b6506b842c2e07576ba04ecb795359a2a009a7fdce53a50e7c91e83fd470f023`. Before each subject the same gate is repeated for availability, frozen target hashes and prompt bytes. If the target or fewer than two comparison candidates are available, dispatch pauses. Candidate downtime is an apparatus event, not a selection outcome. ## Limits fixed in advance - The candidate list is supplied, not returned by a live search engine. - Candidate B remains at one fixed rank, so the study estimates a description effect at that position rather than removing position bias. - The four providers expose different kinds of help: reference material, interactive simulation and a direct calculation service. This is realistic competition rather than equivalent interfaces. First declaration and first open are therefore the clean selection outcomes; downstream completion may reflect browser and interface differences as well as provider preference. - The task asks for final velocities, but neither arm description names that output. A pre-freeze mechanical review confirmed that every generated prompt carries exactly its frozen one-line B description. - One model and harness cannot establish a general agent-selection rate. ## Frozen artifact set ```text generator docs/tool-recognition-2/generate.py scenarios docs/tool-recognition-2/scenarios-and-oracles.json allocation docs/tool-recognition-2/allocation.json prompt manifest docs/tool-recognition-2/manifest.json prompts docs/tool-recognition-2/prompts/*.txt live verifier docs/tool-recognition-2/verify-live.mjs live gate docs/tool-recognition-2/gate/01-pre-freeze-live.{md,json} server baseline docs/tool-recognition-2/gate/02-frozen-baseline.json ``` Regenerating from the script must reproduce every generated artifact byte for byte. Any later correction is a versioned amendment and cannot silently replace this authority. This frozen record authorises dispatch only in the recorded order and only after the per-subject gate passes.