{
  "study_id": "causal-relational-knockout-24law-v1",
  "status": "frozen-before-any-study-model-output",
  "frozen_at": "2026-09-02T11:03:03.653464+00:00",
  "scientific_question": "Does a development-fitted relational coordinate make a selective causal contribution to ordinary correct decisions, mediate counterfactual answer changes, and repair initially incorrect answer margins?",
  "cohort": {
    "law_identities": 24,
    "direct": 12,
    "inverse": 12,
    "prompts": 192,
    "factors": [
      "two numerical directions",
      "higher/lower and greater/smaller answer vocabularies",
      "both presentation orders"
    ],
    "independent_unit": "law identity",
    "equation_free": true,
    "disjoint_from_direction_fit_laws": true
  },
  "models": {
    "4b": {
      "model": "google/gemma-4-E4B-it",
      "revision": "a4c2d58be94dda072b918d9db64ee85c8ed34e3f",
      "probe_layer": 34,
      "development_manifest": "experiments/elicited-physics-abstraction-2026-07-18/prompt_manifest.json",
      "development_states": "experiments/elicited-physics-abstraction-2026-07-18/representations.npz"
    },
    "12b": {
      "model": "google/gemma-4-12B-it",
      "revision": "707f0a3b8a3c7ad586ed01e27eafbad8a27dd0f7",
      "probe_layer": 39,
      "development_manifest": "experiments/gemma4-12b-equation-free-relational-v1/development_prompt_manifest.json",
      "development_states": "experiments/gemma4-12b-equation-free-relational-v1/development_states.npy"
    },
    "31b": {
      "model": "google/gemma-4-31B-it",
      "revision": "842da3794eaa0b77d5f08bae87a17459d91ff475",
      "probe_layer": 49,
      "development_manifest": "experiments/gemma4-31b-equation-free-relational-v1/development_prompt_manifest.json",
      "development_states": "experiments/gemma4-31b-equation-free-relational-v1/development_states.npy"
    }
  },
  "direction": "One unit physical-outcome centroid direction per model, fitted only on the pre-existing 16-law development cohort at the prespecified layer.",
  "position": "final prompt token after the registered transformer block",
  "interventions": {
    "clean": "Unmodified forward pass.",
    "neutralize": "Set only the normalized-state coordinate along the frozen direction to the development midpoint, retaining the orthogonal residual.",
    "counterfactual_coordinate": "Set only that coordinate to the value in the exact matched prompt with reversed numerical change.",
    "correct_centroid": "Set only that coordinate to the development centroid for the prompt's registered physical outcome; evaluated as error repair only on all initially wrong answer-margin cases.",
    "wrong_centroid": "Set the coordinate to the opposite development centroid as a signed falsification.",
    "full_counterfactual": "Replace the complete state with its exact matched counterfactual state.",
    "full_counterfactual_direction_restored": "Apply the full counterfactual state but restore its frozen-direction coordinate to the clean receiver value.",
    "random_controls": "Three deterministic unit directions orthogonal to the frozen direction; each receives exactly the same receiver-specific L2 perturbation as neutralization or counterfactual-coordinate replacement."
  },
  "primary_endpoints": {
    "necessity": "Law-level clean correct-answer margin minus neutralized margin; the 95% law bootstrap interval must exceed zero and the effect must exceed the mean matched random-control effect.",
    "counterfactual_sufficiency": "Law-level movement toward the matched counterfactual answer under the one-coordinate swap; interval above zero and larger than random control.",
    "causal_mediation": "Ratio of one-coordinate counterfactual shift to full-state counterfactual shift, reported with an untruncated law bootstrap interval.",
    "direction_restoration": "Reduction of the full-state counterfactual effect when the frozen coordinate is restored to its clean value.",
    "error_repair": "On every clean case whose registered answer margin is below zero, change in correct-answer margin and fraction crossing above zero after the correct-centroid intervention. No minimum error count is guaranteed."
  },
  "secondary_endpoints": [
    "answer-margin accuracy before and after each intervention",
    "higher/lower versus greater/smaller strata",
    "direct versus inverse laws",
    "answer-order agreement",
    "next-token KL divergence and registered-answer probability mass",
    "4B, 12B, and 31B replication without assuming monotonic scaling"
  ],
  "inference": {
    "law_bootstrap_resamples": 30000,
    "bootstrap_seed": 20260902,
    "law_sign_permutations": 100000,
    "permutation_seed": 20260903,
    "random_direction_seeds": [
      1701,
      1702,
      1703
    ]
  },
  "guardrails": [
    "Every frozen prompt and intervention row is retained.",
    "No layer, direction, prompt, answer vocabulary, or control is selected from study output.",
    "Necessity is claimed only for a selective contribution of the tested linear coordinate, never unique or global necessity.",
    "A negative neutralization result leaves the prior sufficiency claim unchanged.",
    "The 31B study uses the same intervention definitions despite having only one archived Jacobian lens; the primary direction is raw-state based and lens independent."
  ]
}