data/worked_examples.jsonl

{"example_id": "empty-dimension-zero", "dimension": 0, "initial_state_json": "{\"x\":[],\"A\":[]}", "controls_json": "[]", "all_controls_legal": true, "first_illegal_step": 0, "final_legal_prefix_state_json": "{\"x\":[],\"A\":[]}", "final_rank": 0, "final_rho_squared": "0", "note": "Empty history; endpoint, area, rank, and radius are zero.", "source_file": "manuscript/Avenyra_Area_Feedback_v1.0.0.tex"}
{"example_id": "one-dimensional-return", "dimension": 1, "initial_state_json": "{\"x\":[\"0\"],\"A\":[[\"0\"]]}", "controls_json": "[[\"1\"], [\"-1\"]]", "all_controls_legal": true, "first_illegal_step": 0, "final_legal_prefix_state_json": "{\"x\":[\"0\"],\"A\":[[\"0\"]]}", "final_rank": 0, "final_rho_squared": "0", "note": "No signed area can be written in dimension one.", "source_file": "manuscript/Avenyra_Area_Feedback_v1.0.0.tex"}
{"example_id": "two-dimensional-shutdown", "dimension": 2, "initial_state_json": "{\"x\":[\"0\",\"0\"],\"A\":[[\"0\",\"0\"],[\"0\",\"0\"]]}", "controls_json": "[[\"1\", \"0\"], [\"0\", \"1\"]]", "all_controls_legal": true, "first_illegal_step": 0, "final_legal_prefix_state_json": "{\"x\":[\"1\",\"1\"],\"A\":[[\"0\",\"1\"],[\"-1\",\"0\"]]}", "final_rank": 2, "final_rho_squared": "2", "note": "The resulting rank-two memory permits only zero moves.", "source_file": "manuscript/Avenyra_Area_Feedback_v1.0.0.tex"}
{"example_id": "three-dimensional-kernel-rotation", "dimension": 3, "initial_state_json": "{\"x\":[\"0\",\"0\",\"0\"],\"A\":[[\"0\",\"0\",\"0\"],[\"0\",\"0\",\"0\"],[\"0\",\"0\",\"0\"]]}", "controls_json": "[[\"1\", \"0\", \"0\"], [\"0\", \"1\", \"0\"], [\"0\", \"0\", \"1\"]]", "all_controls_legal": true, "first_illegal_step": 0, "final_legal_prefix_state_json": "{\"x\":[\"1\",\"1\",\"1\"],\"A\":[[\"0\",\"1\",\"1\"],[\"-1\",\"0\",\"1\"],[\"-1\",\"-1\",\"0\"]]}", "final_rank": 2, "final_rho_squared": "8/3", "note": "The kernel rotates to span(1,-1,1); rho squared is 8/3.", "source_file": "manuscript/Avenyra_Area_Feedback_v1.0.0.tex"}
{"example_id": "three-dimensional-optimal-projection", "dimension": 3, "initial_state_json": "{\"x\":[\"0\",\"0\",\"0\"],\"A\":[[\"0\",\"0\",\"0\"],[\"0\",\"0\",\"0\"],[\"0\",\"0\",\"0\"]]}", "controls_json": "[[\"1\", \"0\", \"0\"], [\"0\", \"1\", \"0\"], [\"0\", \"0\", \"1\"], [\"-1/3\", \"1/3\", \"-1/3\"]]", "all_controls_legal": true, "first_illegal_step": 0, "final_legal_prefix_state_json": "{\"x\":[\"2/3\",\"4/3\",\"2/3\"],\"A\":[[\"0\",\"5/3\",\"1\"],[\"-5/3\",\"0\",\"1/3\"],[\"-1\",\"-1/3\",\"0\"]]}", "final_rank": 2, "final_rho_squared": "8/3", "note": "The unique finite minimum from the three-step state is (2/3,4/3,2/3).", "source_file": "manuscript/Avenyra_Area_Feedback_v1.0.0.tex"}
{"example_id": "hidden-parameter-one-after-probe", "dimension": 3, "initial_state_json": "{\"x\":[\"0\",\"0\",\"0\"],\"A\":[[\"0\",\"0\",\"0\"],[\"0\",\"0\",\"0\"],[\"0\",\"0\",\"0\"]]}", "controls_json": "[[\"1\", \"0\", \"0\"], [\"0\", \"1\", \"0\"], [\"0\", \"0\", \"1\"]]", "all_controls_legal": true, "first_illegal_step": 0, "final_legal_prefix_state_json": "{\"x\":[\"1\",\"1\",\"1\"],\"A\":[[\"0\",\"1\",\"1\"],[\"-1\",\"0\",\"1\"],[\"-1\",\"-1\",\"0\"]]}", "final_rank": 2, "final_rho_squared": "8/3", "note": "Lambda=1; the common e3 probe leaves rho squared 8/3.", "source_file": "manuscript/Avenyra_Area_Feedback_v1.0.0.tex"}
{"example_id": "hidden-parameter-two-after-probe", "dimension": 3, "initial_state_json": "{\"x\":[\"0\",\"0\",\"0\"],\"A\":[[\"0\",\"0\",\"0\"],[\"0\",\"0\",\"0\"],[\"0\",\"0\",\"0\"]]}", "controls_json": "[[\"2\", \"0\", \"0\"], [\"-1\", \"1\", \"0\"], [\"0\", \"0\", \"1\"]]", "all_controls_legal": true, "first_illegal_step": 0, "final_legal_prefix_state_json": "{\"x\":[\"1\",\"1\",\"1\"],\"A\":[[\"0\",\"2\",\"1\"],[\"-2\",\"0\",\"1\"],[\"-1\",\"-1\",\"0\"]]}", "final_rank": 2, "final_rho_squared": "7/3", "note": "Lambda=2; the same probe leaves rho squared 7/3 and kernel span(1,-1,2).", "source_file": "manuscript/Avenyra_Area_Feedback_v1.0.0.tex"}
{"example_id": "rectangle-gate-failure", "dimension": 2, "initial_state_json": "{\"x\":[\"0\",\"0\"],\"A\":[[\"0\",\"0\"],[\"0\",\"0\"]]}", "controls_json": "[[\"1\", \"0\"], [\"0\", \"1\"], [\"-1\", \"0\"], [\"0\", \"-1\"]]", "all_controls_legal": false, "first_illegal_step": 3, "final_legal_prefix_state_json": "{\"x\":[\"1\",\"1\"],\"A\":[[\"0\",\"1\"],[\"-1\",\"0\"]]}", "final_rank": 2, "final_rho_squared": "2", "note": "The third control is illegal. Final state records only the legal prefix; no illegal update is performed.", "source_file": "manuscript/Avenyra_Area_Feedback_v1.0.0.tex"}