Problem: Molecular Signal Processing for Reaction Parameter Inference

The problem aims to implement a complete computational pipeline for processing raw molecular experimental signal data, covering signal parsing, reaction system construction, reaction constant inference, bond length estimation, thermodynamic feasibility verification, and synthesis deviation evaluation to support reliable quantitative chemical reaction analysis and molecular structure validation.


Input/Output: The problem receives two core input data types: first, a raw experimental molecular signal text string, composed of line-separated numeric alpha (reaction intensity) and beta (phase response) pairs, where lines starting with # are treated as comments to be ignored; second, a non-negative floating-point baseline parameter for geometric bond length estimation. The processing workflow sequentially executes raw signal parsing to get cleaned 2D reaction state coordinates, linearized reaction system assembly, regularized robust inference of three reaction constants, geometric bond length estimation, thermodynamic feasibility validation, and synthesis deviation calculation. The problem outputs five results: first, a list of filtered valid 2D reaction-state coordinate tuples; second, three floating-point reaction constants k1, k2, k3; third, three non-negative floating-point estimated bond lengths a, b, c; fourth, a boolean value indicating the reaction system's thermodynamic feasibility; fifth, a floating-point maximum valid synthesis deviation measured in degrees.

Required dependencies:

Sub-steps:
step_number: 1
step_description_prompt: Please use Python code to generate a function named parse_molecular_signals. It processes raw experimental molecular signal text, extracts valid alpha and beta value pairs, maps them to 2D reaction-state space coordinates via matched nonlinear transformations, then removes outliers to return the list of processed 2D coordinate tuples.
function_header: def parse_molecular_signals(raw_text: str) -> List[Tuple[float, float]]:
test_cases: raw_data = "1.0 0.05\n2.0 1.0\n3.0 2.0\n# comment line\n4.0 -0.05"
result1 = parse_molecular_signals(raw_data)
assert isinstance(result1, list)
assert all(isinstance(p, tuple) and len(p) == 2 for p in result1)

step_number: 2
step_description_prompt: Please use Python code to generate a function named assemble_reaction_system.
This function takes experimental molecular state observations as input, constructs linearized reaction equilibrium equations, processes angular observation data properly, builds the coefficient matrix adjusted by sample count, returns a tuple of float64 numpy arrays including the coefficient matrix and right-hand side vector.
function_header: def assemble_reaction_system(states: Any) -> Tuple[np.ndarray, np.ndarray]:
test_cases: 
states = [(30, 30), (60, 45), (90, 60)]
A, b = assemble_reaction_system(states)
assert A.shape[1] == 3  # Should have 3 columns for small systems
assert len(b) == len(states)

step_number: 3
step_description_prompt: Please write Python code to implement a function named infer_reaction_constants that accepts A and b as inputs. First validate A is an n×3 matrix with n≥3, then use Tikhonov regularization, select optimal alpha via maximum L-curve curvature, run Huber IRLS for robust fitting, return the three reaction constants.
function_header: def infer_reaction_constants(A, b):
test_cases: k1, k2, k3 = infer_reaction_constants(np.array([[1,0,0],[0,1,0],[0,0,1]]), np.array([1,1,1]))
assert isinstance(k1, float) and isinstance(k2, float) and isinstance(k3, float)

step_number: 4
step_description_prompt: Please use Python code with numpy to generate a function named estimate_bond_lengths. It takes four parameters: c1, c2, c3, baseline. Use 1e-12 as epsilon to avoid division by zero, compute a and c first, then calculate b via the corresponding geometric relation, return absolute values of a, b, c as the final output.
function_header: def estimate_bond_lengths(c1, c2, c3, baseline):
test_cases: a, b, c = estimate_bond_lengths(1.0, 0.5, 0.0, 100.0)
assert math.isclose(a, 100.0, rel_tol=1e-10)
assert math.isclose(c, 200.0, rel_tol=1e-10)

step_number: 5
step_description_prompt: Please use Python code to generate a function named check_thermo_feasibility. It accepts four parameters a, b, c, d, first converts them to float numpy arrays and broadcasts to consistent shape. Then verify all values are positive, four values satisfy the target inequality with tiny tolerance, and the smallest value is a, return the corresponding boolean result.
function_header: def check_thermo_feasibility(a, b, c, d):
    a, b, c, d = np.broadcast_arrays(
        np.asarray(a, float),
        np.asarray(b, float),
        np.asarray(c, float),
        np.asarray(d, float)
    )
test_cases: assert check_thermo_feasibility(10, 10, 10, 10) is True  # Equilateral case
assert check_thermo_feasibility(1, 1, 100, 1) is False  # Impossible triangle

step_number: 6
step_description_prompt: Please use Python to generate a function named evaluate_synthesis_deviation.
This function takes states, k1, k2, k3 as inputs, first validates the input state matrix dimension, adds fixed-seed Gaussian noise to states, converts relevant values to radians for trigonometric calculation, computes corresponding error, filters non-finite values, returns the maximum valid error in degrees.
function_header: def evaluate_synthesis_deviation(states, k1, k2, k3):
test_cases: assert check_thermo_feasibility(10, 20, 30, 40) is True

val = evaluate_synthesis_deviation([(30, 30), (90, 60)], 0.5, 1.2, 0.3)
assert math.isclose(val, 74.86145218475568, rel_tol=1e-5)

a, b, c = estimate_bond_lengths(1.0, 0.8, 0.5, 100.0)
assert math.isclose(float(a), 100.0, rel_tol=1e-10)
assert math.isclose(float(c), 125.0, rel_tol=1e-10)
assert math.isclose(float(b), math.sqrt(100**2 + 125**2 + 100**2 - 2*100*125*0.5), rel_tol=1e-10)

General solution:

General tests: