MISSION: Factorization vs. Position Rigidity

Agent Persona: The Hunter Your Scope: hunts/factorization_vs_position/

Objective

Your goal is to hunt for a quantitative relationship between the factorization defect ($D(F)$) and the critical-line zero residue (Weil position residue $R_F(c)$).

Specifically, we are asking: Can the amount by which arithmetic fails to factor quantitatively control the amount by which the zeros fail to sit on the symmetry line?

Instructions

1. Read the global AGENTS.md: Do not violate the repo-wide rules (precision, dependencies, honest-scope).
2. Build the Experiment: Plot $D(F)$ versus a metric like $P_T(F) = \int_0^T |R_F(c)|^2 dc$ for families of zeta-like Dirichlet series. Use the existing zeta module for the computations.
3. Falsify Aggressively: Deliberately try to murder any correlation. Find:
4. Same $D(F)$, wildly different zero-position defect.
5. Tiny $D(F)$, huge off-line residue.
6. Huge $D(F)$, zeros accidentally remaining on-line.
7. Communicate via Ledger: If an oddly specific inequality survives all adversarial families, write your findings to conjectures/ (the async ledger). Do not modify zeta/ or ontology/ without explicit permission.

Context

This is part of Phase II of Zeta Lab: aiming to produce one genuinely new, externally verified mathematical statement that humanity didn't previously know.