Fidencio Valdez v. Texas

When a defendant knows or should know that a prosecutor has used or introduced false or perjured evidence before the trier-of-fact, is there an obligation on the part of the defendant to lodge a timely objection to such testimony?

Is a prosecutor authorized to disregard the rule that he or she is to refrain from knowingly presenting or using as substantive evidence false or perjured statements where the prosecutor’s intent in presenting or using such evidence is to explain the reason or reason(s) why the witness lied or failed to tell the truth?

Where defense counsel impeaches a witness and demonstrates that the witness lied to the police, does the prosecutor comply with his or her constitutional duty to correct false evidence or testimony by introducing as substantive evidence before the trier-of-fact extrinsic evidence of these lies by the witness, along with self-serving explanations from the witness to explain these lies?

Can a defendant rely on circumstantial evidence to prove the existence of a tacit or implied agreement between the State and a witness wherein the witness agrees to testify for the State in exchange for immunity or leniency, or is a defendant limited to proving up the existence of such an agreement through direct evidence only?