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You should get a hold of a lawyer and have them explain how wrong you are about everything you just posted.
If you think a cop who just saw you commit a crime needs a warrant and an investigation beforehand, you are obviously in serious need of further High School education.
The ONLY thing a cop needs to arrest you for ANYTHING is Probable Cause. You can argue against this fact all you want, but you will still be wrong.
http://www.nolo.com/legal-encyclopedia/when-police-can-make-arrest-probable-cause.html
http://criminal.findlaw.com/criminal-rights/probable-cause.html
http://criminal.findlaw.com/criminal-rights/when-is-an-arrest-a-legal-arrest.html
The Fourth Amendment of the U.S. Constitution authorizes police to make an arrest as long as they have "probable cause". The Fourth Amendment states:
The right of the people to be secure in their persons, houses, papers, and effects, against unreasonable searches and seizures, shall not be violated, and no Warrants shall issue, but upon
probable cause, supported by Oath or affirmation, and particularly describing the place to be searched, and the persons or things to be seized.
The idea behind probable cause is to prevent the sort of police states that exist in other countries, where officials can simply round up people they don't like as "undesirables" or "threats" without any justification. This standard is deliberately vague, but over time the interpretation of what constitutes probable cause has become fairly solidified:
- Probable cause is established through factual evidence, and not just suspicions or hunches.
- Probable cause can be established through observation alone (sight, smell, sound, etc), and includes observations that create suspicion based on a familiar pattern of criminal activity, such as when an officer sees a car circling around an area repeatedly or when someone is flashing their headlights.
- Probable cause can be based on information derived from witnesses, victims and informants.
- Probable cause can be based on police expertise, such as recognition of gang signs, detection of tools appropriate for committing certain crimes, or knowledge of movements and gestures that indicate criminal activity.
- Probable cause can be based on circumstantial evidence that only indirectly indicates that a crime has occurred, such as a broken window.
http://www.flexyourrights.org/faqs/probable-cause/
http://en.wikipedia.org/wiki/Reasonable_suspicion
http://nationalparalegal.edu/conLawCrimProc_Public/ProtectionFromSearches&Seizures/ExToWarrantReq.asp
A search incident to lawful arrest does not require issuance of a warrant.
Good luck to you in any future LEO encounters. You are going to need it as your education on the subject is going to lead to problems when you try to assert that the cops can't arrest you without a investigation and warrant first.