Reach out to the NYCHA at tel:718-707-7771 and ask for a transfer. You seem to have exhausted your other remedies.
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Your landlord is responsible, if you have brought it to his attention, to take steps to stop your neighbors from creating excessive noise or disturbances that affect your ability to live in your apartment in peace. You appear to be alleging that they have deprived you of your right to quietly enjoy your apartment by failing to take effective steps to abate allegedly excessive noise emanating from the neighboring tenant's apartment - this constitutes a breach of the warranty of habitability, and may entitle you to an abatement on your rent. You should consult with an attorney if you want to commence such an action against your landlord.
There are noise laws, and a law that requires that a large percentage of an apartment must be carpeted. You should check with the clerk in the housing part to see how you enforce them.
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