There is no "+" terminal on the mains, but judging by the naming of one terminal as "N" it seems you are in the USA, yes?
The RC values are more appropriate for a 230VAC/50Hz dimmer circuit - try reducing the fixed resistor to 3.3k and the capacitor to 100nF (note that it should be a high voltage film type for safety reasons). Other possible problems are: bad or miswired pot (center and right terminals, with knob facing you); 10k resistor not really 10k (too high or open circuit); diac breakover voltage too high (needs to be around 30V); bad triac; shorted capacitor; insufficient or missing or highly inductive load present - this dimmer circuit will not work without a predominantly resistive load (like a... wait for it... incandescent lamp!).
Triac connections are wrong.. The triac gate has a reference, in this case pin 1. Using the other way round it likely will either be on always or off, depending on the capacitor charging.
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Incorrect. Triacs can be triggered by any combination of gate polarity with respect to MT1 (T1) or MT2 (T2) polarity. See relevant excerpt from the BT136 datasheet you posted: