A tethered plastic screw stopper, comprising: a closure shell and a tamper band; and an annular ring formed between: a bottom weakness line separably linked through bottom bridges to the top edge of the tamper band and to the bottom edge of the annular ring; and a top weakness line separably linked through top bridges to the top edge of the annular ring and to the bottom edge of the closure shell, wherein: at least one of the bottom bridges is a remaining bottom bridge configured to prevent disconnection of the annular ring from the tamper band; at least one of the top bridges is a remaining top bridge configured to prevent disconnection of the annular ring from the closure shel and the remaining bottom bridge and the remaining top bridge having a section exceeding at least 30% relative to the section of the bottom bridges and top bridge:, respectively, characterized in that at least another of the bottom bridges is another remaining bottom bridge: at least another of the top bridges is another remaining top bridge; and the another remaining bottom bridge and the another remaining top bridge having a section exceeding at least 30% relative to the thickness of the bottom and/or top bridges (110, 114), the another remaining bottom bridge is located near the remaining bottom bridge. and the another remaining top bridge is located near the remaining top bridge. a closure shell and a tamper band; and an annular ring formed between: a bottom weakness line separably linked through bottom bridges to the top edge of the tamper band and to the bottom edge of the annular ring; and a top weakness line separably linked through top bridges to the top edge of the annular ring and to the bottom edge of the closure shell, a bottom weakness line separably linked through bottom bridges to the top edge of the tamper band and to the bottom edge of the annular ring; and a top weakness line separably linked through top bridges to the top edge of the annular ring and to the bottom edge of the closure shell, wherein: at least one of the bottom bridges is a remaining bottom bridge configured to prevent disconnection of the annular ring from the tamper band; at least one of the top bridges is a remaining top bridge configured to prevent disconnection of the annular ring from the closure shel and the remaining bottom bridge and the remaining top bridge having a section exceeding at least 30% relative to the section of the bottom bridges and top bridge:, respectively, characterized in that at least another of the bottom bridges is another remaining bottom bridge: at least another of the top bridges is another remaining top bridge; and the another remaining bottom bridge and the another remaining top bridge having a section exceeding at least 30% relative to the thickness of the bottom and/or top bridges (110, 114), the another remaining bottom bridge is located near the remaining bottom bridge. and the another remaining top bridge is located near the remaining top bridge. at least one of the bottom bridges is a remaining bottom bridge configured to prevent disconnection of the annular ring from the tamper band; at least one of the top bridges is a remaining top bridge configured to prevent disconnection of the annular ring from the closure shel and the remaining bottom bridge and the remaining top bridge having a section exceeding at least 30% relative to the section of the bottom bridges and top bridge:, respectively, characterized in that at least another of the bottom bridges is another remaining bottom bridge: at least another of the top bridges is another remaining top bridge; and the another remaining bottom bridge and the another remaining top bridge having a section exceeding at least 30% relative to the thickness of the bottom and/or top bridges (110, 114), the another remaining bottom bridge is located near the remaining bottom bridge. and the another remaining top bridge is located near the remaining top bridge. at least another of the top bridges is another remaining top bridge; and the another remaining bottom bridge and the another remaining top bridge having a section exceeding at least 30% relative to the thickness of the bottom and/or top bridges (110, 114), the another remaining bottom bridge is located near the remaining bottom bridge. and the another remaining top bridge is located near the remaining top bridge.