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  1. ❙✉r✈❡② ■♥tr♦❞✉❝t✐♦♥ ❆str♦♠❡tr✐❝ ❛♥❞ ❙♣❡❝tr♦♣❤♦t♦♠❡tr✐❝ ❝❛❧✐❜r❛t✐♦♥ ❋✐rst r❡s✉❧ts ❛♥❞ ❞❛t❛ r❡❧❡❛s❡ ❚❤❡ ❈❛❧❛r ❆❧t♦ ▲❡❣❛❝② ■♥t❡❣r❛❧ ❋✐❡❧❞ s♣❡❝tr♦s❝♦♣② ❆r❡❛ ✭❈❆▲■❋❆✮ s✉r✈❡② ❇❡r♥❞ ❍✉s❡♠❛♥♥ ✶ ❙✳ ❋✳ ❙á♥❝❤❡③ ✭P■✮ ✷ ✱ ❉✳ ▼❛st ✷ ✱ ❘✳ ●❛r❝✐❛ ❇❡♥✐t♦ ✷ ✱ ❈❆▲■❋❆ ❝♦❧❧❛❜♦r❛t✐♦♥ ✶ ▲❡✐❜♥✐③✲■♥st✐t✉t❡ ❢♦r ❆str♦♣❤②s✐❝s P♦ts❞❛♠ ✭❆■P✮ ✷ ■♥st✐t✉t♦ ❞❡ ❆str♦♣❤②s✐❝❛ ❞❡ ❆♥❞❛❧✉❝✐❛ ✭■❆❆✮ ✷✵✶✶ ❆♣r✐❧ ✶✽

  2. ❙✉r✈❡② ■♥tr♦❞✉❝t✐♦♥ ❆str♦♠❡tr✐❝ ❛♥❞ ❙♣❡❝tr♦♣❤♦t♦♠❡tr✐❝ ❝❛❧✐❜r❛t✐♦♥ ❋✐rst r❡s✉❧ts ❛♥❞ ❞❛t❛ r❡❧❡❛s❡ ❖✉t❧✐♥❡ ❙✉r✈❡② ■♥tr♦❞✉❝t✐♦♥ ✶ ❆str♦♠❡tr✐❝ ❛♥❞ ❙♣❡❝tr♦♣❤♦t♦♠❡tr✐❝ ❝❛❧✐❜r❛t✐♦♥ ✷ ❋✐rst r❡s✉❧ts ❛♥❞ ❞❛t❛ r❡❧❡❛s❡ ✸

  3. ✷✺✵ ❞❛r❦ ♥✐❣❤ts ✐♥ ✸ ②❡❛rs ❛t ❈❛❧❛r ❆❧t♦ ❖❜s❡r✈❛t♦r② ✭❙♣❛✐♥✮ ✷ ✺ ▼✐❧❧✐♦♥ ❊✉r♦s ✐♥ t❡❧❡s❝♦♣❡ t✐♠❡ ❈♦♠♣❡t✐t✐✈❡ r❡✈✐❡✇ ♣r♦❝❡ss ❈♦❧❧❛❜♦r❛t✐♦♥ ♦❢ ✽✷ ♠❡♠❜❡rs ✐♥ ✶✸ ❝♦✉♥tr✐❡s P■✿ ❙✳ ❋✳ ❙á♥❝❤❡③ ✭■❆❆✮ P❙✿ ❏✳ ❲❛❧❝❤❡r ✭❆■P✮ ❇♦❛r❞ ✭❈❤❛✐r✿ ❘✳ ❑❡♥♥✐❝✉tt P✳ ❱✐❧❝❤❡③✮ ▼♦st❧② ②♦✉♥❣ r❡s❡❛r❝❤❡rs ✭ ✸✺ ②❡❛rs✮ Pr♦❥❡❝t st❛rt❡❞ ♦♥ ❏✉❧② ✶st ✷✵✶✵ ❙✉r✈❡② ■♥tr♦❞✉❝t✐♦♥ ❆str♦♠❡tr✐❝ ❛♥❞ ❙♣❡❝tr♦♣❤♦t♦♠❡tr✐❝ ❝❛❧✐❜r❛t✐♦♥ ❋✐rst r❡s✉❧ts ❛♥❞ ❞❛t❛ r❡❧❡❛s❡ ❚❤❡ ✐❞❡❛ ♦❢ ❈❆▲■❋❆ ▲❡❣❛❝② ❙✉r✈❡② ♦❢ ❛ ❧❛r❣❡ ❛♥❞ r❡♣r❡s❡♥t❛t✐✈❡ s❛♠♣❧❡ ♦❢ ❣❛❧❛①✐❡s ✐♥ t❤❡ ❧♦❝❛❧ ❯♥✐✈❡rs❡ ✉s✐♥❣ ♦♣t✐❝❛❧ ✐♥t❡❣r❛❧ ✜❡❧❞ s♣❡❝tr♦s❝♦♣②

  4. ❈♦❧❧❛❜♦r❛t✐♦♥ ♦❢ ✽✷ ♠❡♠❜❡rs ✐♥ ✶✸ ❝♦✉♥tr✐❡s P■✿ ❙✳ ❋✳ ❙á♥❝❤❡③ ✭■❆❆✮ P❙✿ ❏✳ ❲❛❧❝❤❡r ✭❆■P✮ ❇♦❛r❞ ✭❈❤❛✐r✿ ❘✳ ❑❡♥♥✐❝✉tt P✳ ❱✐❧❝❤❡③✮ ▼♦st❧② ②♦✉♥❣ r❡s❡❛r❝❤❡rs ✭ ✸✺ ②❡❛rs✮ Pr♦❥❡❝t st❛rt❡❞ ♦♥ ❏✉❧② ✶st ✷✵✶✵ ❙✉r✈❡② ■♥tr♦❞✉❝t✐♦♥ ❆str♦♠❡tr✐❝ ❛♥❞ ❙♣❡❝tr♦♣❤♦t♦♠❡tr✐❝ ❝❛❧✐❜r❛t✐♦♥ ❋✐rst r❡s✉❧ts ❛♥❞ ❞❛t❛ r❡❧❡❛s❡ ❚❤❡ ✐❞❡❛ ♦❢ ❈❆▲■❋❆ ▲❡❣❛❝② ❙✉r✈❡② ♦❢ ❛ ❧❛r❣❡ ❛♥❞ r❡♣r❡s❡♥t❛t✐✈❡ s❛♠♣❧❡ ♦❢ ❣❛❧❛①✐❡s ✐♥ t❤❡ ❧♦❝❛❧ ❯♥✐✈❡rs❡ ✉s✐♥❣ ♦♣t✐❝❛❧ ✐♥t❡❣r❛❧ ✜❡❧❞ s♣❡❝tr♦s❝♦♣② ✷✺✵ ❞❛r❦ ♥✐❣❤ts ✐♥ ✸ ②❡❛rs ❛t ❈❛❧❛r ❆❧t♦ ❖❜s❡r✈❛t♦r② ✭❙♣❛✐♥✮ ∼ ✷ . ✺ ▼✐❧❧✐♦♥ ❊✉r♦s ✐♥ t❡❧❡s❝♦♣❡ t✐♠❡ ❈♦♠♣❡t✐t✐✈❡ r❡✈✐❡✇ ♣r♦❝❡ss

  5. ❙✉r✈❡② ■♥tr♦❞✉❝t✐♦♥ ❆str♦♠❡tr✐❝ ❛♥❞ ❙♣❡❝tr♦♣❤♦t♦♠❡tr✐❝ ❝❛❧✐❜r❛t✐♦♥ ❋✐rst r❡s✉❧ts ❛♥❞ ❞❛t❛ r❡❧❡❛s❡ ❚❤❡ ✐❞❡❛ ♦❢ ❈❆▲■❋❆ ▲❡❣❛❝② ❙✉r✈❡② ♦❢ ❛ ❧❛r❣❡ ❛♥❞ r❡♣r❡s❡♥t❛t✐✈❡ s❛♠♣❧❡ ♦❢ ❣❛❧❛①✐❡s ✐♥ t❤❡ ❧♦❝❛❧ ❯♥✐✈❡rs❡ ✉s✐♥❣ ♦♣t✐❝❛❧ ✐♥t❡❣r❛❧ ✜❡❧❞ s♣❡❝tr♦s❝♦♣② ✷✺✵ ❞❛r❦ ♥✐❣❤ts ✐♥ ✸ ②❡❛rs ❛t ❈❛❧❛r ❆❧t♦ ❖❜s❡r✈❛t♦r② ✭❙♣❛✐♥✮ ∼ ✷ . ✺ ▼✐❧❧✐♦♥ ❊✉r♦s ✐♥ t❡❧❡s❝♦♣❡ t✐♠❡ ❈♦♠♣❡t✐t✐✈❡ r❡✈✐❡✇ ♣r♦❝❡ss ❈♦❧❧❛❜♦r❛t✐♦♥ ♦❢ ✽✷ ♠❡♠❜❡rs ✐♥ ✶✸ ❝♦✉♥tr✐❡s P■✿ ❙✳ ❋✳ ❙á♥❝❤❡③ ✭■❆❆✮ P❙✿ ❏✳ ❲❛❧❝❤❡r ✭❆■P✮ ❇♦❛r❞ ✭❈❤❛✐r✿ ❘✳ ❑❡♥♥✐❝✉tt → P✳ ❱✐❧❝❤❡③✮ ▼♦st❧② ②♦✉♥❣ r❡s❡❛r❝❤❡rs ✭ ∼ ✸✺ ②❡❛rs✮ Pr♦❥❡❝t st❛rt❡❞ ♦♥ ❏✉❧② ✶st ✷✵✶✵

  6. PP❆❑ ✜❜❡r ❜✉♥❞❧❡ ■❋❯ ✲ ✸✸✶ s❝✐❡♥❝❡ ✜❜❡rs ✲ ✸✻ ❞❡❞✐❝❛t❡❞ s❦② ✜❜❡rs ✲ ✷ ✼ ❞✐❛♠❡t❡r ✜❜❡rs ✲ ✷✴✸ ✜❧❧✐♥❣ ❢❛❝t♦r ❙✉r✈❡② ■♥tr♦❞✉❝t✐♦♥ ❆str♦♠❡tr✐❝ ❛♥❞ ❙♣❡❝tr♦♣❤♦t♦♠❡tr✐❝ ❝❛❧✐❜r❛t✐♦♥ ❋✐rst r❡s✉❧ts ❛♥❞ ❞❛t❛ r❡❧❡❛s❡ ❚❤❡ P▼❆❙ ✐♥t❡❣r❛❧ ✜❡❧❞ s♣❡❝tr♦❣r❛♣❤ P♦ts❞❛♠ ▼✉❧t✐ ❆♣❡rt✉r❡ ❙♣❡❝tr♦♣❤♦t♦♠❡t❡r ✭P▼❆❙✮ ✸✳✺♠ t❡❧❡s❝♦♣❡ ✭❈❛ss❡❣r❛✐♥ ❢♦❝✉s✮ ❖♣t✐♠✐③❡❞ ❢♦r ✸✺✵♥♠✲✾✵✵♥♠ ❍✐❣❤ t❤r♦✉❣❤♣✉t ≤ ✸✵ % ❊①❝❤❛♥❣❡❛❜❧❡ ❛♥❞ r♦t❛t❛❜❧❡ ❣r✐s♠s ✷ ✐♥t❡❣r❛❧ ✜❡❧❞ ✉♥✐ts ✭■❋❯s✮✿ ▲❡♥s ❆rr❛② ✶✻ × ✶✻ ❧❡♥s❧❡ts ✭✵ . ✺ ′′ s❛♠♣❧✐♥❣✮ P♠❛s ✜❜❡r P❆❝❑ ✭PP❆❑✮ ❝♦❛rs❡ ✜❜❡r ❜✉♥❞❧❡ ∼ ✶ ′ ❋✐❡❧❞ ♦❢ ❱✐❡✇ ✭❋♦❱✮ ⇒ ❆♠♦♥❣ t❤❡ ❧❛r❣❡st ■❋❯ ❋♦❱✬s

  7. ❙✉r✈❡② ■♥tr♦❞✉❝t✐♦♥ ❆str♦♠❡tr✐❝ ❛♥❞ ❙♣❡❝tr♦♣❤♦t♦♠❡tr✐❝ ❝❛❧✐❜r❛t✐♦♥ ❋✐rst r❡s✉❧ts ❛♥❞ ❞❛t❛ r❡❧❡❛s❡ ❚❤❡ P▼❆❙ ✐♥t❡❣r❛❧ ✜❡❧❞ s♣❡❝tr♦❣r❛♣❤ P♦ts❞❛♠ ▼✉❧t✐ ❆♣❡rt✉r❡ PP❆❑ ✜❜❡r ❜✉♥❞❧❡ ■❋❯ ❙♣❡❝tr♦♣❤♦t♦♠❡t❡r ✭P▼❆❙✮ ✸✳✺♠ t❡❧❡s❝♦♣❡ ✭❈❛ss❡❣r❛✐♥ ❢♦❝✉s✮ ❖♣t✐♠✐③❡❞ ❢♦r ✸✺✵♥♠✲✾✵✵♥♠ ❍✐❣❤ t❤r♦✉❣❤♣✉t ≤ ✸✵ % ❊①❝❤❛♥❣❡❛❜❧❡ ❛♥❞ r♦t❛t❛❜❧❡ ❣r✐s♠s ✷ ✐♥t❡❣r❛❧ ✜❡❧❞ ✉♥✐ts ✭■❋❯s✮✿ ▲❡♥s ❆rr❛② ✶✻ × ✶✻ ❧❡♥s❧❡ts ✭✵ . ✺ ′′ s❛♠♣❧✐♥❣✮ ✲ ✸✸✶ s❝✐❡♥❝❡ ✜❜❡rs P♠❛s ✜❜❡r P❆❝❑ ✭PP❆❑✮ ✲ ✸✻ ❞❡❞✐❝❛t❡❞ s❦② ✜❜❡rs ❝♦❛rs❡ ✜❜❡r ❜✉♥❞❧❡ ✲ ✷ . ✼ ′′ ❞✐❛♠❡t❡r ✜❜❡rs ∼ ✶ ′ ❋✐❡❧❞ ♦❢ ❱✐❡✇ ✭❋♦❱✮ ✲ ✷✴✸ ✜❧❧✐♥❣ ❢❛❝t♦r ⇒ ❆♠♦♥❣ t❤❡ ❧❛r❣❡st ■❋❯ ❋♦❱✬s

  8. ❙✉r✈❡② ■♥tr♦❞✉❝t✐♦♥ ❆str♦♠❡tr✐❝ ❛♥❞ ❙♣❡❝tr♦♣❤♦t♦♠❡tr✐❝ ❝❛❧✐❜r❛t✐♦♥ ❋✐rst r❡s✉❧ts ❛♥❞ ❞❛t❛ r❡❧❡❛s❡ ❲❛✈❡❧❡♥❣t❤ ❝♦✈❡r❛❣❡ ❢♦r ❈❆▲■❋❆ ❚✇♦ s❡t✉♣s ❛r❡ ✉s❡❞ t♦ ❝♦✈❡r t❤❡ ❡♥t✐r❡ ♦♣t✐❝❛❧ ✇❛✈❡❧❡♥❣t❤ r❛♥❣❡✿ ❤✐❣❤❡r r❡s♦❧✉t✐♦♥ ⇒ ●❛❧❛①② ❦✐♥❡♠❛t✐❝s ❢r♦♠ ❈❛ ❍✰❑ r❡❣✐♦♥ ❧♦✇❡r r❡s♦❧✉t✐♦♥ ⇒ ❙t❡❧❧❛r ♣♦♣✉❧❛t✐♦♥ ❛♥❞ ✐♦♥✐s❡❞ ❣❛s

  9. ❙✉r✈❡② ■♥tr♦❞✉❝t✐♦♥ ❆str♦♠❡tr✐❝ ❛♥❞ ❙♣❡❝tr♦♣❤♦t♦♠❡tr✐❝ ❝❛❧✐❜r❛t✐♦♥ ❋✐rst r❡s✉❧ts ❛♥❞ ❞❛t❛ r❡❧❡❛s❡ ❚❤❡ ❈❆▲■❋❆ ❣❛❧❛①② s❛♠♣❧❡ ▼♦t❤❡r s❛♠♣❧❡ ✐s ❞r❛✇♥ ❢r♦♠ ❙❉❙❙✿ ❈♦❧♦r✲▼❛❣♥✐t✉❞❡ s♣❛❝❡ ✶ ❉✐❛♠❡t❡r ❝✉ts✿ ✹✺ “ < ❉ ✷✺ < ✽✵ ′′ ⇒ ❡✛❡❝t✐✈❡ ✉s❛❣❡ ♦❢ ❋♦❱ ✷ ❘❡❞s❤✐❢t ❝✉ts✿ ✵ . ✵✵✸ < ③ < ✵ . ✵✸ ⇒ ❡①❝❧✉❞❡s ❞✇❛r❢ ❣❛❧❛①✐❡s ✾✽✼ ❣❛❧❛①✐❡s ✇✐t❤✐♥ ❙❉❙❙ ♠❛t❝❤ t❤❡s❡ ❜❛s✐❝ ❝r✐t❡r✐♦♥s ❈❆▲■❋❆ ✇✐❧❧ ♦❜s❡r✈❡ ✻✵✵ ❣❛❧❛①✐❡s✦ ❙❛♥❝❤❡③ ❡t ❛❧✳ ✷✵✶✷✱ ❆✫❆✱ ✺✸✽✱ ❆✽

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