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  1. ■❞❡♥t✐❢②✐♥❣ ❝♦✲♠❡t❤②❧❛t❡❞ ❣❡♥♦♠✐❝ r❡❣✐♦♥s✿ ❛♥ ▼❉▲ ❛♣♣r♦❛❝❤ ❙❛r♥❛s❡❧t ♠❡tü❧❡❡r✐t✉❞ ❉◆❆ ♣✐✐r❦♦♥❞❛❞❡ t✉✈❛st❛♠✐♥❡ ❑❛s♣❛r ▼ärt❡♥s ❙✉♣❡r✈✐s♦r✿ ❘❛✐✈♦ ❑♦❧❞❡ ✶✼ ❉❡❝❡♠❜❡r ✷✵✶✷ ❑❛s♣❛r ▼ärt❡♥s ■❞❡♥t✐❢②✐♥❣ ❝♦✲♠❡t❤②❧❛t❡❞ ❣❡♥♦♠✐❝ r❡❣✐♦♥s

  2. ❚❤❡ ▼✐♥✐♠✉♠ ❉❡s❝r✐♣t✐♦♥ ▲❡♥❣t❤ ✭▼❉▲✮ Pr✐♥❝✐♣❧❡ ✐s ❜❛s❡❞ ♦♥ t❤❡ ✐♥s✐❣❤t t❤❛t ❛♥② r❡❣✉❧❛r✐t② ✐♥ t❤❡ ❞❛t❛ ❝❛♥ ❜❡ ✉s❡❞ t♦ ❝♦♠♣r❡ss t❤❡ ❞❛t❛✳ ❲❡ ✐♥tr♦❞✉❝❡ t❤❡ t❡r♠ ❞❡s❝r✐♣t✐♦♥ ❧❡♥❣t❤ ✱ ❞❡♥♦t❡❞ ❜② ▲ ✱ t❤❛t r❡♣r❡s❡♥ts t❤❡ ♥✉♠❜❡r ♦❢ ❜✐ts ♥❡❡❞❡❞ t♦ ❞❡s❝r✐❜❡ ❛♥ ♦❜❥❡❝t✳ ❙♦✱ ❝♦♠♣r❡ss✐♥❣ t❤❡ ❞❛t❛ ♠❡❛♥s t❤❛t ✇❡ ❝❛♥ ❞❡s❝r✐❜❡ t❤❡ ❞❛t❛ ✉s✐♥❣ ❧❡ss ❜✐ts✳ ❚❤❡ ▼❉▲ ♣r✐♥❝✐♣❧❡ t❡❧❧s ✉s t❤❛t✱ ❢♦r ❛ ❣✐✈❡♥ s❡t ♦❢ ♠♦❞❡❧s ❛♥❞ ❞❛t❛ ❉ ✱ ✇❡ s❤♦✉❧❞ ❝❤♦♦s❡ t❤❡ ♠♦❞❡❧ ▼ t❤❛t ❝♦♠♣r❡ss❡s ❉ ♠♦st✳ ❙♦ t❤✐s ♣r✐♥❝✐♣❧❡ ❝❛♥ ❜❡ ✉s❡❞ ❢♦r ♠♦❞❡❧ s❡❧❡❝t✐♦♥ ❛♥❞ ✇✐❧❧ ❜❡ ✐♥ t❤✐s r❡♣♦rt✳ ❚❤❡ ▼❉▲ ♣r✐♥❝✐♣❧❡ ❑❛s♣❛r ▼ärt❡♥s ■❞❡♥t✐❢②✐♥❣ ❝♦✲♠❡t❤②❧❛t❡❞ ❣❡♥♦♠✐❝ r❡❣✐♦♥s

  3. ❲❡ ✐♥tr♦❞✉❝❡ t❤❡ t❡r♠ ❞❡s❝r✐♣t✐♦♥ ❧❡♥❣t❤ ✱ ❞❡♥♦t❡❞ ❜② ▲ ✱ t❤❛t r❡♣r❡s❡♥ts t❤❡ ♥✉♠❜❡r ♦❢ ❜✐ts ♥❡❡❞❡❞ t♦ ❞❡s❝r✐❜❡ ❛♥ ♦❜❥❡❝t✳ ❙♦✱ ❝♦♠♣r❡ss✐♥❣ t❤❡ ❞❛t❛ ♠❡❛♥s t❤❛t ✇❡ ❝❛♥ ❞❡s❝r✐❜❡ t❤❡ ❞❛t❛ ✉s✐♥❣ ❧❡ss ❜✐ts✳ ❚❤❡ ▼❉▲ ♣r✐♥❝✐♣❧❡ t❡❧❧s ✉s t❤❛t✱ ❢♦r ❛ ❣✐✈❡♥ s❡t ♦❢ ♠♦❞❡❧s ❛♥❞ ❞❛t❛ ❉ ✱ ✇❡ s❤♦✉❧❞ ❝❤♦♦s❡ t❤❡ ♠♦❞❡❧ ▼ t❤❛t ❝♦♠♣r❡ss❡s ❉ ♠♦st✳ ❙♦ t❤✐s ♣r✐♥❝✐♣❧❡ ❝❛♥ ❜❡ ✉s❡❞ ❢♦r ♠♦❞❡❧ s❡❧❡❝t✐♦♥ ❛♥❞ ✇✐❧❧ ❜❡ ✐♥ t❤✐s r❡♣♦rt✳ ❚❤❡ ▼❉▲ ♣r✐♥❝✐♣❧❡ ❚❤❡ ▼✐♥✐♠✉♠ ❉❡s❝r✐♣t✐♦♥ ▲❡♥❣t❤ ✭▼❉▲✮ Pr✐♥❝✐♣❧❡ ✐s ❜❛s❡❞ ♦♥ t❤❡ ✐♥s✐❣❤t t❤❛t ❛♥② r❡❣✉❧❛r✐t② ✐♥ t❤❡ ❞❛t❛ ❝❛♥ ❜❡ ✉s❡❞ t♦ ❝♦♠♣r❡ss t❤❡ ❞❛t❛✳ ❑❛s♣❛r ▼ärt❡♥s ■❞❡♥t✐❢②✐♥❣ ❝♦✲♠❡t❤②❧❛t❡❞ ❣❡♥♦♠✐❝ r❡❣✐♦♥s

  4. ❙♦✱ ❝♦♠♣r❡ss✐♥❣ t❤❡ ❞❛t❛ ♠❡❛♥s t❤❛t ✇❡ ❝❛♥ ❞❡s❝r✐❜❡ t❤❡ ❞❛t❛ ✉s✐♥❣ ❧❡ss ❜✐ts✳ ❚❤❡ ▼❉▲ ♣r✐♥❝✐♣❧❡ t❡❧❧s ✉s t❤❛t✱ ❢♦r ❛ ❣✐✈❡♥ s❡t ♦❢ ♠♦❞❡❧s ❛♥❞ ❞❛t❛ ❉ ✱ ✇❡ s❤♦✉❧❞ ❝❤♦♦s❡ t❤❡ ♠♦❞❡❧ ▼ t❤❛t ❝♦♠♣r❡ss❡s ❉ ♠♦st✳ ❙♦ t❤✐s ♣r✐♥❝✐♣❧❡ ❝❛♥ ❜❡ ✉s❡❞ ❢♦r ♠♦❞❡❧ s❡❧❡❝t✐♦♥ ❛♥❞ ✇✐❧❧ ❜❡ ✐♥ t❤✐s r❡♣♦rt✳ ❚❤❡ ▼❉▲ ♣r✐♥❝✐♣❧❡ ❚❤❡ ▼✐♥✐♠✉♠ ❉❡s❝r✐♣t✐♦♥ ▲❡♥❣t❤ ✭▼❉▲✮ Pr✐♥❝✐♣❧❡ ✐s ❜❛s❡❞ ♦♥ t❤❡ ✐♥s✐❣❤t t❤❛t ❛♥② r❡❣✉❧❛r✐t② ✐♥ t❤❡ ❞❛t❛ ❝❛♥ ❜❡ ✉s❡❞ t♦ ❝♦♠♣r❡ss t❤❡ ❞❛t❛✳ ❲❡ ✐♥tr♦❞✉❝❡ t❤❡ t❡r♠ ❞❡s❝r✐♣t✐♦♥ ❧❡♥❣t❤ ✱ ❞❡♥♦t❡❞ ❜② ▲ ( · ) ✱ t❤❛t r❡♣r❡s❡♥ts t❤❡ ♥✉♠❜❡r ♦❢ ❜✐ts ♥❡❡❞❡❞ t♦ ❞❡s❝r✐❜❡ ❛♥ ♦❜❥❡❝t✳ ❑❛s♣❛r ▼ärt❡♥s ■❞❡♥t✐❢②✐♥❣ ❝♦✲♠❡t❤②❧❛t❡❞ ❣❡♥♦♠✐❝ r❡❣✐♦♥s

  5. ❚❤❡ ▼❉▲ ♣r✐♥❝✐♣❧❡ t❡❧❧s ✉s t❤❛t✱ ❢♦r ❛ ❣✐✈❡♥ s❡t ♦❢ ♠♦❞❡❧s ❛♥❞ ❞❛t❛ ❉ ✱ ✇❡ s❤♦✉❧❞ ❝❤♦♦s❡ t❤❡ ♠♦❞❡❧ ▼ t❤❛t ❝♦♠♣r❡ss❡s ❉ ♠♦st✳ ❙♦ t❤✐s ♣r✐♥❝✐♣❧❡ ❝❛♥ ❜❡ ✉s❡❞ ❢♦r ♠♦❞❡❧ s❡❧❡❝t✐♦♥ ❛♥❞ ✇✐❧❧ ❜❡ ✐♥ t❤✐s r❡♣♦rt✳ ❚❤❡ ▼❉▲ ♣r✐♥❝✐♣❧❡ ❚❤❡ ▼✐♥✐♠✉♠ ❉❡s❝r✐♣t✐♦♥ ▲❡♥❣t❤ ✭▼❉▲✮ Pr✐♥❝✐♣❧❡ ✐s ❜❛s❡❞ ♦♥ t❤❡ ✐♥s✐❣❤t t❤❛t ❛♥② r❡❣✉❧❛r✐t② ✐♥ t❤❡ ❞❛t❛ ❝❛♥ ❜❡ ✉s❡❞ t♦ ❝♦♠♣r❡ss t❤❡ ❞❛t❛✳ ❲❡ ✐♥tr♦❞✉❝❡ t❤❡ t❡r♠ ❞❡s❝r✐♣t✐♦♥ ❧❡♥❣t❤ ✱ ❞❡♥♦t❡❞ ❜② ▲ ( · ) ✱ t❤❛t r❡♣r❡s❡♥ts t❤❡ ♥✉♠❜❡r ♦❢ ❜✐ts ♥❡❡❞❡❞ t♦ ❞❡s❝r✐❜❡ ❛♥ ♦❜❥❡❝t✳ ❙♦✱ ❝♦♠♣r❡ss✐♥❣ t❤❡ ❞❛t❛ ♠❡❛♥s t❤❛t ✇❡ ❝❛♥ ❞❡s❝r✐❜❡ t❤❡ ❞❛t❛ ✉s✐♥❣ ❧❡ss ❜✐ts✳ ❑❛s♣❛r ▼ärt❡♥s ■❞❡♥t✐❢②✐♥❣ ❝♦✲♠❡t❤②❧❛t❡❞ ❣❡♥♦♠✐❝ r❡❣✐♦♥s

  6. ❙♦ t❤✐s ♣r✐♥❝✐♣❧❡ ❝❛♥ ❜❡ ✉s❡❞ ❢♦r ♠♦❞❡❧ s❡❧❡❝t✐♦♥ ❛♥❞ ✇✐❧❧ ❜❡ ✐♥ t❤✐s r❡♣♦rt✳ ❚❤❡ ▼❉▲ ♣r✐♥❝✐♣❧❡ ❚❤❡ ▼✐♥✐♠✉♠ ❉❡s❝r✐♣t✐♦♥ ▲❡♥❣t❤ ✭▼❉▲✮ Pr✐♥❝✐♣❧❡ ✐s ❜❛s❡❞ ♦♥ t❤❡ ✐♥s✐❣❤t t❤❛t ❛♥② r❡❣✉❧❛r✐t② ✐♥ t❤❡ ❞❛t❛ ❝❛♥ ❜❡ ✉s❡❞ t♦ ❝♦♠♣r❡ss t❤❡ ❞❛t❛✳ ❲❡ ✐♥tr♦❞✉❝❡ t❤❡ t❡r♠ ❞❡s❝r✐♣t✐♦♥ ❧❡♥❣t❤ ✱ ❞❡♥♦t❡❞ ❜② ▲ ( · ) ✱ t❤❛t r❡♣r❡s❡♥ts t❤❡ ♥✉♠❜❡r ♦❢ ❜✐ts ♥❡❡❞❡❞ t♦ ❞❡s❝r✐❜❡ ❛♥ ♦❜❥❡❝t✳ ❙♦✱ ❝♦♠♣r❡ss✐♥❣ t❤❡ ❞❛t❛ ♠❡❛♥s t❤❛t ✇❡ ❝❛♥ ❞❡s❝r✐❜❡ t❤❡ ❞❛t❛ ✉s✐♥❣ ❧❡ss ❜✐ts✳ ❚❤❡ ▼❉▲ ♣r✐♥❝✐♣❧❡ t❡❧❧s ✉s t❤❛t✱ ❢♦r ❛ ❣✐✈❡♥ s❡t ♦❢ ♠♦❞❡❧s M ❛♥❞ ❞❛t❛ ❉ ✱ ✇❡ s❤♦✉❧❞ ❝❤♦♦s❡ t❤❡ ♠♦❞❡❧ ▼ ∈ M t❤❛t ❝♦♠♣r❡ss❡s ❉ ♠♦st✳ ❑❛s♣❛r ▼ärt❡♥s ■❞❡♥t✐❢②✐♥❣ ❝♦✲♠❡t❤②❧❛t❡❞ ❣❡♥♦♠✐❝ r❡❣✐♦♥s

  7. ❚❤❡ ▼❉▲ ♣r✐♥❝✐♣❧❡ ❚❤❡ ▼✐♥✐♠✉♠ ❉❡s❝r✐♣t✐♦♥ ▲❡♥❣t❤ ✭▼❉▲✮ Pr✐♥❝✐♣❧❡ ✐s ❜❛s❡❞ ♦♥ t❤❡ ✐♥s✐❣❤t t❤❛t ❛♥② r❡❣✉❧❛r✐t② ✐♥ t❤❡ ❞❛t❛ ❝❛♥ ❜❡ ✉s❡❞ t♦ ❝♦♠♣r❡ss t❤❡ ❞❛t❛✳ ❲❡ ✐♥tr♦❞✉❝❡ t❤❡ t❡r♠ ❞❡s❝r✐♣t✐♦♥ ❧❡♥❣t❤ ✱ ❞❡♥♦t❡❞ ❜② ▲ ( · ) ✱ t❤❛t r❡♣r❡s❡♥ts t❤❡ ♥✉♠❜❡r ♦❢ ❜✐ts ♥❡❡❞❡❞ t♦ ❞❡s❝r✐❜❡ ❛♥ ♦❜❥❡❝t✳ ❙♦✱ ❝♦♠♣r❡ss✐♥❣ t❤❡ ❞❛t❛ ♠❡❛♥s t❤❛t ✇❡ ❝❛♥ ❞❡s❝r✐❜❡ t❤❡ ❞❛t❛ ✉s✐♥❣ ❧❡ss ❜✐ts✳ ❚❤❡ ▼❉▲ ♣r✐♥❝✐♣❧❡ t❡❧❧s ✉s t❤❛t✱ ❢♦r ❛ ❣✐✈❡♥ s❡t ♦❢ ♠♦❞❡❧s M ❛♥❞ ❞❛t❛ ❉ ✱ ✇❡ s❤♦✉❧❞ ❝❤♦♦s❡ t❤❡ ♠♦❞❡❧ ▼ ∈ M t❤❛t ❝♦♠♣r❡ss❡s ❉ ♠♦st✳ ❙♦ t❤✐s ♣r✐♥❝✐♣❧❡ ❝❛♥ ❜❡ ✉s❡❞ ❢♦r ♠♦❞❡❧ s❡❧❡❝t✐♦♥ ❛♥❞ ✇✐❧❧ ❜❡ ✐♥ t❤✐s r❡♣♦rt✳ ❑❛s♣❛r ▼ärt❡♥s ■❞❡♥t✐❢②✐♥❣ ❝♦✲♠❡t❤②❧❛t❡❞ ❣❡♥♦♠✐❝ r❡❣✐♦♥s

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