Hahaha gosh ππππβ¨β¨β¨β¨
But it's amazing how touching it was that his emotions convinced her! But at the same time it's so funny he's so stressed and in a rage, and that's what makes her go:
So she spoke, and made trial of her husband. But Odysseus, in a burst of anger, spoke to his true-hearted wife, and said: βWoman, truly this is a bitter word that thou hast spoken. Who has set my bed elsewhere? Hard would it be for one, [185] though never so skilled, unless a god himself should come and easily by his will set it in another place. But of men there is no mortal that lives, be he never so young and strong, who could easily pry it from its place, for a great token is wrought in the fashioned bed, and it was I that built it and none other.
Hom.Od.23.181-189
So everyone loves the moment of recognition between Penelope and Odysseus and how Penelope basically "forces the true Odysseus" come out with her own trick. Many believe that the recognition happens because of the detailed account of how he made the bed and how it was the secret only a few knew but in my opinion this is not 100% true.
Penelope did not recognize her husband because he analyzed their secret; she recognized him because of his reaction.
Odysseus replied "in a burst of anger". He is exaspirated, afraid, worried and surprised. That is the husband she wants to see; the husband who wants nothing else but his home, his roots and his wife. Anyone could reveal to any mortal the secret of her bed; from one of the servants till one of the gods but there is one thing no one can fake;
The GENUINE emotion. Odysseus replied so immediately and so abruptly in such a genuine emotion that left Penelope no doubt yet that this was her husband. Odysseus didn't just ask her how it is possible to move the bed; he asked her in ANGER a genuine exaspiration and disbelief. No actor or god could mimic that genuine emotion. Odysseus spent about half his time in Ithaca hiding his emotions so he would survive. At that moment of the mention of moving the imovable bed his emotions just showed.
The sign she recognized was not the information he gave her it was his heart.