Eruvin 5A

ומאן דאמר ארבעה, קסבר: אסור להשתמש תחת הקורה!

And the one who said 4 handbreadths holds that the alleyway is considered as if it were sealed from the inside edge of the cross beam, and consequently it is prohibited to utilize the area beneath the cross beam. As the area beneath the cross beam is not part of the alleyway, a significant demarcation, i.e., one of 4 handbreadths, is required within the alleyway itself.

לא, דכולי עלמא קסברי מותר להשתמש תחת הקורה, ובהא קא מיפלגי: מר סבר קורה משום היכר, ומר סבר קורה משום מחיצה.

The Talmud rejects this explanation: No, everyone agrees that it is permitted to utilize the area beneath the cross beam, and they disagree with regard to this: This Master, Rav Yosef, holds that a cross beam functions in an alleyway as a conspicuous marker that demarcates the alleyway from the public domain, and consequently a mere handbreadth is sufficient, as even a handbreadth is sufficiently conspicuous. And this Master, Abaye, holds that a cross beam serves as a partition, and a partition is not effective for an area of less than 4 handbreadths. The principle that an outer edge descends and seals the alleyway does not apply if the beam is higher than 20 cubits. In order for it to be considered a partition, there must be at least 4 handbreadths that are less than 20 cubits beneath the cross beam.

ואיבעית אימא, דכולי עלמא קורה משום היכר, והכא ⁠— בהיכר של מטה ובהיכר של מעלה קא מיפלגי, דמר סבר אמרינן היכר של מטה כהיכר של מעלה, ומר סבר לא אמרינן היכר של מטה כהיכר של מעלה.

The Talmud proposes an alternative explanation: And if you wish, say instead that everyone agrees that a cross beam serves as a conspicuous marker, and here they disagree with regard to the relationship between a conspicuous marker below, i.e., the raised area of the alleyway, and a conspicuous marker above, i.e., the cross beam. This Master, Rav Yosef, holds that we say that the halakha that governs the conspicuous marker below is like the halakha that applies to the conspicuous marker above, and one handbreadth suffices. And this Master, Abaye, holds that we do not say that the halakha that governs the conspicuous marker below is like the halakha that applies to the conspicuous marker above. The lower sign must be more prominent and extend 4 handbreadths.