yes, i think this makes more sense

daij, meikyo

On second thought, this is probably a better split. Sense 2 doesn't just have the "public ownership" meaning.

@@ -23 +23 @@
-<gloss>public (use, facility, etc.)</gloss>
+<gloss>public (use, matter, forum, etc.)</gloss>
@@ -27 +26,0 @@
-<pos>&adj-no;</pos>
@@ -30,2 +29,4 @@
-<gloss>public (matter, place, etc.)</gloss>
-<gloss>(out in the) open</gloss>
+<s_inf>as 公にする or 公になる</s_inf>
+<gloss>being public knowledge</gloss>
+<gloss>being out in the open</gloss>
+<gloss>exposure to public view</gloss>

Sense 2 is public in the 公共 sense, and sense 3 in the 表ざた sense.
I put "public place" with sense 3 because it's one of daijs's examples for that sense: "「―の場に持ち出す」". That seemed logical to me because a "public place" is simply somewhere in open view; it's not necessarily publicly *owned*, unlike a public facility.

@@ -21,0 +22,2 @@
+<xref type="ant" seq="2842390">私・わたくし・2</xref>
+<xref type="ant" seq="2842390">私・わたくし・2</xref>

the sense splitting seems odd here. should "public facility" (s2) and "public place" (s3) really be in different senses?

it seems like sense 3 should be reserved for "public" in the sense of "not secret"

whichever sense is intended to mean "not private(ly owned)" should xref to わたくし as an antonym