Chance me for math PhD admissions?

Hello! I am a current senior at a very small, unknown liberal arts college in the south. I’m a math major hoping to pursue a PhD at the top schools! I have applied and still waiting for decisions. I’m worried about admissions because I have seen A LOT of qualified (in my opinion) people get rejected from my dream schools. I plan a pure math course over applied math. Here are my stats:

White domestic female
GPA: 3.95, Major GPA: 4.0, on track for summa cum laude
Dean’s list one semester, President’s list for the rest
GRE: Q: 167 (92th percentiles) V: 165 (96th) W: 4.5 (82th)
MGRE: 165 (96th)

Research experience: individual research project spring semester freshman year (applied math), summer after freshman year research program through my university (graph theory) & continued with throughout sophomore year, REU summer after sophomore year (geometry), individual research project fall/spring/summer of junior year (topology), research in my study abroad in budapest in the spring (algebra), REU summer after junior year (cryptography), honors senior thesis fall and spring of senior year (low dimension topology).
From my research projects, I have 5 published papers and 2 pre-prints

Other: like I stated before, I attended the budapest semester in math. I’ve been tutoring math one-on-one for 3.5 years, and an ‘on call’ position for a little bit over 3.5 years. I received the Goldwater scholarship my junior year and 2 departmental scholarships from my home institution. Sophomore year I published a short (100 page) fun/weird math book and also established a math enrichment program for middle and high schoolers in the area around my university.

I believe my letters of recommendation will be very good, since my school and department is so small I have gotten to know my advisors and mentors very well. 2 letters come from research advisors from my college and 1 letter is coming from an REU where my advisor and I really connected.

Places I’m applying:
Yale (dream!!)
Berkeley
MIT
Princeton

UI Urbana Champaign
U Texas Austin
CU Boulder
Boston University
Cornell

I don’t know. I feel like my stats are good? But I know there are so many more people more accomplished than me and there are only so many spots at my top schools.

It could turn on where the professors who write your recommendations did their PhDs. Unknown small liberal Arts school is a problem. Did you participate and excel in any international math competitions?

Otherwise, your stats are strong and you should place in some PhD program, but not necessarily your top choice programs.

Just my opinion. I’m no expert

In fact all of these seem like very difficult schools to get in