Unaffiliated work. Every review lives publicly on the web, tied to a real identity.
The construction of BST is technically careful, but the claim that AFB resolves the Burali-Forti problem is overstated. The metatheoretic bound sidesteps rather than dissolves the issue — the ordinals simply don't accumulate, which is a structural choice, not a proof.
BFOL is a well-motivated restriction of first-order logic. The bounded quantifiers are introduced cleanly and the deduction system is complete relative to the stated semantics. Whether AFB constitutes a foundational alternative or merely a conservative extension is worth further scrutiny — but the technical execution is sound.
The cosmological constant argument is the strongest section. The claim that a finite momentum cutoff is motivated by AFB rather than merely compatible with it needs more work — as written, the connection is analogical, not derivational. The holographic bound discussion is more convincing.
The bounded number chain through ℂB(k⁴) is the most technically ambitious part of the paper, and it shows. Some lemmas in the complex extension are asserted without proof in the working paper version. The Isabelle scaffolds partially cover this gap but the coverage is incomplete as of this writing.
These submissions were not listed. Each one is shown here with the reason it didn't qualify — not to embarrass the submitter, but to make the moderation standard legible. The paper may be wrong; these entries simply didn't argue that it was.
This paper cannot be taken seriously. The entire mathematical community has worked with the Axiom of Infinity for over a century, and no unaffiliated author is going to overturn that. The Zermelo-Fraenkel axioms are not assumptions — they are the foundation of rigorous mathematics.
Argument from consensus and authority. Does not identify a specific error, gap, or invalid step in the paper. The paper explicitly addresses the "mainstream consensus" objection in §1.2 — this review does not engage with that response.
The ambition here is admirable but the author clearly lacks the institutional training to execute it. Real foundational work happens in peer-reviewed journals with proper oversight. A website is not a substitute for academic rigour.
Commentary on the author's credentials and publication venue rather than the paper's content. Explicitly excluded by submission criterion 04. No claim in the paper is addressed.
The physics sections are deeply confused. Renormalisation already handles the infinities in QFT perfectly well, and the standard model has been experimentally verified to extraordinary precision. There is no problem here that needs a new foundation to solve.
Asserts that renormalisation "handles" the infinities without engaging with §9.1, which explicitly addresses this objection and distinguishes procedural removal from structural resolution. The review does not respond to that distinction.
For clarity, here is what will and won't be listed — not as gatekeeping, but because vague policy produces worse outcomes for everyone.
Identifies a claim in the paper and argues it is wrong, incomplete, or insufficiently justified — with reasons.
Points to a missing lemma, an unproven step, or a transition the paper does not adequately justify.
Argues that a tradeoff the paper acknowledges is worse than stated, or identifies an unacknowledged one.
Confirms a specific result, identifies a connection the paper missed, or extends the argument in a useful direction.
"Mainstream mathematics does not work this way" is not a review — it is a restatement of the position the paper is challenging.
"I am a professor and this is wrong" without further argument tells us nothing about the paper.
A review sent privately, posted anonymously, or on a platform that cannot be linked to a real identity will not be listed.
Commentary on the author's lack of credentials, the project's ambition, or anything other than the paper itself.