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Number-Theoretic Conjectures

Number-Theoretic Conjectures

This page only routes: three lines of research about the integers — Goldbach's conjecture (the reverse-structure closure program, 77 documents in three sub-series), Legendre's conjecture (the base-space prime-fitting operator program, the Program plus Phases 1–32) and the perfect cuboid (rational points, elliptic curves on a fixed slice and bounded exact searches, plus Radical-FDRS and four method lines). The actual content of each line is on its own pages. None of the lines claims to prove its conjecture, and none claims to have found or excluded a counterexample; their own pages say item by item what they did and did not do, which figures were reproduced and which were corrected by later papers. The Collatz conjecture is a separate case (the Collatz conjecture); the Riemann hypothesis, BSD and the others are under the seven great conjectures.

The author lines of the three lines differ: Goldbach and its three sub-series read 'Neo.K; Aletheia (GPT-5.6 Sol)' (some documents are unsigned); Legendre reads 'Neo.K × AI collaboration' without naming any AI; the perfect-cuboid documents almost all have no author line (TIFV reads 'Neo.K / EveMissLab'). This site presents them as the originals state and does not guess who directed and who executed. The selected pages of these three cases load the original text in full (Traditional Chinese with English terminology; on English pages the title, abstract and claim statement are translated into English while the full-text translation is not finished).