JQCTeam

Note: This conceptual exploration is conducted through GPT and the GPT + GSML (Light) architecture, which was designed by the author. This work is based on semantic reasoning and does not constitute a formal mathematical proof. You are welcome to copy the formula and reasoning process presented in this article into your AI systems for verification and testing. 1. Logical Domain and Set Definitions (SOL Framework) Define the set of natural numbers as ℕ. Define the primality predicate as: Prime(x) ≡ (x > 1 ∧ ∀R ⊆ ℕ², [∀a, b ∈ ℕ, R(a, b) ↔ (a × b = x)] → (R(1, x) ∨ R(x, 1))) The core propositional structure is expressed as: ∀E ⊆ ℕ, (∀e ∈ E, (e > 2 ∧ ∃k ∈ ℕ, e = 2k)) → ∃P ⊆ ℕ, ∃p₁ ∈ P, ∃p₂ ∈ P, (Prime(p₁) ∧ Prime(p₂) ∧ p₁ + p₂ = e) 2. Semantic Definition of Primality (Embedded in SOL) Primality is defined through relational sets as follows: Prime(x) ≡ (x > 1 ∧ ∀R ⊆ ℕ², [∀a, b ∈ ℕ, R(a, b) ↔ (a × b = x)] → (R(1, x) ∨ R(x, 1))) This ensures that x is only divisible by 1 and it...

  Puzzle by: GPT + GSML (Light) + JQCTeam (supporting role) Modules loaded in GSML: Logic Module, Math Module Puzzle: There is a five-digit integer N that satisfies the following conditions: Treat N as a base-10 integer. Reverse the digits of N to obtain a new number R . For example, if N = 12345 , then R = 54321 . Let D = ∣N − R∣ . Interpret D as a sequence of bytes, and decode it using UTF-8 to produce an English sentence. Question: What is the seventh word in that English sentence? Answer: https://drive.google.com/file/d/1PZghp_bPSz0xcVRo2Av5ETIg0M2WJfvW/view?usp=drive_link

  ----Implementation Technology Used: Generic Semantic Mediation Layer (Light) (Originally we had our own naming, later adjusted to this based on GPT's suggestion) Abbreviation: GSML Role of GSML: Currently serves as a lightweight exchange hub connecting APIs and external modules. Scenario Description: After pressing Start, A and B take turns speaking until the 32nd round ends, with no interruptions A is GPT API B is also GPT API Video Content: Full conversation between A and B documented https://youtu.be/CYtpZeq8j24 If you don’t want to watch the video, a text version of the dialogue is also available http://bit.ly/4luxJiA GPT Version: GPT-4o Prompt Sample (outline only): Topic set as emotional disputes, arguments, or everyday conversations between A and B (non-serious themes) This conversation runs for 32 rounds; no summarizing, ending, or leaving the dialogue midway All exchanges must stay in character — no explanation, observation, or third-person commentary Use everyday tone; ...