A Proof of Goldbach Conjecture by Mirror Prime Decomposition
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Bibliographic record
Abstract
This work presents a formal proof of Goldbach conjecture based on a novel theory of Mirror-Prime Decomposition (MPD) for arbitrary even integers. A new concept of mirror primes is introduced as a set of pairs of primes that are symmetrically adjacent to any pivotal even number on both sides in finite distance k bounded by 1 k (ne/2) -2. As a counterpart of the Euclidean Fundamental Theorem of Arithmetic for natural number factorization, the MPD theory enables arbitrary even number decomposition by mirror primes. MPD paves a way to prove the Goldbach conjecture, i.e., where denoted by the big-R calculus for representing recursive structures and manipulating recursive functions. An algorithm of Goldbach conjecture testing is designed for demonstrating the formal proof of the Goldbach theorem. i.e where denoted by the big-R calculus for representing recursive structures and manipulating recursive functions. An algorithm of Goldbach conjecture testing is designed for demonstrating the formal proof of the Goldbach theorem.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it