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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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.002 | 0.007 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.002 | 0.005 |
| Scholarly communication | 0.002 | 0.006 |
| Open science | 0.001 | 0.005 |
| Research integrity | 0.001 | 0.004 |
| Insufficient payload (model declined to judge) | 0.010 | 0.002 |
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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".