On the Universal Presence of Mathematics for Incompletely Predictable Problems in Rigorous Proofs for Riemann Hypothesis, Modified Polignac’s and Twin Prime Conjectures
Bibliographic record
Abstract
We validly ignore even prime number 2. Based on all arbitrarily large number of even Prime gaps 2, 4, 6, 8, 10...; the complete set and its derived subsets of Odd Primes fully comply with the Prime number theorem for Arithmetic Progressions, and our derived Generic Squeeze theorem and Theorem of Divergent-to-Convergent series conversion for Prime numbers. With these conditions being satisfied by all Odd Primes, we argue Polignac's and Twin prime conjectures are proven to be true when they are usefully treated as Incompletely Predictable Problems. In so doing [and with Riemann hypothesis being a special case], this action also support the generalized Riemann hypothesis formulated for Dirichlet L-function. By broadly applying Hodge conjecture, Grothendieck period conjecture and Pi-Circle conjecture to Dirichlet eta function (proxy function for Riemann zeta function), Riemann hypothesis is separately proven to be true when it is usefully treated as Incompletely Predictable Problem. Crucial connections exist between these Incompletely Predictable Problems and Quantum field theory whereby eligible (sub-)functions and (sub-)algorithms are treated as infinite series.
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How this classification was reachedexpand
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 | 0.013 | 0.010 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.000 | 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, 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".