Similarities and differences between positive and negative particle masses in the bicubic equation limiting particle velocity formalism: positive or negative muon neutrino mass?
Bibliographic record
Abstract
Here, rather detailed numerical comparisons of energies and momenta for$\ $\ positive $m_{+}=m\succ 0$ \ and negative \ $m_{-}=-m\prec 0$ \ \particle masses with $m_{+}^{2}=m_{-}^{2}=$ $m^{2}$ , within the bicubic equation limiting particle velocity formalism with three particle limiting velocities $c_{1},$ $c_{2}$\ and $c_{3}$, are done. Already these limiting velocities, on a global scale, can differentiate positive, $m_{+}$ and negative \ $m_{-}$ particle masses. While $c_{1}(m_{+})$, $c_{2}(m_{+})$ and $c_{3}(m_{+})$ are real, imaginary and real, corresponding, respectively, to primary, obscure and normal particles; $c_{1}(m_{-})$, $c_{2}(m_{-})$ and $% c_{3}(m_{-})$ are respectively imaginary, real and real, now representing respectively, obscure, primary and normal particles. In fact, from limiting velocity solutions, one identifies: $c_{1}^{2}(m_{+})=$ $% c_{2}^{2}(m_{-}),c_{1}^{2}(m_{-})=c_{2}^{2}(m_{+})$, $c_{3}^{2}(m_{-})=$ $% c_{3}^{2}(m_{+})$.\ \ The unified particle mass-shell like forms with particle energies and momenta are readily expressible for $m_{+}=m\succ 0$ and $m_{-}=-m\prec 0$ masses with respective limiting velocities, separating $c_{3}(m_{+})$ from $c_{3}(m_{-})$ as well as $c_{1}(m_{+})$ from $% c_{1}(m_{-})$ and $c_{2}(m_{+})$ from $c_{2}(m_{-}).$ We assume that flavor neutrinos, which, while in process do not change flavor, belong to normal limiting velocity $c_{3}$ class. Then the muon neutrino from OPERA velocity measurement should maintain the same velocity squares $v^{2}$ and $c_{3}^{2}$ when one changes the positive neutrino mass $% m_{+\nu }\left( \mu \right) \succ 0$ into the negative neutrino mass $% m_{-\nu }\left( \mu \right) \prec 0$ , since theoretically $% c_{3}^{2}(m_{+\nu }(\mu ))=c_{3}^{2}(m_{-\nu }(\mu ))$. For OPERA measurements this is verified perturbatively by simultaneously evaluating squares of normal limiting velocities with $m_{+\nu }(\mu )$ and $m_{-\nu }(\mu )$ masses, yielding the same result $c_{3}^{2}(m_{+\nu }(\mu )=c_{3}^{2}(m_{-\nu }(\mu )\simeq v_{\nu }^{2}\left( \mu \right) \simeq c^{2} $.
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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 | 0.001 | 0.002 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.005 | 0.001 |
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".