Saved in:
| Main Author: | |
|---|---|
| Format: | Recurso digital |
| Language: | |
| Published: |
Zenodo
2026
|
| Online Access: | https://doi.org/10.5281/zenodo.18880941 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
Table of Contents:
- <p>This note is a companion to the "additive/multiplicative/spectral" vocabulary paper. Its purpose is not to develop a full theory of the triad, but to state more precisely where modern mathematics already provides strong bridges and where an obvious structural gap remains.</p> <p>We briefly recall the viewpoint encoded by the shorthand $(0,1, s)_b$ : additive neutrality (0), multiplicative neutrality (1), spectral degrees of freedom ( $s$ ), and blur $b$ as a tuning knob regulating how strongly the regimes communicate. We then argue that most existing bridges are historically routed through additive foundations: multiplication and spectral methods are typically introduced as extra structure on additive carriers (groups, rings, vector spaces, Hilbert spaces), rather than treated as coequal anchors from the start. If one takes 0,1 , and $s$ seriously as meta-level observational stances, one is naturally led to ask for native structural definitions of each regime and for bridges that do not treat addition as the universal mediator. We highlight the relative underdevelopment of the $1 \leftrightarrow s$ edge (multiplicative-spectral) and indicate a concrete template in this direction: a "continuous prime transform" program whose operational content lives on the dilation group and is spectrally diagonalized by Mellin characters, with additive linearization used only as temporary scaffolding.</p>