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Foundational model

Irreducible directions and quotient geometry

The abstract multiplicative-geometric critical model that precedes the prime-specialized branches.

Framework stages

01
Irreducible directions
Factorization becomes a coordinate system.
02
Logarithmic height
\(\lambda_p=\log p\)
03
Quotient geometry
\(w=\log(n/m)\)
04
Native / observed ledger
Two ledgers on a common support.
05
Discrepancy
Retained obstruction class.
06
Transport
Aligned and nonaligned propagation.
07
Terminal readout
Contradiction or positivity.
\[n=\prod_p p^{v_p(n)},\qquad L(n)=\sum_p v_p(n)\log p,\qquad w=\log(n/m).\]

Foundational role in the corpus

The foundational model supplies the abstract multiplicative-geometric critical stage. It is the starting point for the later prime specialization, arithmetic fibres and branch-specific terminal mechanisms.

Cite this work

10.5281/zenodo.19000684

@misc{gotanegra2026foundational,
  author       = {Jaume Gotanegra},
  title        = {Internal critical-line alignment in multiplicative geometric models},
  year         = {2026},
  month        = {Mar},
  doi          = {10.5281/zenodo.19000684},
  url          = {https://doi.org/10.5281/zenodo.19000684},
  note         = {Preprint}
}
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