[Depreciated and replaced by V3] The Continuum Was the Bug: The Riemann Line, the Yang-Mills Mass Gap, and Navier-Stokes Regularity, Answered by Removing the Continuum
- 1Ernos Labs
Abstract
[Depreciated and replaced by V3] This pre-V3 paper is replaced by the corresponding V3 clean-room reconstruction: From Fold to Mathematics: An Exact, Parameter-Free and Machine-Closed Derivation of Mathematical Foundations from Smithian Fold Theory; From Fold to Physics: An Exact, Parameter-Free and Machine-Closed Reconstruction of Physical Science from Smithian Fold Theory. The V3 source platform is https://github.com/MettaMazza/ernos-labs-sft-platform. The original DOI, concept DOI, version number and files are preserved for transparent historical provenance; this record must not be presented or cited as current V3 work. One axiom. One operation. Zero free parameters. Three Clay Millennium problems — the Riemann hypothesis, the Yang–Mills mass gap, and Navier–Stokes regularity — share a hidden assumption: the continuum. This paper shows the assumption is the obstruction. With no continuum (the line replaced by the fold lattice, which has a smallest scale and no zero), each has a direct structural answer. RIEMANN: the critical line Re(s)=1/2 is the unique self-antipodal axis of the fold reflection x ↔ 1−x — the involution of the zeta functional equation — so the self-dual zeros are forced onto the half-One. YANG–MILLS: the spectrum is discrete with a positive least element (the floor 1/2^d), so a mass gap exists by construction and equals the floor. NAVIER–STOKES: the energy cascade is repeated halving that reaches the floor in finitely many folds and stops — no sub-floor scale, no blow-up. Each is the fold removing the continuum and reading off what remains (the fold-native structural answer/mechanism, not the continuum-formulation Clay proof). Machine-checked; reproduces from one command. A standalone result within the Smithian Fold Theory of Everything (SFTOE). Full corpus, code, and the run-it-yourself VERIFY.md protocol: https://github.com/MettaMazza/Smithian-Fold-Theory
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BibTeX
@article{smith2026depreciated,
title = {{[Depreciated and replaced by V3] The Continuum Was the Bug: The Riemann Line, the Yang-Mills Mass Gap, and Navier-Stokes Regularity, Answered by Removing the Continuum}},
author = {Maria Smith},
journal = {Zenodo (CERN European Organization for Nuclear Research)},
year = {2026},
month = jun,
doi = {10.5281/zenodo.21026490},
url = {https://doi.org/10.5281/zenodo.21026490},
note = {CC BY},
}
RIS
TY - JOUR
TI - [Depreciated and replaced by V3] The Continuum Was the Bug: The Riemann Line, the Yang-Mills Mass Gap, and Navier-Stokes Regularity, Answered by Removing the Continuum
AU - Maria Smith
PY - 2026
DA - 2026/06/29
JO - Zenodo (CERN European Organization for Nuclear Research)
DO - 10.5281/zenodo.21026490
UR - https://doi.org/10.5281/zenodo.21026490
AB - [Depreciated and replaced by V3] This pre-V3 paper is replaced by the corresponding V3 clean-room reconstruction: From Fold to Mathematics: An Exact, Parameter-Free and Machine-Closed Derivation of Mathematical Foundations from Smithian Fold Theory; From Fold to Physics: An Exact, Parameter-Free and Machine-Closed Reconstruction of Physical Science from Smithian Fold Theory. The V3 source platform is https://github.com/MettaMazza/ernos-labs-sft-platform. The original DOI, concept DOI, version number and files are preserved for transparent historical provenance; this record must not be presented or cited as current V3 work. One axiom. One operation. Zero free parameters. Three Clay Millennium problems — the Riemann hypothesis, the Yang–Mills mass gap, and Navier–Stokes regularity — share a hidden assumption: the continuum. This paper shows the assumption is the obstruction. With no continuum (the line replaced by the fold lattice, which has a smallest scale and no zero), each has a direct structural answer. RIEMANN: the critical line Re(s)=1/2 is the unique self-antipodal axis of the fold reflection x ↔ 1−x — the involution of the zeta functional equation — so the self-dual zeros are forced onto the half-One. YANG–MILLS: the spectrum is discrete with a positive least element (the floor 1/2^d), so a mass gap exists by construction and equals the floor. NAVIER–STOKES: the energy cascade is repeated halving that reaches the floor in finitely many folds and stops — no sub-floor scale, no blow-up. Each is the fold removing the continuum and reading off what remains (the fold-native structural answer/mechanism, not the continuum-formulation Clay proof). Machine-checked; reproduces from one command. A standalone result within the Smithian Fold Theory of Everything (SFTOE). Full corpus, code, and the run-it-yourself VERIFY.md protocol: https://github.com/MettaMazza/Smithian-Fold-Theory
ER -