The Residual Computer:A Universal Residual Architecture Based on Analytic Structure Article Swipe
We demonstrate the first universal digital computer that requires no physical hardware. Arbitrary bitstrings are encoded as localized phase pulses in the critical-line trajectory of an analytic function. The resulting residual deviation field $\delta(t)$ performs storage, retrieval, and universal computation. For the abstract two-input gate model we define the effective gate energy\[E_{\text{gate}}(a,b) = \bigl|\lambda (a + b) + \kappa (a \cdot b)\bigr| \cdot A_0,\quad a,b\in\{0,1\},\; A_0 = 5.0.\]A systematic grid search over $(\lambda, \kappa)$ reveals AND gates in 87.1\%, OR gates in 98.8\%, and XOR gates at $(\lambda, \kappa) = (-1.0, 2.0)$. Cascading these gates yields error-free half-adders, full-adders, and a 4-bit ripple-carry adder that correctly computes $7 + 9 = 16$ under Gaussian noise $\sigma = 0.2$ with 100\% fidelity in 200 trials. All operations occur within a single immutable mathematical object with zero energy cost and perfect theoretical persistence.
Related Topics
Concepts
Algorithm
Logic gate
Residual
Mathematics
Adder
Noise (video)
Energy (signal processing)
Trajectory
Gaussian
Topology (electrical circuits)
Computer science
Object (grammar)
Field (mathematics)
XOR gate
Gaussian noise
Phase (matter)
Representation (politics)
Arithmetic
Logic synthesis
Quadratic equation
Scheme (mathematics)
AND-OR-Invert
Point (geometry)
Electronic engineering
Face (sociological concept)
AND gate
Key (lock)
Grid
Metadata
- Type
- article
- Landing Page
- https://doi.org/10.5281/zenodo.17795828
- OA Status
- green
- OpenAlex ID
- https://openalex.org/W7108325632
All OpenAlex metadata
Raw OpenAlex JSON
- OpenAlex ID
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https://openalex.org/W7108325632Canonical identifier for this work in OpenAlex
- DOI
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https://doi.org/10.5281/zenodo.17795828Digital Object Identifier
- Title
-
The Residual Computer:A Universal Residual Architecture Based on Analytic StructureWork title
- Type
-
articleOpenAlex work type
- Publication year
-
2025Year of publication
- Publication date
-
2025-12-03Full publication date if available
- Authors
-
Li, Y.N.N.List of authors in order
- Landing page
-
https://doi.org/10.5281/zenodo.17795828Publisher landing page
- Open access
-
YesWhether a free full text is available
- OA status
-
greenOpen access status per OpenAlex
- OA URL
-
https://doi.org/10.5281/zenodo.17795828Direct OA link when available
- Concepts
-
Algorithm, Logic gate, Residual, Mathematics, Adder, Noise (video), Energy (signal processing), Trajectory, Gaussian, Topology (electrical circuits), Computer science, Object (grammar), Field (mathematics), XOR gate, Gaussian noise, Phase (matter), Representation (politics), Arithmetic, Logic synthesis, Quadratic equation, Scheme (mathematics), AND-OR-Invert, Point (geometry), Electronic engineering, Face (sociological concept), AND gate, Key (lock), GridTop concepts (fields/topics) attached by OpenAlex
- Cited by
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0Total citation count in OpenAlex
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| abstract_inverted_index.demonstrate | 1 |
| abstract_inverted_index.theoretical | 139 |
| abstract_inverted_index.computation. | 39 |
| abstract_inverted_index.full-adders, | 98 |
| abstract_inverted_index.half-adders, | 97 |
| abstract_inverted_index.mathematical | 131 |
| abstract_inverted_index.persistence. | 140 |
| abstract_inverted_index.ripple-carry | 102 |
| abstract_inverted_index.\bigl|\lambda | 53 |
| abstract_inverted_index.critical-line | 22 |
| abstract_inverted_index.a,b\in\{0,1\},\; | 64 |
| abstract_inverted_index.energy\[E_{\text{gate}}(a,b) | 51 |
| cited_by_percentile_year | |
| countries_distinct_count | 0 |
| institutions_distinct_count | 1 |
| citation_normalized_percentile.value | 0.90988674 |
| citation_normalized_percentile.is_in_top_1_percent | False |
| citation_normalized_percentile.is_in_top_10_percent | True |