Published May 29, 2026
| Version v1
Preprint
Open
The Dialetheic Kernel: A Substrate for Self-Referential Computation
Authors/Creators
Description
We present a machine-verified formalization of a computational substrate that does not merely tolerate paradox but operationalizes it. The paraconsistent kernel runs a three-stage Frobenius cycle (ENGAGR->FSPLIT->FFUSE) on the Belnap four-valued lattice, sustaining the dialetheic value B (both true and false) as a fixed point across arbitrarily many cycles.
Files
DIALETHEIC_KERNEL.pdf
Additional details
Related works
- Is part of
- Other: https://github.com/umpolungfish/Imscribing_Grammar.git (URL)
Dates
- Created
-
2026-05-29
Software
- Repository URL
- https://github.com/umpolungfish/MillenniumAnkh.git
- Programming language
- Lean
References
- Belnap, N. D. (1977). How a computer should think. In G. Ryle (Ed.), Contemporary Aspects of Philosophy (pp. 30–56). Oriel Press.
- Belnap, N. D. (1977). A useful four-valued logic. In J. M. Dunn & G. Epstein (Eds.), *Modern Uses of Multiple-Valued Logic* (pp. 8–37). D. Reidel.
- Priest, G. (2006). *In Contradiction: A Study of the Transconsistent* (2nd ed.). Oxford University Press.
- Riemann, B. (1859). Über die Anzahl der Primzahlen unter einer gegebenen Grösse. *Monatsberichte der Berliner Akademie*, 671–680.
- Cook, S. A. (1971). The complexity of theorem-proving procedures. In *Proceedings of the 3rd Annual ACM Symposium on Theory of Computing* (STOC '71), pp. 151–158. ACM.
- Renes, J. M., Blume-Kohout, R., Scott, A. J., & Caves, C. M. (2004). Symmetric informationally complete quantum measurements. *Journal of Mathematical Physics*, 45(6), 2171–2180.
- Yang, C. N., & Mills, R. L. (1954). Conservation of isotopic spin and isotopic gauge invariance. *Physical Review*, 96(1), 191–195.
- Jaffe, A., & Witten, E. (2000). Quantum Yang-Mills theory. In J. Carlson, A. Jaffe, & A. Wiles (Eds.), *The Millennium Prize Problems* (pp. 129–152). Clay Mathematics Institute.
- Lee, T. D., & Yang, C. N. (1952). Statistical theory of equations of state and phase transitions. I. Theory of condensation. *Physical Review*, 87(3), 404–409.
- Moura, L. de, & Ullrich, S. (2021). The Lean 4 theorem prover and programming language. In *Proceedings of the 28th International Conference on Automated Deduction* (CADE-28), LNAI 12699, pp. 625–635. Springer.
- The Mathlib Community. (2020). The Lean mathematical library. In *Proceedings of the 9th ACM SIGPLAN International Conference on Certified Programs and Proofs* (CPP 2020), pp. 367–381. ACM. Mathlib v4.28.0 used in this work.
- umpolungfish. (2024–2026). *MillenniumAnkh*. Lean 4 formalization of the Imscribing Grammar, paraconsistent kernel, and structural Millennium bridges (43+ modules, Mathlib v4.28.0). GitHub. <https://github.com/umpolungfish/MillenniumAnkh>
- umpolungfish. (2024–2026). *Imscribing_Grammar*. Primary Imscribing Grammar repository — IG catalog, genetic engine, crystal of types, ZFCₜ navigator, manuscript sources, and proof-path tooling. GitHub. <https://github.com/umpolungfish/Imscribing_Grammar>
- umpolungfish. (2024–2026). *priests-engine*. Python Imscribing Grammar engine and corpus bootstrap — 13 modules, three-way mirror between Python, categorical digital layers 26–30, and MillenniumAnkh Lean formalizations. GitHub. <https://github.com/umpolungfish/priests-engine>
- [[15]](#ref-15) Mills, L. (2026). *As Above: A Pre-Grammatical Convergent Derivation of the Universal Imscriptive Grammar*. Zenodo. <https://doi.org/10.5281/zenodo.20186611>
- Mills, L. (2026). *So Below: Empirical Exploration of the Universal Imscriptive Grammar*. Zenodo. <https://doi.org/10.5281/zenodo.20186679>
- Mills, L. (2026). *The Hecke-Landau Conjecture: A Proof and Its Architecture*. Zenodo. <https://doi.org/10.5281/zenodo.20115640>
- Mills, L. (2026). *The Lefschetz (1,1) Theorem as the First Case of the Hodge Conjecture*. Zenodo. <https://doi.org/10.5281/zenodo.20176006>
- Mills, L. (2026). *The Aether and Its Vessel — E₈ & G₂*. Zenodo. <https://doi.org/10.5281/zenodo.20032180>
- Mills, L. (2026). *A ⊙-Critical Framework for the Perfect Cuboid Problem*. Zenodo. <https://doi.org/10.5281/zenodo.20110842>
- Mills, L. (2026). *Euler's Theorem and Touchard's Congruence on Odd Perfect Numbers*. Zenodo. <https://doi.org/10.5281/zenodo.19909057>
- Mills, L. (2026). *The Voynich Engine: A Complete Technical Translation of the Voynich Manuscript into Executable IMASM Architecture*. Zenodo. <https://doi.org/10.5281/zenodo.20232872>
- Mills, L. (2026). *Proof That 10 Is Solitary*. Zenodo. <https://doi.org/10.5281/zenodo.20041211>