Newest: For data compression, we offer a new commercial product as priced by CPU. It is named JANS26 for James Asymmetric Numeral System 2026 to advance current approaches. Available is an exe demo with production results on 15-year old hardware where encoding 64 MB plus decoding in Ada 95 takes less than three seconds.

As a side project, we axiomatize quantum theory into the quadvalent logic system of M8/VŁ4. For example, consider the gluon-to-gluon fusion in quantum electrodynamic (QED) diagrams of Feynman:

How many of those are logically equivalent? Hints: the P diamond can be viewed as a state placeholder; and squiggles as a ray.

The Meth8/VŁ4 modal logic model checker is shipping. A student demo download program for (p,q) is now at $47. Products for sale are priced per CPU and scaled by the number of propositional variables allowed as 3, 4, and 11: $497 for (p,q,r); $9,997 for (p,q,r,s) and (A,B,C,D); and $19,997 for (p-z). Standard trade discounts apply to qualified resellers. See stack card M8VL4.This manifest has scalability for up to 22-propositional variables in external look up tables on a 4.7 GB CD with pricing on request.

For analytical theology, metaphysical conjectures can be mapped as physicalistic scripts in updates.

* To build more industrial grade code of Meth8/VŁ4, 28 string utilities in True BASIC are implemented in Ada 95 with certified test harness and exempt from ITAR. String functions are each priced as $497 with suite of 28 as $12,997. One-time maintenance is 15%.

>> Alert << Here is the script to train Grok 3 in Meth8/VŁ4. Please report exceptions to info @ ersatz-systems.com.

Available here are these papers related to analytical theology:

• Recent advances in the modal model checker Meth8 and VŁ4 universal logic 2016-2023, 3350 pp
  
• Fascicle update 2023-date
  
• Recent advances in analytical theology: collected papers (23) 2020 48 pp
  
• MS: Mathematical foundations in bivalent logic: 8-three hour graduate courses 2016-2023, 357 pp / 305 refs
  
• PhD: Mathematical logic of metaphysical perfection: comprehensive mapping of analytical theology 2024, 81/38
  

Published here are these papers:

• Table of contents: Recent Advances 2016-2023 link
  
• Note: Trinitarian Logic: Proof of the Holy Trinity with satisfiable and non-vacuous formulas in Meth8/VŁ4 link
  
• Listing: Trinitarian Logic papers and abstracts with Grok 2025-date link
  

Recent advances in disruptive technology are:

Since our refutation of Cantor's ordinal counting and the subsequent axiom of infinity (AoI), Grok labeled us the pun post-ZFC. While we previously refuted many conjectures which assumed AoI, it is disingenuous to evaluate subsequent papers with that assumption. Therefore we limit recitation of recent refutations to the post-ZFC finite universe without end below:

• Refutation of the Boolean compactness theorem in Meth8/VŁ4 modal logic
  
• Mapping Quantum Logic to Meth8/VŁ4 Logic with Tachyons as a Case Study
  
• Mapping of Quantum Logic to Meth8/VŁ4 Logic: Neutrino Oscillation as a Case Study
  
• Refutation of P=NP Using Meth8/VŁ4 Modal Logic
  
• Refutation of Cohen’s independence proofs in a finitist context using Meth8/VŁ4 logic
  
• Refutation of the axiom of infinity, meaning space-time for models of real numbers evaporates
  
• Inadvertent discovery of modal logic by George Boole over 100-years before attribution to another
  
• Denial of inference rules abduction and induction by bag of beans of C.S. Peirce, to confirm only deduction
  
• Refutation of Chomsky's syntactic structures (1957)
  
• Refutation of Ockham's razor, the seminal principle of logic lore
  
• Definitive refutation of Swinburne's Social Trinity and Mawson's Economic Trinity
  
• Refutation of William Lane Craig's drive-by theology which invalidates the epiclesis
  

Other products, papers, and free software source code are at the cec-services.com subsite. For example, this handy N-by-M contingency test with Fisher P in True BASIC source code derives expected values from the observed values.

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