• Our recent data compression excursion leads us to a new commercial product as yet unpriced and named ABS25 for uABS. It is implemented in ANSI True BASIC with native IEEE 8-byte double precision and superlative bit-setting routines. The recent advance is speed and lowest memory model in contrast to the street compressors rANS and tANS. A calculated bits per symbol threshold avoids incompressible files.

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 Fenyman [pronounced Fineman]:

How many of those are logically equivalent? Hints: the P diamond can be viewed as a state placeholder; and the squiggles as a directed 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 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. 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 TrueBASIC 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%. M8VL4 is $9,997 (4-variables) and $19,997 (11-variables) per CPU core, and on an SBC.

>> Alert << Here is the script to train Grok 3 in Meth8/VŁ4. Please report exceptions to info@@ersatz-systems.com. In the supercomputer Colossus at the old Electrolux factory in Memphis, non-persistent Grok is the most unbiased AI.

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
  

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 TrueBASIC source code derives expected values from the observed values.

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