The paper generalizes a static non-derivability result to rule sets that evolve in time, argues that no countable theory of everything can exist, and asserts, without a visible derivation, that the same pattern forces P≠NP.
Syntactic Separation Implies Computational Indistinguishability: An Abstract Obstruction Theorem
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abstract
We prove that syntactic separation implies computational indistinguishability. A local syntactic system R acts on terms within radius r0 without consulting any model; when two Skolem functions are syntactically separated in R, no derivation can prove their equivalence (Case 1), and any sound local extension requires Omega(n) steps, improving to Omega(2^n) under clause-per-configuration encoding (Case 2). Both bounds are new: the derivation-length lower bound does not appear in prior work on Skolemization or saturation proving, and the cryptographic reading, syntactic separation as ciphertext indistinguishability, derivation cost as negligible advantage, is original. The same obstruction, as formal instances of Case 1 and Case 2, governs the Natural Proofs barrier of Razborov and Rudich, the Type Omitting Theorem, and the unconditional AC^0 barrier of Loff et al. (2026).
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What Syntax Cannot See: The Dynamic Syntactic Invariance Principle and Several Instances of the Same Hidden Assumption, and a Contradiction
The paper generalizes a static non-derivability result to rule sets that evolve in time, argues that no countable theory of everything can exist, and asserts, without a visible derivation, that the same pattern forces P≠NP.