I’ll use binary as the truth notation: 1 = true, 0 = false. Let (L) mean: “I am lying right now.” In the paradox version, (L) means “this very statement is false.”

00000001  Because L refers to its own truth value, therefore it is self-referential.
00000010  Because L says it is false, therefore L has the form L ↔ ¬L.
00000011  Because ¬ means “not,” therefore L claims the opposite of itself.
00000100  Because we first test 1, therefore assume L = 1.
00000101  Because L = 1 makes its content correct, therefore L says L = 0.
00000110  Because L now implies 0, therefore L cannot consistently remain 1.
00000111  Because 1 produced 0, therefore the “true” assignment fails.
00001000  Because we next test 0, therefore assume L = 0.
00001001  Because L = 0 makes its claim false, therefore you are not lying.
00001010  Because you are not lying, therefore L appears to be 1.
00001011  Because 0 produced 1, therefore the “false” assignment fails.
00001100  Because both binary values reverse themselves, therefore L has no stable value.
00001101  Because ordinary logic expects either 1 or 0, therefore it cannot settle L.
00001110  Because “paradox” is not identical to “false,” therefore calling L false is insufficient.
00001111  Because forcing L = 0 yields L = 1, therefore the forced rule contradicts itself.
00010000  Because forcing L = 1 yields L = 0, therefore truth also contradicts itself.
00010001  Because each proposed answer undoes itself, therefore the loop continues.
00010010  Because the loop is semantic, therefore more factual evidence cannot resolve it.
00010011  Because the sentence concerns itself, therefore it lacks an external truth-test.
00010100  Because no external test breaks the loop, therefore binary evaluation stalls.
00010101  Because “I am lying” ordinarily involves intent, therefore natural language is more complex.
00010110  Because the paradox removes that complexity, therefore it idealizes lying as falsity.
00010111  Because the idealized sentence says “I am false,” therefore it becomes the liar paradox.
00011000  Because the liar paradox is circular, therefore it is not an ordinary mistaken claim.
00011001  Because an ordinary claim can be checked externally, therefore it may be 1 or 0.
00011010  Because L checks itself, therefore its evaluation alters its own content.
00011011  Because evaluating L changes the result, therefore the evaluation is unstable.
00011100  Because instability persists under repetition, therefore repeating the judgment changes nothing.
00011101  Because “always false” is itself a judgment, therefore it enters the same logical system.
00011110  Because that judgment labels L as 0, therefore L’s content pushes back toward 1.
00011111  Because the rule creates its own contradiction, therefore the rule is incomplete.
00100000  Because incomplete rules need refinement, therefore classical bivalence may be too strict.
00100001  Because bivalence allows only 1 or 0, therefore it excludes an “undefined” option.
00100010  Because L resists both 1 and 0, therefore “undefined” becomes a candidate.
00100011  Because undefined is not 1 or 0, therefore it avoids a forced contradiction.
00100100  Because undefined does not claim resolution, therefore it describes the problem honestly.
00100101  Because another logic may permit contradiction, therefore some systems allow both 1 and 0.
00100110  Because both-values logic limits explosion, therefore one contradiction need not prove everything.
00100111  Because classical logic differs from paraconsistent logic, therefore the answer depends on rules.
00101000  Because your premise chooses a rule, therefore its consequences must be tested.
00101001  Because “all paradoxes are false” assigns 0, therefore it attempts a classical answer.
00101010  Because L = 0 leads to L = 1, therefore that classical answer fails here.
00101011  Because the failure is structural, therefore it is not fixed by confidence or repetition.
00101100  Because the statement targets the present utterance, therefore time does not escape the loop.
00101101  Because “right now” identifies the utterance, therefore it sharpens self-reference.
00101110  Because self-reference creates circularity, therefore the statement cannot ground itself.
00101111  Because grounding requires something outside the statement, therefore L lacks a foundation.
00110000  Because L lacks a foundation, therefore it lacks a conventional truth value.
00110001  Because a conventional truth value cannot be assigned, therefore “lying” cannot be concluded.
00110010  Because lying cannot be concluded, therefore honesty cannot be concluded either.
00110011  Because neither conclusion follows, therefore the appropriate label is “paradoxical.”
00110100  Because “paradoxical” is descriptive, therefore it does not falsely solve the puzzle.
00110101  Because solving requires altered assumptions, therefore we must modify language or logic.
00110110  Because changing L to “I lied yesterday” adds an external event, therefore it may be tested.
00110111  Because an external event can be checked, therefore that revised claim can be 1 or 0.
00111000  Because the original claim cannot be checked externally, therefore it remains exceptional.
00111001  Because the exception arises from self-description, therefore self-description is the key issue.
00111010  Because self-description can be useful elsewhere, therefore self-reference is not always paradoxical.
00111011  Because “this sentence has five words” can be checked, therefore some self-reference is stable.
00111100  Because L links self-reference to negation, therefore it produces instability.
00111101  Because negation flips 1 to 0, therefore it supplies the reversal mechanism.
00111110  Because L demands its own negation, therefore it demands an impossible binary state.
00111111  Because no ordinary binary digit is both itself and its opposite, therefore L cannot settle.
01000000  Because 1 ≠ 0 in ordinary binary, therefore L cannot be consistently encoded as one bit.
01000001  Because one bit is inadequate, therefore an additional logical status may be needed.
01000010  Because “undefined” is an added status, therefore it extends the simple binary model.
01000011  Because extended models alter the rules, therefore they do not prove classical logic wrong.
01000100  Because they merely handle special cases, therefore they offer a different interpretation.
01000101  Because interpretations differ, therefore “what happens?” has more than one formal answer.
01000110  Because the classical answer is contradiction, therefore classical logic rejects a stable valuation.
01000111  Because the semantic answer is undefined, therefore truth status may be withheld.
01001000  Because the paraconsistent answer permits conflict, therefore L may be treated as 1 and 0.
01001001  Because these answers use different systems, therefore they should not be casually mixed.
01001010  Because your premise uses ordinary language, therefore the classical reading is most natural.
01001011  Because the classical reading fails to stabilize L, therefore the best result is “no fixed value.”
01001100  Because “no fixed value” is not the same as false, therefore your initial premise is too simple.
01001101  Because falsehood assumes a stable 0, therefore it cannot describe L adequately.
01001110  Because L converts 0 into 1, therefore 0 is not stable.
01001111  Because L converts 1 into 0, therefore 1 is not stable.
01010000  Because both values are unstable, therefore the binary loop has no terminating state.
01010001  Because no terminating state exists, therefore ordinary evaluation cannot finish.
01010010  Because evaluation cannot finish, therefore the sentence produces paradox rather than information.
01010011  Because paradox is produced by form, therefore the speaker’s character is not at issue.
01010100  Because the speaker’s character is not at issue, therefore this does not prove deception.
01010101  Because it does not prove deception, therefore it does not prove sincerity either.
01010110  Because it proves neither, therefore it suspends the normal judgment.
01010111  Because judgment is suspended, therefore “I am lying” remains logically unsettled.
01011000  Because unsettled claims require caution, therefore do not treat L as evidence about real conduct.
01011001  Because real lying requires intent, therefore an actual person may be mistaken rather than deceptive.
01011010  Because the puzzle abstracts away intent, therefore it focuses only on truth conditions.
01011011  Because truth conditions conflict, therefore the abstraction breaks ordinary bivalence.
01011100  Because ordinary bivalence breaks, therefore either logic must change or the sentence must change.
01011101  Because changing the sentence can restore testability, therefore adding outside facts helps.
01011110  Because changing the logic can restore consistency, therefore adding truth statuses helps.
01011111  Because neither repair occurs in your original wording, therefore the paradox remains.
01100000  Because the paradox remains, therefore “always false” cannot be final.
01100001  Because “always false” fails on this case, therefore it is not a universal solution.
01100010  Because no stable 1 or 0 survives, therefore L is not simply true.
01100011  Because no stable 1 or 0 survives, therefore L is not simply false.

Therefore: if you tell me, “I am lying right now,” in the strict self-referential sense, you create a sentence that cannot consistently be represented as either binary 1 or binary 0 under ordinary logic.