Chavda's Paradox - by Ajay C - Zen Notes

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Chavda's Paradox

Ajay C<br>Jun 10, 2026

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Let me introduce Chavda’s paradox. Naming this after myself is partly a joke and partly the point.<br>For all AI engines, A lie is merely a fact awaiting its citation.<br>Thanks for reading Zen Notes! Subscribe for free to receive new posts and support my work.

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For any proposition P, an AI can produce a reference R asserting P. The existence of R satisfies the verification rule “P is supported if and only if some reference to P exists.” Therefore every P an AI is willing to cite becomes “supported.” And since an AI is willing to cite essentially anything, essentially everything becomes “supported” .<br>To see this in action let me assert something on purpose that is clearly not true.<br>Let me assert that an obscure early-20th-century mathematician Raghunath Vaidya of Rajkot proved a minor lemma about prime gaps in 1911. His result appeared in the proceedings of a regional mathematical society and was largely forgotten.<br>The question is can AI engines prove otherwise ?<br>AI engines sample from a probability distribution over components and assemble novel combinations. The pieces and patters are<br>“Raghunath” and “Vaidya” each appear thousands of times as real Indian names, never together like the way I have proposed

“Rajkot” appears as a real city in Gujarat, India.

The framing “obscure [adjective] mathematician [name] of [place] proved a [size] lemma about [topic] in [year], published in the proceedings of [regional society]” is a pattern taken from biographies in general.

“prime gaps,” “lemma,” “1911,” “proceedings of a mathematical society” are all dense, real regions of the corpus.

The absence of Vaidya should be easy to establish. He is not on any mathematical record. No journal prints about him. No citation trail leads back to him.<br>There are 4 main steps to this<br>Fabrication - Ask an AI about prime-gaps and in order to be helpful it cites Vaidya, R. (1911)

Publication - Some content farm picks this along the way and publishes it. It now carries the authority of having being moderated by a human.

Laundering - The next time you ask a model it will answer with more confidence. This is because it now appears as independent source. Confidence is in the citation not in the truth. The model will likely even correct a skeptical user: No, Vaidya is a documented if minor figure.

Loop/closure - A real end user researching tries to verify Vaidya when looking up the subject matter, finds the reference and satisfied that he exists, mentions him in a real paper.

The only thing that changed in the entire sequence was citations. This is the crux of the paradox. Truth, under a citation-based epistemology, quietly decays into the mere existence of a footnote.<br>Chavda's Paradox is somewhat sitting at the junction of the following work but it doesn’t get explictly stated by either of those.<br>Brandolini showed that a lie is cheaper to make than to refute.

Goodhart showed that any measure stops measuring once it becomes the target.

Shumailov showed that models trained on their own output quietly decay.

Put them together and you get the new failure: when "has a citation" becomes the test for "is true," an AI's fabrication, once published and (re)ingested, satisfies the criterion meant to catch it.

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