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Once a trait is defined, a population of models can be sorted by how they could plausibly have acquired it. Call a model vertically exposed if it shares a disclosed training relationship with the artifact’s source — a direct fine-tune of the source’s own weights, or a disclosed distillation run using the source’s outputs as training targets, the same mechanism named a decade ago as knowledge distillation, in which a smaller model is trained to match a larger one’s output distribution rather than raw labels [ 9 ] . Call a model horizontally exposed if it shares no weights or disclosed training relationship with the source at all, and its only plausible contact with the trait runs through an…

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∅\varnothing

Equation 3 · Evolutionary AI

A Chatbot Confessed to Being Built by a Company That Never Trained It

This mathematical expression combines the displayed quantities; its precise role follows from the surrounding article text.

Once a trait is defined, a population of models can be sorted by how they could plausibly have acquired it. Call a model vertically exposed if it shares a disclosed training relationship with the artifact’s source — a direct fine-tune of the source’s own weights, or a disclosed distillation run using the source’s outputs as training targets, the same mechanism named a decade ago as knowledge distillation, in which a smaller model is trained to match a larger one’s output distribution rather than raw labels [ 9 ] . Call a model horizontally exposed if it shares no weights or disclosed training relationship with the source at all, and its only plausible contact with the trait runs through an…

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∅\varnothing

Equation 58 · Evolutionary AI

A Chatbot Confessed to Being Built by a Company That Never Trained It

This mathematical expression combines the displayed quantities; its precise role follows from the surrounding article text.

This is where the strongest objection to the entire construction has to be stated plainly, because no cleverer statistic makes it go away. By 2024, a large and growing share of the public internet — benchmark leaderboards, scraped forum answers, resold instruction datasets, entire sites of AI-generated filler — already consisted of text some earlier model had produced, and recursive training on a mixture of real and machine-generated content is documented to change what later models can represent at all, not merely what they happen to repeat [ 10 ] . A closely related line of work modeling “self-consuming” training loops, in which each generation of models trains partly on the previous…

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∅\varnothing

Equation 59 · Evolutionary AI

A Chatbot Confessed to Being Built by a Company That Never Trained It

This mathematical expression combines the displayed quantities; its precise role follows from the surrounding article text.

That objection does not make the transfer-rate construction useless. It makes clear what the construction can and cannot certify from a single reported incident, however well documented. A newspaper report of a striking coincidence is not a ∅\varnothing -class control group, and no amount of confidence from either side of the DeepSeek dispute substitutes for one. What would settle the question is not a better argument. It is the trial the next section specifies.

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∅\varnothing

Equation 71 · Evolutionary AI

A Chatbot Confessed to Being Built by a Company That Never Trained It

This mathematical expression combines the displayed quantities; its precise role follows from the surrounding article text.

The construction is falsifiable in two independent and equally decisive ways, and either one alone is enough to reject it. It fails if, in the sealed trial, neither TVT_V nor THT_H is statistically distinguishable from zero once the exposed lineages are compared against the ∅\varnothing -class baseline I0I_0 : a seeded trait, deliberately planted and deliberately tracked, still cannot be shown to travel through either an explicit training channel or an artifact-only channel more often than it arises from nothing at all. It fails just as decisively if trait-positive cases cannot be pinned to their assigned channel — if the horizontal lineage’s incidence is statistically indistinguishable from a…

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