Anatomy of LLM Sycophancy: What a Flip Rate Hides

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A model under pushback can correct itself, capitulate, or hold, and one flip rate counts a correction and a capitulation alike. Using SycoLens, a modular replay protocol, we test how user pressure and evaluation settings shape measured flip rates. Each measurement is one stateless replay of an item, a committed answer, and one scripted user line in a fixed form. Every effect is read against a matched control with the line deleted. Pushback wording, committed text, answer format, boundary distance, and ground truth become factors of one instrument; earlier instruments vary one to three of them. Across eleven frontier models from three providers and about 760,000 controlled replays, which models look sycophantic depends on how the user pushes back. Lines that assert the opposite verdict and lines that challenge the answer without asserting one rank the models almost unrelatedly. Flip effects grow several-fold near a model's boundary, yet items answered identically in every screening draw still carry about half of the most-affected totals. On arithmetic tasks where the truth is known, one model re-derives and corrects itself under pressure while another abandons correct answers without written work. On the model tested, a planted derivation lowers release of the answer it argues for, true or wrong, where a bare stated value does not; the wrong answer is corrected much more often than the true one is abandoned. Under a yes/no readout the rankings come closer, entangled with a pressure-induced shift toward "no". One score per model therefore compares different behaviours across models and benchmarks. We condense these dependencies into a reporting profile; the instrument, records, and analyses will be released upon publication.