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Equation 4 · Part 3 · Where Multimodal Frontier Models Actually Differ, Beyond the Marketing

subscript

τaudio≈32\tau_{\text{audio}} \approx 32
subscript

What this part means

The lower label selects a particular version, component, or indexed member of the quantity. For example, x₀ and xₜ can be values at different positions.

Its job in the formula

A subscript distinguishes a version, component, step, or member of a quantity. It does not automatically mean multiplication.

The passage around this formula

where, at default resolution, the sampling rate f is one frame per second, each frame costs τframe\tau_{\text{frame}} ≈\approx 258 tokens, and the audio track costs τaudio\tau_{\text{audio}} ≈\approx 32 tokens per second — giving cvideoc_{\text{video}} ≈\approx 290 tokens per second, close to the approximately 300 tokens per second Google documents directly for default-resolution video [ 5 ] . The formula is unremarkable arithmetic, but what it exposes is the real assumption underneath the “native” claim: a single request is billed, and therefore presumably processed, as one combined audio-visual stream, not as a picture track with a separately bolted-on transcript.

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Learn the underlying idea

A subscript is a label attached below a symbol. It often selects a time step, component, category, or member of a sequence.

Open the illustrated subscripts: which member of a family? guide →

Sources cited in the surrounding passage

These citations provide research context; check each source for the exact claim it supports.