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Equation 1 · Part 8 · How Claude Code's Memory Actually Persists Across Sessions

Symbol M_i

Tstart=Tsys+Tmem+Tenv+Ttools+∑i=1kMiT_{\mathrm{start}} = T_{\mathrm{sys}} + T_{\mathrm{mem}} + T_{\mathrm{env}} + T_{\mathrm{tools}} + \sum_{i=1}^{k} M_i
MiM_i

What this part means

the token count of the i -th memory file discovered along the walk from the filesystem root to the working directory, summed over however many, k , are found.

Its job in the formula

MiM_i is one of the signed contributions combined to compute the quantity on the left.

Where the article explains it

where MiM_i is the token count of the i -th memory file discovered along the walk from the filesystem root to the working directory, summed over however many, k , are found.

The passage around this formula

…these “representative numbers” rather than fixed constants — actual figures move with every project’s own files — but the shape they describe is stable and worth writing down as an identity: Tstart=Tsys+Tmem+Tenv+Ttools+∑i=1kMiT_{\mathrm{start}} = T_{\mathrm{sys}} + T_{\mathrm{mem}} + T_{\mathrm{env}} + T_{\mathrm{tools}} + \sum_{i=1}^{k} M_i. where MiM_i is the token count of the i -th memory file discovered along the walk from the filesystem root to the working directory, summed over however many, k , are found. Every term is committed before the developer types a word. The point is not the specific numbers; it is that TstartT_{\mathrm{start}} is…

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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.

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Sources cited in the surrounding passage

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