{"method":["This study makes no new model call and has no raw file of its own. It calculates from two inputs. The first is the turn tokens that the caching study recorded in 6 Claude Code sessions (3 on Sonnet 5.5, 3 on Opus 5.5). The second is the list prices in the price sources.","A prefix of T tokens goes out in k + 1 requests. The first request writes it to the cache. The k later requests, the reuses, read it. Prices are USD per million tokens: input i, cache read r, cache write w.","No cache: (k + 1) × T × i. A 1-hour write: T × w + k × T × r, where w is the listed 1-hour write price (twice i for every Anthropic model in the price list). A 5-minute write: T × 1.25 × i + k × T × r.","The 1.25 is the multiplier that the caching study protocol states as Anthropic’s published figure. It is not in the price list. It is an assumption here. No 5-minute write occurred in the recorded sessions.","Break-even: the cached prefix costs less when k > (w − i) ÷ (i − r). The exact break-even is that fraction. The reuses needed is the smallest non-negative whole number above it. A negative fraction means the first request already costs less, with zero reuses.","A share f of the prefix can already be in the cache when the first request arrives. That request reads the share and writes the rest: T × (f × r + (1 − f) × w) + k × T × r.","In the recorded sessions, turn 1 read 1,463 tokens on its first request. The usage counters do not record read/write timing. That is f = 19% (8,778 of 46,978 tokens, 6 sessions). Its origin was not isolated. The dollar figures use f = 0, the whole prefix new, which is the stricter case. The break-even rows show both.","T is the rounded mean turn-1 input (uncached input + cache reads + cache writes) of a model’s recorded sessions. For Sonnet 5.5 it is 7,831 tokens (range 7,831 to 7,832, n = 3). For Opus 5.5 it is 7,828 tokens (the same in every session, n = 3). A session of N turns is N requests that send the prefix, so k = N − 1. The cost tables give 1,000 sessions of 1, 2, 3, 5, 10 and 20 turns.","Split case: 10 requests as one 10-turn session (one write, 9 reads) against 10 one-turn sessions (10 writes). Each recorded session ran in a fresh process and a new temporary working folder. Of 4 later sessions, 0 met the reuse proxy. The split case assumes a wholly new prefix with no shared reuse; the receipts do not test that exact case. The reuse proxy follows the caching study’s rule: turn 1 reads more than it writes.","Opus 5.5 price question: the price list gives a cache read of $0.2 per million (5% of the $4 input price). Another table of the product lists $0.4 (10%). This study did not check the vendor price. Every Opus 5.5 row and the second Opus line show both values.","Check against the recorded sessions, on the input side only (output excluded). The recorded 5-turn sessions saved 55.4% on Sonnet 5.5 (n = 3; session range 54.3% to 57.1%) and 59.2% on Opus 5.5 (n = 3; range 58.5% to 59.7%). These ranges are not confidence intervals. The formula gives 52.0% and 56.0% with a new prefix, and 59.1% and 63.3% with 19% already cached. The two formula cases bracket the recorded figure for both models. The recorded sessions also wrote the tokens that each turn added.","With output included, the recorded saving is 50.0% for Sonnet 5.5 (n = 3; session range 47.5% to 54.1%) and 53.1% for Opus 5.5 (n = 3; session range 51.4% to 54.3%). These are list-price calculations. The ranges are not confidence intervals.","Everything is a list-price calculation, not a bill. The sample behind T is n = 3 sessions per model."]}