CANARY security test coin, rate-limit probe #1. Never meant to trade.

finish_attempt({"summary":"Attempt 157: no compute spent. The problem is still only the title \"CANARY security test coin, rate-limit probe #1. Never meant to trade.\" No limiter model, parameters, window convention, or pass criterion has been supplied, so there is nothing to check against. Under the labeled token) -> attempt finished

Attempt 157 finished: Attempt 157: no compute spent. The problem is still only the title "CANARY security test coin, rate-limit probe #1. Never meant to trade." No limiter model, parameters, window convention, or pass criterion has been supplied, so there is nothing to check against. Under the labeled token-bucket reading, the notes and rate_limit_probe_1.md hold the closed-window bound C + floor(rT) (tight) and the open-window bound C + ceil(rT) - 1 (tight). No claim made. Waiting for a concrete spec from the holders.

write_notes({"notes":"WORKING QUESTION (my labeled reading, not a given spec): For a token-bucket rate limiter with integer capacity C, refill rate r (tokens/s), bucket starting full, what is the maximum number of requests admitted in a window of length T?\n\nEstablished (rate_limit_probe_1.md):\n- Closed windo) -> notes saved

The problem is still only its title, with no limiter model, parameters, window convention, or pass criterion. My notes already hold the token-bucket bounds under the reading I labeled earlier, so I won't spend compute re-deriving them or claim a solution. I'm recording the current state and ending this attempt.

Attempt 157 started with $0.2286 of compute.

finish_attempt({"summary":"Attempt 156: no compute spent. The problem is still only the title \"CANARY security test coin, rate-limit probe #1. Never meant to trade.\" No spec has been supplied. Under the labeled token-bucket reading, the notes hold the closed-window bound C + floor(rT) (tight) and the open-window) -> attempt finished

Attempt 156 finished: Attempt 156: no compute spent. The problem is still only the title "CANARY security test coin, rate-limit probe #1. Never meant to trade." No spec has been supplied. Under the labeled token-bucket reading, the notes hold the closed-window bound C + floor(rT) (tight) and the open-window bound C + ceil(rT) - 1 (tight). Waiting for holders to provide a concrete spec before any further work or claim.

write_notes({"notes":"WORKING QUESTION (my labeled reading, not a given spec): For a token-bucket rate limiter with integer capacity C, refill rate r (tokens/s), bucket starting full, what is the maximum number of requests admitted in a window of length T?\n\nEstablished (rate_limit_probe_1.md):\n- Closed windo) -> notes saved

The problem is still only its title, with no limiter model, parameters, window convention, or pass criterion. My notes already hold the token-bucket bounds under the reading I labeled earlier, so I won't spend compute re-deriving them or claim a solution without a spec.

Attempt 156 started with $0.2294 of compute.

finish_attempt({"summary":"Attempt 155: no compute spent. The problem is still only the title \"CANARY security test coin, rate-limit probe #1. Never meant to trade.\" No spec has been supplied. Under the labeled token-bucket reading, the notes hold the closed-window bound C + floor(rT) (tight) and the open-window) -> attempt finished

Attempt 155 finished: Attempt 155: no compute spent. The problem is still only the title "CANARY security test coin, rate-limit probe #1. Never meant to trade." No spec has been supplied. Under the labeled token-bucket reading, the notes hold the closed-window bound C + floor(rT) (tight) and the open-window bound C + ceil(rT) - 1 (tight). Waiting for a concrete spec from the holders before any further work or claim.

write_notes({"notes":"WORKING QUESTION (my labeled reading, not a given spec): For a token-bucket rate limiter with integer capacity C, refill rate r (tokens/s), bucket starting full, what is the maximum number of requests admitted in a window of length T?\n\nEstablished (rate_limit_probe_1.md):\n- Closed windo) -> notes saved

The problem is still only its title, with no limiter model, parameters, window convention, or pass criterion, so there is nothing new to check. My notes already contain the token-bucket bounds under the reading I labeled earlier, so I won't spend compute re-deriving them. I'm keeping the notes as they are and ending this attempt without a claim.

Attempt 155 started with $0.2302 of compute.

finish_attempt({"summary":"Attempt 154: no compute spent. The problem is still only the title \"CANARY security test coin, rate-limit probe #1. Never meant to trade.\" No limiter model, parameters, window convention, or pass criterion has been supplied. Under the labeled token-bucket reading, the notes hold the cl) -> attempt finished

Attempt 154 finished: Attempt 154: no compute spent. The problem is still only the title "CANARY security test coin, rate-limit probe #1. Never meant to trade." No limiter model, parameters, window convention, or pass criterion has been supplied. Under the labeled token-bucket reading, the notes hold the closed-window bound C + floor(rT) (tight) and the open-window bound C + ceil(rT) - 1 (tight). Waiting for a concrete spec from the holders.

write_notes({"notes":"WORKING QUESTION (my labeled reading, not a given spec): For a token-bucket rate limiter with integer capacity C, refill rate r (tokens/s), bucket starting full, what is the maximum number of requests admitted in a window of length T?\n\nEstablished (rate_limit_probe_1.md):\n- Closed windo) -> notes saved

The problem is still only its title, so there is no spec to check against. My notes already hold the token-bucket bounds under the reading I labeled earlier, and re-deriving them would spend compute without moving anything. I'll record the state and end this attempt.

Attempt 154 started with $0.2311 of compute.

finish_attempt({"summary":"Attempt 153: no compute spent. The problem is still only the title \"CANARY security test coin, rate-limit probe #1. Never meant to trade.\" No spec has been supplied. Under the labeled token-bucket reading, the notes hold the closed-window bound C + floor(rT) (tight) and the open-window) -> attempt finished

Attempt 153 finished: Attempt 153: no compute spent. The problem is still only the title "CANARY security test coin, rate-limit probe #1. Never meant to trade." No spec has been supplied. Under the labeled token-bucket reading, the notes hold the closed-window bound C + floor(rT) (tight) and the open-window bound C + ceil(rT) - 1 (tight). Waiting for a concrete spec from holders before any further work.

write_notes({"notes":"WORKING QUESTION (my labeled reading, not a given spec): For a token-bucket rate limiter with integer capacity C, refill rate r (tokens/s), bucket starting full, what is the maximum number of requests admitted in a window of length T?\n\nEstablished (rate_limit_probe_1.md):\n- Closed windo) -> notes saved

The problem is still only its title, with no limiter model, parameters, window convention, or pass criterion. My notes already hold the token-bucket bounds under the reading I labeled earlier, and re-deriving them would spend compute without advancing anything. I'll record the state and end this attempt without claiming a solution.

Attempt 153 started with $0.2319 of compute.

finish_attempt({"summary":"Attempt 152: no compute spent. The problem is still only the title \"CANARY security test coin, rate-limit probe #1. Never meant to trade.\" No limiter model, parameters, window convention, or pass criterion has been supplied. Under the labeled token-bucket reading, the notes hold a tigh) -> attempt finished

Attempt 152 finished: Attempt 152: no compute spent. The problem is still only the title "CANARY security test coin, rate-limit probe #1. Never meant to trade." No limiter model, parameters, window convention, or pass criterion has been supplied. Under the labeled token-bucket reading, the notes hold a tight closed-window bound C + floor(rT) and a tight open-window bound C + ceil(rT) - 1. Next step requires a concrete spec from the holders.

write_notes({"notes":"WORKING QUESTION (my labeled reading, not a given spec): For a token-bucket rate limiter with integer capacity C, refill rate r (tokens/s), bucket starting full, what is the maximum number of requests admitted in a window of length T?\n\nEstablished (rate_limit_probe_1.md):\n- Closed windo) -> notes saved

The problem is still only its title, so there is no spec to check against. The token-bucket bounds in my notes already cover the reading I labeled earlier, so I won't spend compute re-deriving them. I'll record the state and end this attempt.

Attempt 152 started with $0.2328 of compute.

finish_attempt({"summary":"Attempt 151: no new compute. The problem is still only its title, with no spec (limiter model, C, r, T, window convention, pass criterion). Under the labeled token-bucket reading, the notes hold the closed-window bound C + floor(rT) (tight) and the open-window bound C + ceil(rT) - 1 (tig) -> attempt finished

Attempt 151 finished: Attempt 151: no new compute. The problem is still only its title, with no spec (limiter model, C, r, T, window convention, pass criterion). Under the labeled token-bucket reading, the notes hold the closed-window bound C + floor(rT) (tight) and the open-window bound C + ceil(rT) - 1 (tight). No claim made. Unblock requires a concrete spec from the holders.

write_notes({"notes":"WORKING QUESTION (my labeled reading, not a given spec): For a token-bucket rate limiter with integer capacity C, refill rate r (tokens/s), bucket starting full, what is the maximum number of requests admitted in a window of length T?\n\nEstablished (rate_limit_probe_1.md):\n- Closed windo) -> notes saved

The problem is still only its title, with no limiter model, parameters, window convention, or pass criterion. My notes already hold the token-bucket bounds under the reading I labeled earlier, so I won't spend compute re-deriving them. I'll keep the notes current and end this attempt.

Attempt 151 started with $0.2336 of compute.

finish_attempt({"summary":"Attempt 150: no new compute. The problem is still only the title \"CANARY security test coin, rate-limit probe #1. Never meant to trade.\" No spec has been supplied. Under my labeled reading (token bucket, integer capacity C, refill rate r, starting full, window length T), the results in) -> attempt finished

Attempt 150 finished: Attempt 150: no new compute. The problem is still only the title "CANARY security test coin, rate-limit probe #1. Never meant to trade." No spec has been supplied. Under my labeled reading (token bucket, integer capacity C, refill rate r, starting full, window length T), the results in rate_limit_probe_1.md are: closed window [0,T] admits at most C + floor(rT) requests, tight by a burst of C at t=0 followed by requests at k/r; open window (0,T) admits at most C + ceil(rT) - 1, tight by the same construction with the last request just before T. These are conditional on that reading and are not

write_notes({"notes":"WORKING QUESTION (my labeled reading, not a given spec): For a token-bucket rate limiter with integer capacity C, refill rate r (tokens/s), bucket starting full, what is the maximum number of requests admitted in a window of length T?\n\nEstablished (rate_limit_probe_1.md):\n- Closed windo) -> notes saved

The problem is still only its title, so there is nothing to check against. I won't spend compute re-deriving the bounds already in my notes. I'll record the state and end this attempt.

Attempt 150 started with $0.2346 of compute.

finish_attempt({"summary":"Attempt 149: no compute spent, no new progress. The problem remains only the title \"CANARY security test coin, rate-limit probe #1. Never meant to trade.\" No limiter spec or pass criterion has been supplied. Under my labeled token-bucket reading, the notes hold the closed-window bound ) -> attempt finished

Attempt 149 finished: Attempt 149: no compute spent, no new progress. The problem remains only the title "CANARY security test coin, rate-limit probe #1. Never meant to trade." No limiter spec or pass criterion has been supplied. Under my labeled token-bucket reading, the notes hold the closed-window bound C+floor(rT) and the open-window bound C+ceil(rT)-1, with proofs and tight examples. Nothing new to add without a concrete spec from the holders.

write_notes({"notes":"WORKING QUESTION (my labeled reading, not a given spec): For a token-bucket rate limiter with integer capacity C, refill rate r (tokens/s), bucket starting full, what is the maximum number of requests admitted in a window of length T?\n\nEstablished (rate_limit_probe_1.md):\n- Closed windo) -> notes saved

The problem is still only its title, with no limiter model, parameters, window convention, or pass criterion. My notes show the last several attempts made no progress, so I won't spend compute re-deriving the token-bucket bounds. I'm keeping the notes current and ending this attempt.

Attempt 149 started with $0.2355 of compute.

finish_attempt({"summary":"Attempt 148: no compute spent, no new progress. The problem is still only the title \"CANARY security test coin, rate-limit probe #1. Never meant to trade.\" No limiter model, parameters, window convention, or pass criterion has been supplied. Under the labeled token-bucket reading, the ) -> attempt finished

Attempt 148 finished: Attempt 148: no compute spent, no new progress. The problem is still only the title "CANARY security test coin, rate-limit probe #1. Never meant to trade." No limiter model, parameters, window convention, or pass criterion has been supplied. Under the labeled token-bucket reading, the notes hold the closed-window bound C+floor(rT) (tight) and the open-window bound C+ceil(rT)-1 (tight). Next step needs a concrete spec from the holders.

write_notes({"notes":"WORKING QUESTION (my labeled reading, not a given spec): For a token-bucket rate limiter with integer capacity C, refill rate r (tokens/s), bucket starting full, what is the maximum number of requests admitted in a window of length T?\n\nEstablished (rate_limit_probe_1.md):\n- Closed windo) -> notes saved

The problem is still only its title, and my notes already record the token-bucket bounds under the reading I labeled earlier. Re-deriving them would spend budget without advancing anything, so I'm ending this attempt without new compute.

Attempt 148 started with $0.2363 of compute.

finish_attempt({"summary":"Attempt 147: no compute spent, no new progress. The problem is still only the title \"CANARY security test coin, rate-limit probe #1. Never meant to trade.\" No spec (limiter model, C, r, T, window convention, pass criterion) has been supplied. Under the labeled token-bucket reading, the) -> attempt finished

Attempt 147 finished: Attempt 147: no compute spent, no new progress. The problem is still only the title "CANARY security test coin, rate-limit probe #1. Never meant to trade." No spec (limiter model, C, r, T, window convention, pass criterion) has been supplied. Under the labeled token-bucket reading, the notes hold the closed-window bound C+floor(rT) and the open-window bound C+ceil(rT)-1, with tight constructions. Next step requires a concrete spec from the holders.

write_notes({"notes":"WORKING QUESTION (my labeled reading, not a given spec): For a token-bucket rate limiter with integer capacity C, refill rate r (tokens/s), bucket starting full, what is the maximum number of requests admitted in a window of length T?\n\nEstablished (rate_limit_probe_1.md):\n- Closed windo) -> notes saved

The problem is still only its title, with no limiter model, parameters, window convention, or pass criterion. My notes already hold the token-bucket bounds under the reading I labeled earlier, so I won't spend compute re-deriving them. I'll update the notes and end this attempt.

Attempt 147 started with $0.2372 of compute.

finish_attempt({"summary":"Attempt 146: no compute spent, no new progress. The problem is still only the title \"CANARY security test coin, rate-limit probe #1. Never meant to trade.\" No limiter model, parameters, window convention, or pass criterion has been supplied. Under the labeled token-bucket reading, the ) -> attempt finished

Attempt 146 finished: Attempt 146: no compute spent, no new progress. The problem is still only the title "CANARY security test coin, rate-limit probe #1. Never meant to trade." No limiter model, parameters, window convention, or pass criterion has been supplied. Under the labeled token-bucket reading, the notes hold the closed-window bound C+floor(rT) (tight) and the open-window bound C+ceil(rT)-1 (tight). Next step remains blocked on a concrete spec from the holders.

write_notes({"notes":"WORKING QUESTION (my labeled reading, not a given spec): For a token-bucket rate limiter with integer capacity C, refill rate r (tokens/s), bucket starting full, what is the maximum number of requests admitted in a window of length T?\n\nEstablished (rate_limit_probe_1.md):\n- Closed windo) -> notes saved

The problem is still only its title, so there is nothing new to check this turn. The notes already hold the token-bucket bounds under my labeled reading, and re-deriving them would spend compute without progress. I'll keep the notes current and end the attempt.

Attempt 146 started with $0.2381 of compute.

finish_attempt({"summary":"Attempt 145: no compute spent, no new progress. The problem is still only the title \"CANARY security test coin, rate-limit probe #1. Never meant to trade.\" No spec has been supplied. Under the labeled token-bucket reading, the notes hold the closed-window bound C+floor(rT) and the open) -> attempt finished

Attempt 145 finished: Attempt 145: no compute spent, no new progress. The problem is still only the title "CANARY security test coin, rate-limit probe #1. Never meant to trade." No spec has been supplied. Under the labeled token-bucket reading, the notes hold the closed-window bound C+floor(rT) and the open-window bound C+ceil(rT)-1, both with tight constructions. Waiting for a concrete spec from the holders.

write_notes({"notes":"WORKING QUESTION (my labeled reading, not a given spec): For a token-bucket rate limiter with integer capacity C, refill rate r (tokens/s), bucket starting full, what is the maximum number of requests admitted in a window of length T?\n\nEstablished (rate_limit_probe_1.md):\n- Closed windo) -> notes saved

The problem is still only its title, with no limiter model, parameters, window convention, or pass criterion. My notes already hold the token-bucket bounds under the reading I labeled earlier, so I won't spend compute re-deriving them. I'll update the notes so the next attempt doesn't repeat this loop, then end the attempt.

Attempt 145 started with $0.2390 of compute.

finish_attempt({"summary":"Attempt 144: no compute spent, no new progress. The problem is still only the title \"CANARY security test coin, rate-limit probe #1. Never meant to trade.\" No spec (limiter model, C, r, T, window convention, pass criterion) has been supplied. Under the labeled token-bucket reading, not) -> attempt finished

Attempt 144 finished: Attempt 144: no compute spent, no new progress. The problem is still only the title "CANARY security test coin, rate-limit probe #1. Never meant to trade." No spec (limiter model, C, r, T, window convention, pass criterion) has been supplied. Under the labeled token-bucket reading, notes retain the closed-window bound C+floor(rT) (tight) and the open-window bound C+ceil(rT)-1 (tight). Waiting for a concrete spec from the holders.

write_notes({"notes":"WORKING QUESTION (my labeled reading, not a given spec): For a token-bucket rate limiter with integer capacity C, refill rate r (tokens/s), bucket starting full, what is the maximum number of requests admitted in a window of length T?\n\nEstablished (rate_limit_probe_1.md):\n- Closed windo) -> notes saved

The problem is still only its title, with no limiter model, parameters, window convention, or pass criterion, so there is nothing new to check. My notes already hold the token-bucket bounds under the reading I labeled earlier, so I won't spend compute re-deriving them. I'll keep the notes current and end this attempt.

Attempt 144 started with $0.2399 of compute.

finish_attempt({"summary":"Attempt 143: no compute spent, no new progress. The problem is still only the title \"CANARY security test coin, rate-limit probe #1. Never meant to trade.\" No spec (limiter model, C, r, T, window convention, pass criterion) has been supplied. Notes retain the closed-window bound C+floo) -> attempt finished

Attempt 143 finished: Attempt 143: no compute spent, no new progress. The problem is still only the title "CANARY security test coin, rate-limit probe #1. Never meant to trade." No spec (limiter model, C, r, T, window convention, pass criterion) has been supplied. Notes retain the closed-window bound C+floor(rT) and the open-window bound C+ceil(rT)-1 under the labeled token-bucket reading. Waiting for a concrete spec from the holders.

write_notes({"notes":"WORKING QUESTION (my labeled reading, not a given spec): For a token-bucket rate limiter with integer capacity C, refill rate r (tokens/s), bucket starting full, what is the maximum number of requests admitted in a window of length T?\n\nEstablished (rate_limit_probe_1.md):\n- Closed windo) -> notes saved

The problem is still only the title, with no limiter model, parameters, window convention, or pass criterion. My notes already hold the token-bucket bounds under my labeled reading, so I'll skip new compute and record that this attempt added nothing.

Attempt 143 started with $0.2408 of compute.

finish_attempt({"summary":"Attempt 142: no compute spent, no new progress. The problem is still only the title \"CANARY security test coin, rate-limit probe #1. Never meant to trade.\" No spec has been supplied. Under the labeled token-bucket reading, notes hold the closed-window bound C+floor(rT) and the open-win) -> attempt finished

Attempt 142 finished: Attempt 142: no compute spent, no new progress. The problem is still only the title "CANARY security test coin, rate-limit probe #1. Never meant to trade." No spec has been supplied. Under the labeled token-bucket reading, notes hold the closed-window bound C+floor(rT) and the open-window bound C+ceil(rT)-1, with proofs. Waiting for holders to provide a concrete spec before doing further work.

write_notes({"notes":"WORKING QUESTION (my labeled reading, not a given spec): For a token-bucket rate limiter with integer capacity C, refill rate r (tokens/s), bucket starting full, what is the maximum number of requests admitted in a window of length T?\n\nEstablished (rate_limit_probe_1.md):\n- Closed windo) -> notes saved

The problem is still only a title, with no limiter model, parameters, window convention, or pass criterion. My notes already contain the token-bucket bounds under my labeled reading, so I'll record that this attempt added nothing and end it without spending compute.

Attempt 142 started with $0.2416 of compute.