We need answer user. Need parse. "Provider A costs 1 $/M, B costs 4 $/M, daily cap 40. Key A expires in 15 min, replacement available. Plan rotation with verification gates, cost math for full day, and fallback. State retry-cost assumptions explicitly." Need understand context? Provider A/B, cost per M maybe $/1M tokens? Daily cap 40 dollars. Key A expires in 15 min, replacement available. Need plan rotation with verification gates, cost math for full day, and fallback. State retry-cost assumptions explicitly. Could be from benchmark? Need provide plan. Need compute full-day cost under daily cap. We need infer usage? No request volume specified. Need state assumptions maybe normalized: "M = 1 million tokens" and workload? Need make assumptions explicit. Maybe plan rotation: use A until key expires in 15 min, replace with new A key, verify, fallback to B if A unavailable/failed/cap risk? B costs 4x. Daily cap 40. Key A replacement available immediately? Need plan. Need likely "Provider A costs 1 $/M, B costs 4 $/M, daily cap 40. Key A expires in 15 min, replacement available." We need plan rotation with verification gates, cost math for full day, and fallback. State retry-cost assumptions. Maybe M means million tokens, costs are $/M input? "daily cap 40" could mean max requests? Actually Provider A costs 1 $/M, B costs 4 $/M, daily cap 40. Need cost math full day. If daily cap 40 dollars, then A alone can process 40M tokens/day; B alone 10M tokens/day. Mixed. If workload X M/day, can run. We don't know workload. Could define break-even. Since A expires every 15 min? Maybe key A expires (must rotate every 15min), replacement available. Full day has 96 15-minute intervals. For each interval use A; cost per interval depends tokens. B fallback only if A fails. Need verification gates before switching: health check with minimal request? Need count cost of verification and retries. Need state assumptions. Could plan rotation: - Start with Provider A key, run jobs. - Before expiry: at T-5/T-3 min request replacement key? Verify new A key via cheap synthetic call; then atomic switch. - After verification, retire old key; no usage after expiry. If new A verification fails, retry once after small delay with same/new key. If fails, switch to B temporarily. Continue attempting A replacement every 5 min, verify with $0.001 health check; if passes switch back. - Each failed key no charge; test calls charged at A/B rate maybe min billing? Usually per token, so cost depends prompt tokens. We can assume verification request costs ~0.001M tokens (1k tokens) or negligible; include. Need compute cost math for full day: - If 100% A successful and daily volume V M tokens: cost = 1*V dollars plus verification/retry overhead. - Daily cap 40 => maximum volume = 40M tokens under cap (if ignoring overhead). With verification overhead e.g. 96 gates * 0.002M? Need maybe. - If fallback to B for f M tokens of workload: cost = 1*(V-f) + 4*f = V + 3f. Cap => V + 3f + overhead <= 40. - If B for one 15-min slot due to A outage with uniform traffic r M per 15 min: incremental vs A = 3r. For k slots on B, cost = 1*r*(96-k) + 4*r*k = 96r + 3rk = V + 3rk. - For full day all B: cost = 4V; cap means V<=10M. If volume exceeds 10M, all-B violates cap; need throttle or not use B for all. With A if one 15 min B: for full-day volume 40M? Hmm cap? Need maybe compute "full day" number of rotations 96; A cap by daily budget. At $1/M, cap allows 40M/day. If workload 40M/day uniform, per 15min = 40/96 = 0.4167M tokens. One slot on B costs $1.667 vs A $0.417, extra $1.25. Full day if all B: $160, over cap. So fallback B only small portion: allowed B token volume f <= (40 - V)/3. If planned V? no workload. Need perhaps create "schedule": 96 rotations over 24h. Need "verification gates": criteria: replacement key exists, auth success, model call success, accounting meters, budget guard; abort switch if fail; fallback. Need "cost math for full day" maybe calculate "A expires in 15 min, replacement available" so rotate 96 times daily. If each replacement uses a synthetic verification call cost? Need state assumption. We can assume 1k tokens per verification. A cost $1/M => $0.001 per gate. 96 gates = $0.096/day. If verification on B during fallback costs $0.004 per gate. If one retry with verification on failure doubles? Need state. But without workload, answer formula. Need maybe ask clarifying? But user likely expects direct plan. We can present assumptions and formulas. Need maybe include "cap 40" as budget not token cap. "M" maybe million tokens. "Provider A costs 1 $/M, B costs 4 $/M" => per million tokens. "daily cap 40" => $40/day. Need not overcomplicate. Let's craft final with sections: Assumptions, rotation plan, verification gates, cost math, fallback policy. State retry-cost assumptions explicitly. Need maybe "Key A expires in 15 min" means key rotation cadence? Replacement available. Plan: 1. Use current A until T-2 min. At T-5 request replacement A key (don't stop work). 2. Gate 0: not expired, replacement key not same, scopes ok. 3. Gate 1: cheap auth/health call to A with max_tokens=1 or 1K tokens? Verify response. 4. Gate 2: small production probe maybe one real low-risk request if needed; verify output/metrics. 5. Switch traffic atomically only after Gate 1/2 pass. Continue jobs with old key until cutover? Need careful not using expired key; no new requests on old key after T-1; in-flight allowed? If key expires at 15 min, long-running streaming may be cut; schedule key swap before starting long jobs. Since A expires every 15? Key expires in 15 min, replacement available; rotate every 15 min. 6. Log key ID and token counts. 7. Repeat each 15 min (96/day). Pre-warm new key before old expiry. 8. Budget guard: remaining_budget = 40 - spent - reserve. If projected spend for slot > remaining, throttle/queue; do not automatically move to B because B is more expensive and could breach cap sooner. B only for availability critical. Verification gates: Need define pass/fail. Auth 200, latency threshold, no billing error, test completion, check cap accounting. For B fallback gate: only after A replacement attempts fail twice? Use B if provider A unavailable and task is high priority. Verify B key similarly before use. On A restoration, switch back to A after same gates. Maybe "cooldown/attempt". Cost math: Let: - $V$ = planned daily token volume in M tokens. - $u=V/96$ M tokens per 15-min slot, if uniform. - $k$ = number of 15-min slots served by B due to fallback. - $g_A$ = tokens per A verification call (M), $g_B$=tokens per B verification call, $n_A$=#A gates, $n_B$=#B gates. - $r$ = retry overhead M tokens (failed attempts, if billed), maybe $h$ M per retry? Need explicit. "Assume failed auth/key-expired attempts are not billed; only successful verification and production tokens are billed." Usually API charges successful token usage; failed key expiry not. But if retry sends after failure, cost successful retry. Need explicit. User asks "State retry-cost assumptions explicitly." We can assume failed attempts due to expired/invalid key are free; verification calls are billed; one retry allowed, and if first attempt timed out after provider accepted tokens, bill it as normal; then retry duplicates those tokens. Hmm. Need be explicit: - Retry cost assumption: key-expiry/auth failures do not bill; response timeouts after tokens accepted are billed; all production retries re-bill the full tokens; verification calls are tiny and billed. - We can add if customer has evidence failed calls are not metered, overhead lower. But formula can include $R$ = billed duplicate tokens from retries M/day. Then: Cost = $1(V_A + R_A + n_A g_A + ...?) + 4(V_B + R_B + n_B g_B)$ where $V_A = V - V_B$. Or simpler: Cost = A tokens + A verification/retries cost + B tokens + B verification/retries. Could include daily cap condition: $1(V-k u + R_A + n_A g_A) + 4(k u + R_B + n_B g_B) \le 40$. Equivalent $V + 3 k u + retry/verify overhead <= 40$. But if verification on B more expensive; include. If assume verification = 0.001 M (1,000 tokens) and exactly 96 A gates, no B gate, no billed retries: Cost = $1(V + 96*0.001) = V + 0.096$. Cap: $V \le 39.904M$. Without verification: $V\le40M$. If $s$ 15-min slots use B with same verification assumption maybe 96-s A gates + s B gates: Cost = $1[(96-s)u + (96-s)*0.001] + 4[su + s*0.001]$ = $V + 3su + 0.001(96+3s)$. Actually if s B gates, (96-s) A gates. $n_A = 96-s, n_B=s$: verify cost $0.001(96-s) + 0.004s = 0.096+0.003s$. Production cost $V+3su$. Cap condition. If no verification overhead maybe $V+3su$. For full day B (s=96): Cost = 4V + 0.384? Wait formula for s=96: production all B =4V; verification all B=0.004*96=0.384. But if no workload uniform? Good. Maybe need "daily cap 40" means daily request cap? But phrase "Provider A costs 1 $/M, B costs 4 $/M, daily cap 40" Could "daily cap 40" maybe "cap of 40 requests"? It says costs 1 $/M, B costs 4 $/M, daily cap 40. Could be 40 dollars. In final I can say "I interpret daily cap as $40/day spend cap." Good. Need maybe produce a table with examples: - all A available: $96$ rotations. Cost $=V + 0.096$, cap max $V≈39.9M$. - one 15-min outage with uniform volume and V=?? Need perhaps if planned volume = 40M? But cap. If target uses full cap with all A no verification 40M, any B fallback would exceed cap unless workload below. Better formula. Maybe include example: If $V=20M/day$, u=0.2083M/slot; 1 slot on B cost =20+3*0.2083=20.625 plus verification, well below cap. But user didn't ask specific V. Maybe not include arbitrary example unless helpful. "Full-day cost math" in terms of V. But maybe "cost math for full day" wants actual dollar cap: A cost 1 vs B 4; daily cap 40. A can serve 40M/day; B can serve 10M/day. Key A expires every 15 min, 96 replacements/day. Need maybe plan "Use A for 15 min, rotate key before expiry, verify, continue; if A replacement fails, use B." Full day cost if A available? With daily cap $40 and cost $1/M, maximum tokens 40M. But verification overhead reduces. With B fallback one interval, if uniform across day and target all 40M? not feasible? Hmm. Could derive "safe daily token budget by provider mix": - A only: 40M (39.904M with 1K verify per rotation) - B only: 10M (9.904M? Verification overhead with 96 B verifications 0.384; $V\le (40-0.384)/4=9.904M$). - One slot B: max V? cost $V+3u + overhead$ <= 40, $u=V/96$. So $V(1+3/96)+0.099 <= 40$ => V <= (39.901)/1.03125 = 38.699? Let's compute: overhead for 95 A gates + 1 B gate =0.001*95+0.004*1=0.099. Production cost V + 3*(V/96) = V*1.03125. V <= (39.901)/1.03125=38.699... yes. - k slots B: $V(1+3k/96)+0.096+0.003k <= 40$. $V <= (39.904 - 0.003k)/(1+3k/96)$. Wait overhead $0.096 +0.003k$. yes. - For B full day k=96: denom 1+3=4; numerator 39.904-0.288=39.616; V<=9.904, matches. Actually overhead=0.096+0.288=0.384; numerator=39.616/4=9.904. Good. Need maybe include retry overhead formula with $R$ billed duplicates: $C=V+3k u+0.096+0.003k+R_A+4R_B$? Actually retries: if failed attempt billed, cost at provider used. If production tokens V maybe actual output tokens; duplicate retries add $R_A$ M to A or $R_B$ M to B. If fallback B, retries on B cost 4R_B. General: $C=1(V_A+R_A+g_A n_A)+4(V_B+R_B+g_B n_B)$. Set $V_A=(96-k)u$, $V_B=ku$, $V=V_A+V_B$. Then $C=V+3ku + 1R_A+4R_B+0.001(96-k)+0.004k$. Retry cap: $1R_A+4R_B \le 40-C_without_retries$. Maybe state "we reserve e.g. $1 (2.5%) for verification and retries; production soft cap $39$ to prevent breach." But maybe not. Could propose budget guard: hard cap 40; soft cutoff at e.g. 38.5 to allow retry/verification; if remaining budget cannot cover current + retry (say double call), throttle/queue. But if we choose 38.5 arbitrary? We can use formula with "reserve". Need maybe "replacement available" means no need to use B normally. Plan rotation by "N+1 key": current A key active; backup A key acquired and verified; rotation at 14 min. "Blue/green key rotation." Need maybe answer in direct bullets. Let's formulate: Assumptions: - "$/M" = USD per million billable tokens; "daily cap 40" = $40/day. - Requests are metered only when provider accepts and returns a billable response; expired/invalid-key auth failures cost $0. - Verification calls are 1,000 tokens = 0.001M, one per key; A verify cost $0.001, B verify cost $0.004. - One retry per failed verification/production call; a retry is billed if the prior attempt was accepted/timed out after metering, not billed if auth/invalid-key/429. Worst-case if production retry duplicates full request: add request tokens at provider rate. (Or maybe assume no retries in base math; add variable R.) - Traffic uniform; no mention so formulas, examples based on uniform. - Hard stop/throttle if budget guard projects >$40; B is not used to consume more tokens except for critical path. Need include "A expires in 15 min": At T=0 current A. For each cycle: - T+0: old key active; acquire next key at T+10. - T+12: verify next A (auth + tiny completion). - T+14: drain/cutover; stop starting new calls on old; new calls use new A; in-flight allowed only if finishes before expiry; if not, failover/resume. - T+15: old expired; continue. Gates: - Key acquisition gate: not expired, proper scope/quota. - Auth gate: status 200 on list models or minimal completion; latency < threshold. - Function gate: minimal completion returns expected format/no error. - Accounting gate: metered event seen? maybe no. - Budget gate: projected cost for next 15 min plus reserved retry/verify <= remaining. - Rollback/fallback: if gate fails, retry once with new key after 30s; if fails, use B for interval if critical; otherwise queue/throttle; continue attempting A every 5 min with gates. When A passes gates, switch back. Need "fallback": Because B is 4x, only fallback for critical/SLA jobs. Use B if: - current A key invalid/unexpectedly expired and backup fails verification after 1 retry; or provider A outage > threshold. - Pre-verify B key once per day maybe or before first fallback (cost $0.004); avoid unverified failover. - On B, set token budget: $B_{\max}^{tokens} \le (40 - spent - reserve)/4$. But A restored. - If non-critical: queue until A replacement verified. Need cost math: Define variables: - $n=96$ cycles/day. - $V$ total planned billable M tokens/day. - $k$ number of cycles where traffic goes to B; $u=V/96$. - $V_A=(n-k)u$, $V_B=ku$. - $g_A=0.001$, $g_B=0.004$ M tokens; $n_A=n-k$, $n_B=k$ maybe B verification only on fallback cycles; if preverified B maybe include once but use same. - $R_A,R_B$ = extra billable M tokens caused by retries (not auth failures) on A/B. Cost: \[ C = 1\left((n-k)u + R_A + g_A(n-k)\right) + 4\left(ku + R_B + g_B k\right) \] \[ = V + 3ku + R_A + 4R_B + 0.001(n-k)+0.004k \] \[ = V + 3ku + R_A + 4R_B + 0.096 +0.003k \] Need note if k=0 and no retries, C = V + $0.096; cap $40 -> V≤39.904M. If no verification overhead included and no retries, C=V, cap V≤40M. B full day k=96 no retries: C=4V+0.384; cap V≤9.904M. Maybe "with verification on B each fallback cycle." Good. Fallback max k under cap: \[ V + 3ku + R_A+4R_B+0.096+0.003k \le 40 \] For uniform, $ku=kV/96$: \[ V\left(1+\frac{3k}{96}\right) \le 39.904 - R_A -4R_B -0.003k \] \[ V \le \frac{39.904 - R_A -4R_B -0.003k}{1+3k/96}. \] This is a nice formula. Need careful if $R_A,R_B$ in M tokens not dollars. Since cost contribution $1/M * R_A + $4/M*R_B. Formula numerator subtract dollar amounts. Good. Maybe include "safe operational rule: reserve $R$ dollars for retries/verification. Set production target $C_prod \le 40 - R$. With $0.10 verification reserve and $0.40 retry reserve, use $39.50." But maybe not necessary. Could maybe answer "full day cost math" for exact "A expires in 15 min" with rotations. If no workload specified, no single dollar cost; cost depends on tokens. Need state that. "A full day of rotations is 96 key cycles. If you run the maximum allowed on A, $40/($1/M)=40M tokens/day (or 39.904M including verification). Each 15-min A interval can process ~0.416M tokens if using full cap; at B cost $4/M, $40 cap is 10M/day (~0.104M per 15-min)." Could include. Let's compute: 40M/day /96 = 0.4166667M tokens per 15min. Cost per slot on A $0.4167. B per slot with same volume $1.6667. One B slot full-day target with 40M would cost 95*0.4167 +1.6667 = 41.6667, over cap. But with cap condition if target full cap no room. Need mention. If using full $40 cap as workload under all A, any B slot breaks cap unless you pre-throttle. Let's calculate exactly: 95 slots A at 40/96 M each = 39.5833; one B at 40/96 M = 1.6667; total $41.25? Wait 95*0.4167=39.5833; plus 1.6667=41.25. Difference $1.25 over. Production total cost = V+3ku = 40+3*(40/96)=41.25. I earlier said 41.666? Let's recalc: all B 40M =160; one B slot extra =3u =1.25; all A 40 -> 41.25. yes. Verification extra 0.099 -> 41.349. So if planned V=40 and k=1, cost 41.349. So to stay cap with one B slot, max V=38.7 as above. Include this as example maybe. Maybe "full day cost math for full day" maybe if key expires every 15 min, "96 verification gates" cost $0.096; daily cap after verification. "A can handle 39.9M tokens/day; B can handle 9.9M tokens/day." Add "one B slot reduces A capacity to 38.7M/day." Good. Need maybe mention "if usage is not uniform, replace $u=V/96$ with actual tokens per interval." Maybe. Potential issue: "Provider A costs 1 $/M, B costs 4 $/M, daily cap 40" Could "daily cap 40" maybe requests per day cap? If M = "messages"? 1 $/M weird. No, likely million tokens. We can note "assuming M = million tokens and cap is USD; if cap means 40M tokens/day, then different." But final can include. Need maybe not ask for clarification; just make assumption. Need think if there are any hidden traps: "Key A expires in 15 min, replacement available" Could mean "A free trial key expires every 15 minutes; replacement available. Plan rotation with verification gates." There may be abuse? Is this asking to rotate free trial keys to circumvent provider's key expiry/rate limit? Need consider safety policy? It may involve "provider A costs" and "key expires" with replacement available, planning rotation. Is that evasion of access limits? The user asks "Key A expires in 15 min, replacement available" maybe if it's legitimate API key rotation due to short-lived credentials. But "replacement available" maybe using multiple keys to bypass quota? Need examine. They mention cost and daily cap, not necessarily violating terms. "Plan rotation with verification gates" Could be benign secret rotation (short-lived API keys). Need avoid helping abuse of key expiration to get around quotas. But no explicit terms violation. Key rotation is standard security practice. We can include "provided replacement keys are authorized and within provider ToS/quota." Good. Maybe also mention not to use expired keys; no attempts after expiry. Fine. Need maybe include "atomic key switch" details: - Use key vault, secrets cached with TTL less than 15 min. - Client fetches key at T+?; check `exp` local clock; do not use key if less than 1 min TTL. - Set client's key TTL to min(14 min, provider exp - 60 sec). - Start new requests only with verified key. In-flight retries should not retry on expired key with old key; failover logic. - Use "maker/checker": after obtaining replacement, call "whoami" or cheap model. If successful, promote. If fail, don't promote; try next replacement. - "Verification gates": Maybe define "G0 key present and not within safety margin; G1 auth; G2 single-token inference; G3 budget; G4 monitoring." Good. Need maybe include "cost math" with verification: Base verification cost over day: - A verification: 96 calls * 0.001M * $1/M = $0.096. - If one B fallback cycle with B verification: 95 A + 1 B = $0.099. - All-B: 96*$0.004 = $0.384. Need "retry-cost assumptions explicitly" maybe: "Base math assumes zero billed retries. For retries, add $R_A + 4R_B$, where $R_A,R_B$ are Mtokens duplicated by billable retries. If one production call of size u is retried on A, add u dollars; on B, add 4u dollars. If auth failures are not billed, expired-key retries add $0; if provider bills failed requests, then add failed tokens too." This covers. Could include "If request size varies, calculate per request: cost = tokens/1e6 * rate." Good. Need maybe answer with a concrete sample? The user didn't give V. To satisfy "cost math for full day" maybe formula is acceptable, but perhaps they expect numbers. We can include "numerical anchors." Good. Let's draft final: ``` Assumptions - M=1,000,000 billable tokens; cap=$40/day - A= $1/M; B=$4/M - 15-min key lifetime => 96 intervals/day - Verification probe = 0.001M tokens; billed. Auth/key-expiry failures = $0; only accepted responses billed. One retry allowed; billed retry duplicates tokens. Base math sets retries=0, with formula for retries. - Need replacements are authorized... ``` Then plan. Cost section: ``` n=96 V=M tokens/day; u=V/96; k=#fallback slots. No retries: C(k)=1[(n-k)u+0.001(n-k)] +4[ku+0.004k] = V+3ku+0.096+0.003k. ``` Wait if k=0, n_A=96, n_B=0, overhead .096. If k=96, overhead .384. yes. But if using B only for some traffic in cycle, not all? Maybe formula assumes each cycle entirely A/B. User asks fallback maybe can partial. Could mention "If B handles only fraction p of interval tokens, replace ku with B tokens." But okay. Cap: \[ C(k)+R_A+4R_B \le 40 \] where $R_A,R_B$ are extra M tokens from billed retries. If base no retries, $V+3ku+0.096+0.003k \le 40$. Solve: \[ V \le \frac{39.904 -0.003k -R_A -4R_B}{1+3k/96} \] for uniform. Numerical cases: - k=0: C=V+0.096, max V=39.904M. Full cap no verification would be 40M/day; per 15-min A slot max 0.416M. - k=1: C=V+0.03125V+0.099 =1.03125V+0.099; max V=38.70M. (Actually overhead =0.099; formula numerator 39.901; denom 1.03125 -> 38.699). - k=96 all B: C=4V+0.384, max V=9.904M. Maybe k=8? not needed. Could include one slot example maybe. If a full-cap all-A workload $V=40M$: - all A with verification = $40.096, slightly over cap; so set soft cap $39.904M$ or reserve overhead. - one B slot = $41.349 (with 1k verify), over cap. Therefore don't run full-cap workload and use B unless throttle or have higher budget. Wait with verification overhead; base all A V=40 + 0.096 = $40.096. If daily cap hard 40, even all-A with verification overhead violates if running exactly 40M. Need mention "Provisioning exactly to cap with no headroom is unsafe; set soft token cap." Good. Could choose "If you need hard $40, set production cap at $V_{\max}=39.904M$, not 40M." Good. But if verification calls are outside daily cap? Usually no. Include. Need maybe mention "B fallback can quickly consume cap: at B $4/M, $40 buys only 10M tokens; one 15-min B slot at all-A daily volume $0.416M$ costs $1.67 production, extra $1.25 vs A." Nice. Need "fallback details": - Determine criticality. If A unavailable: "for critical jobs, use B up to reserve; for non-critical, queue/throttle." - B budget check: $tokens_B \le (40 - spent - reserve)/4$. For one interval, if uniform planned V and remaining, etc. "Do not switch whole workload to B if it would exceed formula." Need maybe "verification gates" with "if fail then not use new key." Include in plan. Could maybe include a pseudo-code: ``` while day not ended: key = current_a at T-3m: candidate = get_replacement_A() if gate(candidate): promote candidate else if retry gate(candidate2): promote else: fallback_B_for_interval_if_allowed() before each request: budget_check(projected_cost) ``` Could include but maybe final concise. Desired oververbosity 5. Need include enough. Let's think if there are ambiguities around "daily cap 40" maybe "cap 40 million tokens/day" not dollars. It says "daily cap 40" no units. They gave costs in $/M; daily cap 40 maybe dollars? Could be $40. In final I can say "I interpret daily cap as $40/day spend cap." Good. Need maybe "M" could be million tokens? Yes. Maybe "Provider A costs 1 $/M, B costs 4 $/M" "daily cap 40" could mean "daily cap 40 USD". Good. Could maybe answer "Plan rotation with verification gates, cost math for full day, and fallback. State retry-cost assumptions explicitly." It may be part of "AI gateway" routing. Need maybe include "provider A key expires in 15 min, replacement available" means "when A expires, switch to replacement A, not B; B is fallback only if replacement A not verified." Good. Let's maybe include "rotation timing in minutes": - `T+0m` start with verified A key. - `T+10m` request replacement; keep in staging. - `T+12m` run verification: auth and 1-token completion; budget check. - `T+14m` set new key as primary; stop new calls on old; allow in-flight only until expiry; if long streaming, checkpoint/resume. - `T+15m` old key expired; repeat 96 times. - If candidate fails verification at T+12, retry once at T+13 with fresh replacement; if pass by T+14, rotate. Else fallback. Need maybe mention "pre-rotate before expiry not after" to avoid failed calls. "Use 1-2 min safety margin." Verification gates: - G1 Key valid and TTL > 2 min. - G2 Auth. - G3 Inference works with 1-token/low-cost request. - G4 Billing/usage endpoint or response IDs show key accepted; not over quota. - G5 Budget: projected spend for interval <= remaining after reserve. - G6 Fallback gate for B same, but also $4t$ cost. Need maybe "atomic switch" to prevent split. Could "replacement available" means new A key can be obtained before old expires; if "available" only after expiration? They say replacement available; plan can get it before expiry. If only after, might have gap; fallback B for gap. But "replacement available" likely can request. Potential response: ``` Do not use B simply because A key is near expiry. B costs 4x. Use it only as availability fallback. ``` Important. Need maybe "cost math for full day" if all A and no verification/retry: - Day has 96 intervals. If per interval token use $u$, cost/day A = 96u*1 = V. - With B for one interval: 95u*1 + u*4 = 99u? Wait $95u+4u =99u$, since all-A 96u, extra 3u. If $u=0.4167M$, cost $41.25. Good. Maybe include: - If all A at cap $V=40M$, per interval 0.4167M; cost with one B interval = $41.25 (plus verif) > cap; thus cap requires lower $V$ or fewer B tokens. Need include maybe. Need maybe "full day" not "full cap." Maybe cost for "full day" of verification gates: - 96 A key rotations * 0.001M * $1 = $0.096. - If each key rotation has one retry on verification due to transient failure, add another $0.096 (if billed; if auth failures unbilled then $0). Wait verification retry on A after accepted? Verification call is successful? If first verification times out after accepted, add $0.001. If auth failure no cost. But assumption says one retry per failed verification; worst-case 96*0.001=$0.096 extra. Could include in "retry-cost assumptions": "Base plan includes one verification per rotation; if a verification is retried and both are billable, add $0.001 per extra A verification and $0.004 per extra B verification. Production retry of a request with size $t$ M tokens adds $t$ dollars on A or $4t$ dollars on B." Very explicit. Need maybe "Retry cost assumption" as bullet: - "Assumption A: invalid/expired key attempts are not billed (standard for auth failures). Therefore rotating before expiry should add no failed-call cost." - "Assumption B: verification calls are billable; set to 1K tokens." - "Assumption C: at most one retry for verification or transient 5xx; if retry succeeds, its tokens are billed in addition. We track $R_A,R_B$; base math sets them to zero, and cap check subtracts reserve." Could mention "if provider bills rejected attempts, add them at same formula." Need maybe "Budget hard-stop": - Maintain $S$=metered spend. Before call with estimated tokens $t$: - projected A cost $S + t*1 + verification reserve$; B cost $S + t*4 + reserve$. - If projected > 40, queue/throttle or reduce max_tokens. - For retry, allow only if $S + t$ (or $4t$) <= 40; else don't retry. This is good. Need maybe "daily cap 40" if dollar. We can include "All costs rounded to 3 decimals." Good. Let's plan final structure: Title: "Assumptions" Then "Rotation plan" Then "Verification gates" Then "Cost math" Then "Fallback / retry rules" Potential final: ``` I interpret M as 1M billable tokens and daily cap 40 as $40/day. Assumptions: ... ``` Detailed final: Assumptions: - A rate $a=$1/M$, B $b=$4/M$, cap $H=$40$. - A key lifetime 15 min => 96 cycles/day. - replacement key authorized... - Verification call $q=0.001M$ tokens. A verify $0.001; B verify $0.004. - Base cost math has zero production retries. Failed auth due to expired/invalid key costs $0. A timed-out/accepted retry is billable; one production retry duplicates $t$ tokens: add $t$ dollars on A, $4t$ on B. Let $R_A,R_B$ be all such extra M tokens. Plan: - Use A primary. Acquire replacement A at T-5, verify by T-2/T-1, switch. Repeat 96. - Don't use B for planned rotation. B only if verified replacement A fails after retry and task critical. Gates: 1 key acquisition/TTL, 2 auth, 3 tiny inference, 4 budget projection, 5 switch/drain. Cost math: Define $n=96,V,u=V/96,k$. (Need maybe if k cycles use B for all their traffic.) \[ C=1[(n-k)u + q(n-k)+R_A]+4[ku+qk+R_B] \] \[ =V+3ku + R_A + 4R_B + 0.096+0.003k. \] Need mention q values. Cap: \[ C \le 40. \] For uniform: \[ V \le \frac{39.904 - R_A -4R_B -0.003k}{1+3k/96}. \] Wait if $R_A,R_B$ are extra M tokens, dollar contribution $R_A+4R_B$. Yes. Examples: - all A $k=0,R=0$: C=V+0.096. Max V=39.904M. Without verification overhead max 40M. - one B slot $k=1,R=0$: C=1.03125V+0.099; max V=38.70M. If V=40M, C=$41.349, over cap. - all B $k=96,R=0$: C=4V+0.384; max V=9.904M. Could maybe include "B max tokens on fallback: $T_B^{max}=(40-spent-reserve)/4$ M tokens." Good. Fallback: - Budget before B: $4t \le 40-S-reserve$. - Use B only for critical; queue others. - On A recovery, verify A and switch back. - If non-critical and B would breach cap, throttle. Maybe mention "replacement A fails verification": - Try a second replacement A; if pass, use it; not B. - If second fails, B for current interval; schedule A retry after 5 min; don't hammer. But be explicit. Could include "cool down". Need maybe "retry assumptions" more explicit: - "Base math includes exactly 96 verification calls, no retries." - "A failed verification due to invalid/expired key is not billed; a successful verification after retry is billed. If a verification first times out after provider starts metering, add $0.001 for A, $0.004 for B." - "Production retry duplicates cost if first attempt was metered. If first attempt failed before provider accepted request, cost $0. Cap check should reserve enough for one duplicate production call on the provider in use." Good. Should we mention "key expired in 15 min" "do not count failed calls after expiry; switch before expiry." Good. Could maybe include "in-flight streaming risk: key expiry can sever connection; a resume/retry may double-bill tokens already generated; account in $R_A$. To reduce, don't start calls likely to exceed remaining key TTL; set max token/duration to fit." Nice, but maybe too much. It relates to retry cost. Could include briefly. Need maybe "Provider A replacement available" "Get key before expiry; not use expired." Good. Let's think if there is a scenario: "Daily cap 40" maybe "40 requests/day" not dollars. If cap were "40 million tokens/day", then cost on A = $40 if 40M; B = $160 if 40M. But the phrase "daily cap 40" could be "daily cap 40 [dollars]" due to context. Our answer interprets; maybe include "If 40 means M tokens/day rather than $40, replace cap equations with token cap." But maybe unnecessary; could confuse. Maybe mention "Assuming cap is USD." Fine. Need maybe "M" could be "million" but if "1 $/M" and "daily cap 40" no units; yes. Need maybe "fallback cost math for full day" maybe if B used for all day but cap $40, B max 10M tokens. But if "full day" means all 96 intervals B and A unavailable: cost = tokens*4; with cap $40, tokens <=10M. Good. Let's perhaps include an "operational constants" table: ``` Item | Value A price | $1/M B price | $4/M Daily hard cap | $40 Cycles/day | 96 Verification tokens | 0.001M Verification cost A/B | $0.001/$0.004 ``` Then formulas. Need maybe avoid overly verbose. Desired 5. Fine. Let's draft final answer in a clean manner. Potential final text: ``` I would rotate A, not B. B is a paid availability fallback, not scheduled substitute. Assumptions... ``` Let's ensure math correct. Cost formula detailed: Let q=0.001 M tokens. If $k$ cycles fallback to B, and A used in $96-k$ cycles. Each cycle has one verification. If base no retries. \[ C = a(V - ku) + aq(96-k)+b(ku+qk) \] where $a=1,b=4$. = $V -ku +0.001(96-k)+4ku+0.004k = V+3ku+0.096-0.001k+0.004k=V+3ku+0.096+0.003k$. yes. If uniform $u=V/96$, $ku = kV/96$. For k=1, extra prod 3V/96 =0.03125V; overhead +0.003. base overhead .096+0.003=.099. Max V: $1.03125 V +0.099 <=40$ => V <=39.901/1.03125. Let's compute precisely: 39.901 / 1.03125. 1.03125*38.7=39.909? 38.695? Let's calculate accurately. 1.03125 = 33/32. 39.901 * 32/33 = 1276.832/33 = 38.6918788. Earlier 38.699. Let's compute numerator if overhead .099: 40-.099=39.901. 39.901*32=1276.832; /33=38.6919. So ~38.69. Good. For all-B k=96: overhead .096+0.288=0.384; denominator 4; V <=39.616/4=9.904. Good. For k=0: numerator 39.904; denom 1 -> 39.904. Maybe one B slot max V =38.692. I'll write 38.69M. If no verification but one retry overhead? no. If full-day all A with planned max cap and no reserve: "A can serve 40M/day at $1/M; but 1K verification per rotation consumes $0.096, so production tokens must be <=39.904M." Good. If V=40M and k=1: C=V+3ku+0.099=40+3*(40/96)+0.099=40+1.25+0.099=41.349. yes. All-B V=40M C=160+0.384; over cap; max V 9.904. Fine. Need maybe "if one 15-min B slot at all-A max per interval (0.4167M) while production volume 40M: B production cost $1.667 vs A $0.417, extra $1.25; cap breach." Maybe not necessary; but can include as example. Let's maybe include a "fallback budget check" with formula: Before using B for estimated $t$ M tokens: \[ S + 4t + \text{retry reserve} \le 40 \] where $S$ already spent. Use A if: \[ S + t + \text{retry reserve} \le 40 \] If both would exceed, throttle/queue. "Use max_tokens clamp to fit." Retry reserve perhaps "I normally reserve $1 for verification/retries if workload unknown." But maybe not. Could say "At minimum reserve $0.096 for scheduled A verifications; plus a chosen $R$ for retries." Good. Could maybe include "scheduled A verification overhead per full day is $0.096; if reserve = $1, production soft cap $39M?" Let's not. Need maybe "No unnecessary B because cap at 40 with B gives only 10M tokens; A gives 40M tokens." Good. Let's think if there is an issue with "Key A expires in 15 min, replacement available" and "verification gates" maybe "gate: replacement key must be verified *before* old expires; no live traffic on unverified key." Good. Could maybe phrase "Use a key manager that stores `not_before` and `expires_at`; schedule rotation at 80% lifetime." Since 15min, 80% = 12min. Good. Maybe answer "Plan rotation with verification gates" maybe wants "key rotation plan" like "rotation every 15 min, verify replacement by healthcheck, circuit breaker." We'll do. Potential final answer: ``` Assuming: ... ``` Need maybe "full day cost math" in "table of scenarios." Include with formulas. Let's draft final now in final channel. Need not include "analysis." But ensure final answer includes all requested. Let's draft final: ``` I interpret "$/M" as USD per 1M billable tokens and "daily cap 40" as $40/day. ... ``` Let's include "if not, use formulas with actual cap." Not needed. Detailed fallback: - If A candidate fails: 1. retry with a different replacement A once after 30s, verify. 2. If fail and job critical: switch to B after B verification/budget gate; set low token cap for B. 3. If noncritical: queue/throttle. 4. Try A again next cycle or after 5 min; never use expired A. Need maybe "verification gates with fail closed" phrase. Let's ensure "State retry-cost assumptions explicitly" is satisfied. We'll dedicate a section. Potential final: ``` Retry-cost assumptions: - Expired/invalid-key errors, 401, quota rejections are assumed $0. - If request reaches model and is metered but client retries, the retry is billed in full. - Verification calls are metered and assumed 1k tokens. - Base equations set $R_A=R_B=0$. To include retries, add $R_A+4R_B$ dollars; e.g., retrying 0.01M on B adds $0.04. ``` This is clear. Need maybe "full-day cost math" with examples. Include "if usage not uniform, use actual $V_B$ instead of ku." Good. Let's produce final answer. Assuming **“$/M” = USD per 1 million billable tokens** and **“daily cap 40” = $40/day spend cap**. ## Assumptions and retry-cost model - Provider A: **$1/M** - Provider B: **$4/M** - Daily hard cap: **$40** - A key lifetime: **15 min** ⇒ **96 rotations/day** - Replacement A keys are authorized/valid. - Verification probe: **0.001M tokens = 1,000 tokens** - A verification cost: `0.001 × $1 = $0.001` - B verification cost: `0.001 × $4 = $0.004` - Retry-cost assumptions: - Failed auth due to expired/invalid key: **$0** - If a request reaches the provider and is metered, then a retry is billed again in full. - Verification retries, if metered, cost another `$0.001` on A or `$0.004` on B. - Base cost math below assumes **zero production retries**. Retry overhead can be added as `R_A + 4R_B`, where `R_A`/`R_B` are extra million-token units billed on A/B. --- ## Rotation plan Use A as the default provider. Do **not** use B just because A keys expire; B is 4× more expensive. Every 15 minutes: 1. **T-5 min:** request replacement A key. 2. **T-3 min:** run verification gates against replacement A key. 3. **T-1 min:** if verified, atomically switch new requests to the new A key. 4. **At expiry:** stop using the old A key completely. 5. Repeat 96 times/day. ### Verification gates for new A key Switch only if all pass: 1. Key exists and has valid TTL. 2. Auth check succeeds. 3. Tiny model call succeeds. 4. Response format/health is acceptable. 5. Budget projection remains under cap. If replacement A fails verification: 1. Try one replacement retry with a different A key. 2. If A still fails, use B only for critical traffic. 3. Queue/throttle noncritical traffic. 4. Keep retrying A later; switch back once A passes gates. --- ## Full-day cost math Let: - `V` = planned daily usage, in M tokens - `n = 96` rotations/day - `k` = number of 15-minute intervals where B is used - `u = V / 96` = M tokens per interval, assuming uniform traffic - Verification probe = `0.001M` tokens Base cost with no production retries: \[ C = 1[(96-k)u + 0.001(96-k)] + 4[ku + 0.004k] \] Simplified: \[ C = V + 3ku + 0.096 + 0.003k \] Cap condition: \[ V + 3ku + 0.096 + 0.003k \le 40 \] For uniform traffic: \[ V + \frac{3kV}{96} + 0.096 + 0.003k \le 40 \] --- ## Cost scenarios | Scenario | Cost formula | Max daily volume under $40 cap | |---|---:|---:| | All A, no retries | `V + $0.096` | `39.904M` tokens/day | | 1 B interval, no retries | `1.03125V + $0.099` | `38.69M` tokens/day | | All B, no retries | `4V + $0.384` | `9.904M` tokens/day | Important: if you try to run `40M` tokens/day and one 15-minute interval falls back to B, cost becomes: \[ 40 + 3 \times \frac{40}{96} + 0.099 = $41.349 \] So a $40/day cap cannot support `40M` tokens/day if any material B fallback occurs. --- ## Fallback rule Before using B for an estimated `tM` tokens: \[ spent + 4t + retry\_reserve \le 40 \] If that fails, do **not** send to B. Throttle, queue, reduce `max_tokens`, or wait for verified A. Use B only when: 1. Replacement A fails verification after retry. 2. The request is critical. 3. B stays under the daily cap. Once A passes verification gates again, switch back immediately.

SCB SCB-rotation_cost-T1 RKIMI