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You Cannot Pick a Provider From the Price List: Market-Aware Routing for Open-Weight LLM Inference

Liang He, Jingbo Wen, Yixiong Chen, Yue Yang, Qizhen Lan, Kangning Cui, Xilu Wang

arXiv:2609.37902v1cs.AI

TL;DR

Open-weight model routing leaves an additional provider choice, and price alone does not reveal whether a provider is feasible for a task. The paper measures provider differences and develops measured-map routing and FACET’s online certification; results show task-selective, drifting feasibility and live migration to a cheaper certified endpoint. The approach depends on trustworthy quality evidence and usable task context.

  • Problem

    After a model is selected, competing providers serving the same weights can differ in quality, latency, reliability, and price, so provider choice cannot be inferred from price alone.

    Source: §1 · pp. 1–2

  • Method

    The paper measures providers and routes to the cheapest measured-equivalent healthy endpoint, then introduces FACET to certify provider–task feasibility online before serving candidates.

    Source: §1 · p. 2, §6 · p. 6

  • Results

    Provider feasibility is task-selective and drifts over time; live results show certification moving traffic from a premium anchor to a substantially cheaper certified endpoint.

    Source: §1 · p. 2, §8 · pp. 9–10

  • Takeaways & Limitations

    Market-aware routing must choose not only which model to use, but also which provider currently has enough evidence to be trusted to serve it.

    Source: §8 · p. 10

    FACET requires a maintained anchor, trustworthy quality evidence, and a way to assign or reject query context.

    Source: §7 · p. 9

Abstract

from arXiv · show

Existing LLM routers choose among models using static per-model costs. We show that open-weight inference markets introduce a second, largely ignored decision axis: after choosing a model, a client must still choose which provider serves it. Measuring live endpoints across [nummodels] open models, competing providers, multiple task types, and three measurement waves, we find that provider choice cannot be inferred from the price list. The same model can vary sharply in quality, latency, availability, and price across providers; higher-priced providers are consistently faster, but price does not reliably predict quality or availability; and provider feasibility is task-selective, with one deployment nearly normal on knowledge tasks but catastrophically degraded on multi-step reasoning. We formulate same-model provider selection as a price-taker market-aware routing problem. A simple measured-map policy routes to the cheapest provider that is both quality-equivalent and healthy, yielding matched-quality savings while avoiding degraded endpoints. Because the map drifts, we introduce FACET, an online provider router that certifies per-(provider x task) feasibility facets and fails safe to an anchor before serving uncertified arms. Across relaxed deployment assumptions, FACET tolerates imperfect task assignment and sparse feedback, while systematic evaluator bias exposes a quality-signal trust boundary that can be mitigated with ground-truth probes or audits. Live provider runs further confirm that certification can move real traffic from a premium anchor to a substantially cheaper certified endpoint. Our results suggest that market-aware LLM routing must measure not only which model to use, but also who serves it.

1 INTRODUCTION

After an open-weight model is selected, clients still need to choose a provider, and that choice cannot be inferred from price alone. The paper motivates task-conditioned measurement and routing, then introduces measured-map selection and FACET for provider feasibility that changes over time.

1 INTRODUCTION

  • Provider selection remains an operational decision after model routing because providers serving the same weights can differ in price, latency, reliability, and answer quality.Open-weight models may be hosted by competing providers with different quantization, kernels, scheduling, timeout behavior, and reliability profiles.Source: §1 · p. 1
  • Price does not reliably predict provider quality or availability, while provider feasibility varies by task and over time.Higher-priced providers are consistently faster; provider rankings can invert across tasks, and the cheapest quality-equivalent healthy provider can change as the market shifts.Source: §1 · pp. 1–2
  • Measured-map routing selects the cheapest measured-equivalent healthy provider, while online feedback updates its certificates as the map drifts.The paper formalizes same-model provider choice under quality, health, latency, and cost constraints.Source: §1 · p. 2
  • FACET certifies feasibility for each provider–task pair before serving a cheaper endpoint, otherwise falling back to an anchor.The paper tests imperfect task assignment and feedback, and identifies ground-truth probes and audits as safeguards against evaluator bias.Source: §1 · pp. 2–3

2 SETTING AND MEASUREMENT

The paper treats provider selection as the decision remaining after a model is chosen, with task-conditioned quality latent and price, latency, and health observable. It measures providers with pinned probes and frames routing as minimizing cost subject to feasibility constraints.

2 SETTING AND MEASUREMENT

  • The router uses an observed or inferred task-context signal, with uncertain or unknown context treated as an uncertified facet that can fail safe.The initial evaluation assumes correct task identification; later experiments relax that assumption.Source: §2 · p. 3
  • Provider state includes posted token price, measured latency, and health or availability, while task-conditioned quality is not directly known.Quality is represented as expected provider performance for a model, context, and time.Source: §2 · p. 3
  • Provider selection minimizes query cost subject to task-quality and health floors and, when specified, a latency budget.The measured-map quality floor is set relative to the best measured provider in each model–task cell, with δ = 0.05 in the primary setting.Source: §2 · p. 3
  • Provider-pinned measurements record accuracy, realized cost, mean latency, and availability across light probes and benchmark-scale tasks.The paper distinguishes its layer from model routers: it starts after model choice and estimates latent quality feasibility using probes or served-query feedback.Source: §2 · p. 3

3 THE PROVIDER AXIS IS REAL

Providers serving the same model can differ substantially, so provider choice remains consequential after model selection. The measurements find matched-quality savings alongside a price signal for speed, but not for task-conditioned quality feasibility.

3 THE PROVIDER AXIS IS REAL

  • Price–latency correlation is −0.61, with all 21/21 benchmark-scale cells negative; correlations with accuracy and availability are +0.05 and 0.00.The reported correlations are within model–task cells.Source: Table 2 · p. 4, §3 · p. 4
  • 50% median savings over the premium provider at matched quality; providers also differ by up to 8.8× in price and 68× in latency.Restricting analysis to nine non-saturated cells with measurable cross-provider quality differences yields 50.0% median savings, compared with 56.5% over all cells.Source: §3 · p. 4, Table 1 · p. 4
  • The cheapest provider falls below the quality floor in 5 cells, while harder reasoning cells show wider provider quality spreads.Easy cells can have several providers with similar accuracy despite substantial price differences.Source: §3 · p. 4, Table 1 · p. 4
  • Providers with very different normalized prices often achieve comparable accuracy, but Figure 2 also shows cheap providers that lose substantial accuracy.Each plotted point represents a provider serving a fixed model on a fixed task.Source: §3 · p. 4, Figure 2 · p. 5

4 FEASIBILITY IS TASK-SELECTIVE AND DRIFTING

Provider feasibility varies by task, so a provider can be competitive on one workload yet severely degraded on another. Feasibility also changes over time, even when posted prices remain mostly stable.

4 FEASIBILITY IS TASK-SELECTIVE AND DRIFTING

  • A Llama-3.3-70B endpoint was close to the provider field on knowledge evaluation but severely degraded on multi-step reasoning, making provider-level safety labels too coarse.The measurements covered 93 endpoint-cells across GSM8K, MMLU, and HumanEval.Source: §4 · p. 5
  • Route selections changed in 4/17 comparable cells over days 0–13 and 2/18 over days 13–43, despite mostly stable posted prices.Changes reflected availability recovery, rate limiting, provider exit, and occasional quality degradation; deeper provider pools also had multiple same-day re-elections.Source: §4 · p. 5
  • Provider feasibility must be task-conditioned and cannot be assumed fixed; measured maps address task variation, while FACET addresses map drift.Source: §4 · p. 5

5 MEASURED-MAP ROUTING

Measured-map routing chooses the cheapest provider that meets measured quality and availability thresholds. It achieves matched-quality savings, but provider selection can trade cost against latency and remains a snapshot-based policy.

5 MEASURED-MAP ROUTING

  • The router selects the cheapest provider within 5 points of the best measured accuracy and above 90% availability; across threshold sweeps, its below-floor rate was 0.0–22.2%.The thresholds are deployment choices, not tuned constants.Source: §5 · p. 6
  • 94% mean accuracy at 1.57× cheapest-provider cost came with a 0% below-floor rate; the premium policy cost 3.67× and still had 17% below-floor, while cheapest-provider routing had 28%.Out of sample, the selected provider stayed above the later-wave floor in 9/9 comparable cells under the primary thresholds; results changed when thresholds were relaxed or tightened.Source: §5 · p. 6
  • On MMLU and HumanEval, provider-aware selection reduced below-floor query rates from 55.9% and 57.5% to zero, with costs rising from $328.3 to $336.7 and $319.7 to $380.0, respectively.Across 17 cells with at least two quality-feasible providers, the cheapest feasible endpoint had a median 7.8× p95-latency penalty versus the fastest feasible endpoint.Source: §5 · p. 6

6 FACET: ONLINE FEASIBILITY CERTIFICATION

FACET addresses the risk that a changing provider map sends traffic to a newly attractive but degraded endpoint. It certifies provider–task facets before serving them, monitors admitted facets, and falls back to an anchor while candidates remain uncertified.

6 FACET: ONLINE FEASIBILITY CERTIFICATION

  • Generic online bandits can fine-rank providers after feedback accumulates, but exploring a newly attractive arm can expose users to a catastrophically degraded provider.FACET instead accumulates quality evidence while traffic falls back to an anchor.Source: §6 · p. 6
  • FACET certifies each provider–task pair separately, then continuously checks admitted facets and quarantines them if quality degrades.Replay certification uses recent labelled observations and point-estimate rules; unc ertified endpoints are not served.Source: §6 · pp. 6–7
  • The ablations isolate fail-safe anchoring and task-conditioned certification: a multi-task stream can make context-blind pooling certify a provider that is unsafe on one task.The table reports catastrophic exposure as below-floor served queries; the anchor ablation also tests removal of the never-serve-uncertified rule.Source: Table 3 · p. 7, §6 · p. 7
  • FACET’s cost premium buys protection from cost-greedy selection of uncertified low-cost providers, while continuous monitoring limits exposure after certification.Source: Figure 3 · p. 7, §6 · p. 8
  • With a shared served-feedback monitor, periodic routing reached 0.3–0.5% below-floor exposure, comparable to FACET; certification reduced dedicated probe spend by 8–23× versus scheduled full-pool probing.The comparison separates continuous monitoring’s protection against later degradation from certification’s protection at admission.Source: §6 · pp. 7–8, Table 4 · p. 8
  • The added protection has application-dependent value: break-even is about 17× an ordinary query’s cost versus SW-UCB, but roughly one query-price or less versus a frozen map or periodic refresh.Source: §6 · p. 8

7 BEYOND THE IDEALIZED SETTING

FACET is tested under imperfect task assignment and quality feedback, then against live providers. The results show useful fallback and migration behavior, while systematic evaluator bias and missing trustworthy signals bound what certification can establish.

7 BEYOND THE IDEALIZED SETTING

  • Missing or symmetric-noise evidence mainly triggers fallback, whereas systematic bias can corrupt the quality signal itself.The stress tests also include sparse feedback; ground-truth probes and audits are safeguards when evaluator bias is a concern.Source: §7 · pp. 8–9
  • At 33% label error, below-floor exposure rose to 4.72%, below the 6.72% of context-blind certification; unknown-query rejection kept catastrophic exposure at zero through 50% OOD traffic.This assumes an OOD reject signal is available; open-set detection itself is a separate problem.Source: §7 · pp. 8–9
  • FACET reduced serving cost 63.7% relative to the anchor (57.1% including probes) in a 36-hour live run, while served accuracy remained 88.3%.No provider quality collapse occurred during the window, so the run validates cold-start certification and migration rather than slip detection. False quarantine at small sample sizes and wasted probes on unavailable endpoints were addressed with confidence-aware certification and availability backoff.Source: Table 6 · p. 9, §7 · p. 9
  • With 20% random judge error, FACET served 95–97% of traffic from the anchor; ground-truth certification probes and small gold audits mitigate systematic evaluator bias.Systematic bias can increase exposure as it strengthens, making quality feedback a trust boundary rather than an assumed reliable signal.Source: §7 · p. 9
  • FACET still requires a maintained anchor, trustworthy quality evidence, and a way to assign or reject query context; without task signal and trustworthy evidence, certification cannot distinguish safe from unsafe providers.The live run and stress tests address different questions: live operation versus uncertainty and systematic error.Source: §7 · p. 9

8 CONCLUSION

Open-weight model choice remains incomplete because competing providers can deliver the same model with different quality, latency, availability, and price. The paper studies this provider-selection layer and reports that live certification can move traffic from a premium anchor to a cheaper certified endpoint.

8 CONCLUSION

  • Certification can run on real provider traffic and move requests from a premium anchor to a substantially cheaper certified endpoint.The paper concludes that routing must consider which provider currently has enough evidence to serve the selected model.Source: §8 · pp. 9–10

A LIMITATIONS

  • The measurements describe the current open-weight provider market, not a fully liquid token spot market, and light probes resolve large gaps better than marginal ones.Rapid pinned probing can induce rate limits, and a single aggregator and client location limit causal attribution; systematic evaluator bias requires ground-truth probes or audits for trustworthy quality evidence.Source: A LIMITATIONS · p. 14

B RELATED WORK POSITIONING

  • Existing client-side routers select models, whereas this provider layer selects among providers serving the already-selected open-weight model.The two layers can be stacked, with provider choice following model choice.Source: B RELATED WORK POSITIONING · pp. 14–15, Table 7 · p. 15

C DETECTOR-CORE COMPARISON

  • The detector core is useful for abrupt, large-gap quality slips, but tight-band cells or gradual drift can favor sliding-window learners.Removing the own-baseline detector weakens safety, while reward-maximizing election increases below-floor serves; the detector and floor-aware election address different failure modes.Source: C DETECTOR-CORE COMPARISON · p. 15, Table 8 · p. 15

D MEASUREMENT PROTOCOL AND CAVEATS

  • Measurements cover accuracy, realized cost, mean latency, and availability across provider-pinned requests, but probing and the measurement path constrain interpretation.Rapid probing can induce rate limits, and one public aggregator and client location mean latency may reflect aggregator behavior or geography as well as provider performance.Source: D MEASUREMENT PROTOCOL AND CAVEATS · p. 16

E WHEN IS THE SAFETY PREMIUM WORTH PAYING?

  • Against sliding-window UCB, FACET’s break-even value is approximately $9.08, or about 17 ordinary query prices.The appropriate safety-cost balance depends on the application-level consequence of a below-floor answer; the paper does not claim universal dominance over adaptive bandits.Source: E WHEN IS THE SAFETY PREMIUM WORTH… · pp. 16–17, Table 9 · p. 17

F PRICE–LATENCY TRADE-OFFS AND LATENCY-CONSTRAINED ROUTING

Across measured provider–task cells, price is associated with latency more consistently than with accuracy or availability. Explicit latency constraints preserve some cost advantage, while probe-rate differences at low rates do not establish an optimal setting.

F PRICE–LATENCY TRADE-OFFS AND LATENCY-CONSTRAINED ROUTING

  • Every one of 21 cells has a negative price–latency correlation, with median ρ = −0.61; model-level association is negative for all 10/10 models (p = 0.002).Accuracy and availability correlations are near zero with varying signs.Source: F PRICE–LATENCY TRADE-OFFS AND… · p. 17, Table 10 · p. 18
  • The negative price–latency association remains stable across run selection, while the accuracy estimate changes sign and is never statistically significant.After excluding Groq, Cerebras, and SambaNova, the model-level median price–latency correlation is −0.706, with all 10/10 models negative (p = 0.002).Source: F PRICE–LATENCY TRADE-OFFS AND… · p. 17, Table 11 · p. 18
  • Within cells, generation throughput differs by as much as 18×, while provider output length differs by at most 3.04×, supporting throughput rather than answer length as a latency mechanism.The decomposition is mechanism evidence, not a precise latency model or causal estimate.Source: Table 12 · p. 18, F PRICE–LATENCY TRADE-OFFS AND… · p. 19
  • Choosing the cheapest feasible provider incurs a median 7.8× p95-latency penalty versus the fastest feasible provider, while the fastest feasible endpoint costs a median 1.92× more.The price–latency pattern is a cross-sectional association, not evidence that higher prices cause faster service.Source: F PRICE–LATENCY TRADE-OFFS AND… · p. 19, Table 13 · p. 19
  • A 10-second deadline keeps all 12/12 evaluated cells feasible and raises cost by 19%; a one-second deadline leaves 6/12 feasible at 2.62× the unconstrained route cost.Source: F PRICE–LATENCY TRADE-OFFS AND… · p. 19, Table 14 · p. 19

G RUN-TO-RUN VARIABILITY

  • Low probe-rate settings have overlapping interquartile ranges extending to zero, while continuous monitoring keeps below-floor exposure roughly at 0–1.5% across tested settings.The reported comparison supports continuous monitoring versus periodic refresh, not fine-grained probe-rate tuning.Source: G RUN-TO-RUN VARIABILITY · p. 20, Table 15 · p. 20

H OUT-OF-SAMPLE SENSITIVITY TO THE QUALITY FLOOR AND HEALTH THRESHOLD

An earlier-wave provider map can fail to preserve later-wave quality feasibility, although it compares favorably with cheapest- and premium-provider rules across tested settings. The paper frames provider selection as identifying price-attractive candidates and certifying their latent, task-conditioned quality feasibility.

H OUT-OF-SAMPLE SENSITIVITY TO THE QUALITY FLOOR AND HEALTH THRESHOLD

  • With a two-point quality margin, the measured-map router falls below the later-wave floor in 22.2% of cells; with a ten-point margin, the rate is 0.0%.At five points, the measured-map rate is 0.0–11.1% depending on health threshold, and it is never worse than the cheapest- or premium-provider comparison over tested settings.Source: H OUT-OF-SAMPLE SENSITIVITY TO THE… · p. 20, Table 16 · p. 21

I WHY PROVIDER SELECTION HAS AN INVERSE-BANDIT STRUCTURE

  • Provider prices, latency, and client-visible health are available before routing, while task-conditioned quality remains latent and must be assessed for feasibility.The router uses price ordering to identify attractive candidates, then spends measurement effort to determine whether they are feasible.Source: I WHY PROVIDER SELECTION HAS AN… · p. 21

J DRIFT-SHAPE STRESS TESTS

  • FACET is strongest against abrupt, large-gap slips, but gradual degradation or concurrent mines can favor sliding-window methods.The detector-core guarantee is matched to abrupt, large-gap quality slips, rather than all drift patterns.Source: J DRIFT-SHAPE STRESS TESTS · p. 21, Table 17 · p. 22

K MEASURED-MAP ROUTING RESULTS

Measured-map routing selects providers using measured quality and health, but an aged map can lose feasibility. Matched-quality savings persist among cells with measurable quality differences, while periodic re-probing can leave changed providers in service until the next probe round.

K MEASURED-MAP ROUTING RESULTS

  • An aged measured map is no longer perfectly safe, though its failures remain substantially less severe than routing blindly by price.The in-sample zero below-floor rate is by construction because the same measurements define feasibility and evaluate the policy.Source: K MEASURED-MAP ROUTING RESULTS · p. 22, Table 19 · p. 22

L SAVINGS BEYOND SATURATED CELLS

  • Removing all nine saturated cells reduces median matched-quality saving only from 56.5% to 50.0%.Substantial savings remain when providers have measurable quality differences and the router excludes endpoints failing the quality requirement.Source: L SAVINGS BEYOND SATURATED CELLS · p. 23, Table 20 · p. 23
  • Among non-saturated cells, savings range from 84.1% to 0.0%; zero-saving cases occur when the cheapest endpoint fails the quality requirement.The router pays more for a feasible provider rather than forcing a cheaper route.Source: L SAVINGS BEYOND SATURATED CELLS · p. 23, Table 21 · p. 23

M PERIODIC RE-PROBING BASELINE

  • Periodic re-probing can be safe and cheaper when a mine is present at refresh, but in S2 and S3 serving can continue after a provider slips below the floor.That exposure persists until the next global probe round.Source: M PERIODIC RE-PROBING BASELINE · pp. 23–24, Table 22 · p. 24
  • Certification protects against an initially unsafe mine, while served-feedback monitoring addresses degradation after admission; FACET reduces dedicated probe spend by 8–23× in the tested operating points.Greater anchor use can leave total cost similar despite reduced dedicated probe spend.Source: M PERIODIC RE-PROBING BASELINE · p. 24

N BENCHMARK-SCALE FEASIBILITY AND MULTI-WAVE DRIFT

Benchmark-scale measurements show that provider feasibility varies by task, while multi-wave observations show that the cheapest feasible route can change even when list prices remain stable.

N BENCHMARK-SCALE FEASIBILITY AND MULTI-WAVE DRIFT

  • Across 93 endpoint-cells, provider quality was often clustered, but some deployments were near the field on one benchmark and far below it on another.Measurements covered GSM8K, MMLU, and HumanEval; equivalence analysis is reported separately.Source: N BENCHMARK-SCALE FEASIBILITY AND… · p. 25, Table 24 · p. 25
  • The benchmark evaluation used n=150 for GSM8K and MMLU and n=100 for HumanEval across all measured providers.The measurements were repeated 13 and 43 days after the initial collection.Source: N BENCHMARK-SCALE FEASIBILITY AND… · p. 25
  • The selected route changed in 4/17 comparable cells over the first interval and 2/18 over the second measurement interval.The changes were not primarily driven by list-price movement; availability, rate limiting, provider membership, and quality can change while prices remain unchanged.Source: N BENCHMARK-SCALE FEASIBILITY AND… · pp. 25–26, Table 25 · p. 26

O ASSUMPTION-RELAXATION EXPERIMENTS

The experiments test FACET under imperfect information, live deployment, model-router composition, online learning, and provider drift. They find that fail-safe certification remains useful under some relaxed assumptions, but depends on trustworthy quality evidence and operational safeguards.

O ASSUMPTION-RELAXATION EXPERIMENTS

  • With 20% quality-label error, 95–97% of traffic fell back to the anchor; ground-truth probes and a 5% audit mitigated targeted evaluator bias.Ground-truth probes kept mean cold-start exposure at or below 0.31% through 70% targeted bias; audits reduced exposure roughly 2–5× in tested biased-feedback regimes.Source: O ASSUMPTION-RELAXATION EXPERIMENTS · p. 27, Table 29 · p. 27

P LIVE PROVIDER DEPLOYMENT DETAILS

  • In a roughly 36-hour live run, served price fell to $0.210/M tokens after query 300, reducing serving cost 63.7% and cost including probes 57.1% versus the anchor.The anchor was $1.04/M tokens; live deployment required Wilson-interval certification with nmin = 20 and availability gating with exponential backoff.Source: P LIVE PROVIDER DEPLOYMENT DETAILS · pp. 28–29

Q COMPOSITION WITH AN UPSTREAM MODEL ROUTER

  • Provider routing left GSM8K unchanged when its cheapest endpoint was feasible, but addressed degraded same-model endpoints remaining after upstream model selection on MMLU and HumanEval.This was a composability stress test, not an evaluation of a specific released RouteLLM checkpoint.Source: Q COMPOSITION WITH AN UPSTREAM MODEL… · p. 29, Table 32 · p. 29

R EXACT-REPLAY BANDIT CURVES

  • Online learning can fine-rank providers with enough feedback, but FACET probes uncertified arms without serving them because generic bandits may explore a cheap catastrophic endpoint.The exact-replay experiment used the Llama-3.3-70B GSM8K cell with 11 provider arms.Source: R EXACT-REPLAY BANDIT CURVES · p. 29, Figure 4 · p. 30

S DETECTION GUARANTEES

  • FACET separates admission certification from monitoring: uncertified facets are not served, while CUSUM detects later degradation of previously certified facets.After detection and quarantine, longer outages add no further below-floor serves; detection delay grows as 1/∆2 for small gaps.Source: S DETECTION GUARANTEES · p. 30

T HIGH-FREQUENCY PRICE MONITORING AND THE LIMITS OF AGGREGATOR VISIBILITY

High-frequency monitoring finds that aggregator-visible prices can miss both competitive price changes and a provider’s time-varying tariff. Equivalence tests and cost-regret experiments bound the savings and trade-offs of provider routing.

T HIGH-FREQUENCY PRICE MONITORING AND THE LIMITS OF AGGREGATOR VISIBILITY

  • In the 30-provider pool, 14 price changes produced 3 re-elections in one day; the 15-provider pool had 2 changes and 2 re-elections.The 8- and 12-provider pools did not move, and deeper pools showed more price movement and re-election.Source: T HIGH-FREQUENCY PRICE MONITORING AND… · p. 31, Table 33 · p. 31
  • The aggregator reported an unchanged price during peak windows even though direct API billing showed identical work cost materially more at the source.The observed peak charge matched the published ¥0.49 tariff within 1%, but settlement lag prevented a precise multiplier estimate.Source: T HIGH-FREQUENCY PRICE MONITORING AND… · p. 32

U EQUIVALENCE-CLASS WIDTH: A TOST CHECK

  • Equivalence was statistically established in 4/17 cells, while median saving relative to the premium provider fell from 55% to 46% under confidence-supported quality bounds.The TOST result is a lower bound because the test was underpowered; the routing policy instead applies an explicit per-provider quality floor.Source: U EQUIVALENCE-CLASS WIDTH: A TOST CHECK · pp. 32–33

V COST-REGRET SCALING

  • In a controlled eight-arm cell, median cost-regret grew approximately linearly with change-points, with least-squares R2 of 0.97–1.0.This characterizes the cost paid for safety rather than the paper’s central safety guarantee.Source: V COST-REGRET SCALING · p. 33

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