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Re-derivability Decides What a Staged Agent Pipeline Recovers After an Upstream Fault

Tianqi Bu, YuXuan Peng, Junteng Tu, Henghui Xiao

arXiv:2609.32802v1cs.AIcs.CLcs.LG

TL;DR

The paper asks what determines whether an upstream fault survives in a staged language-model pipeline. It varies how many downstream stages can rebuild needed information from the original problem, finding that re-grounding improves retention under fault; the evidence is bounded to the tested settings and tasks.

  • Problem

    Which property determines whether an upstream mistake survives when staged agents pass information between stages?

    Source: §1 · p. 2

  • Method

    The authors inject one deterministic first-stage fault and re-expose the original problem to k downstream stages while holding the agents, items, fault, and topology fixed.

    Source: §1 · p. 2, §2 · p. 3

  • Results

    Matched retention rises with re-grounding on four of four backbones, reaching 0.692, 0.711, 0.707, and 0.957 at k = 3.

    Source: §1 · p. 2

  • Takeaways & Limitations

    Teams that run a pipeline anyway should ground the stage that lost the information, and ground it first.

    Source: §11 · p. 9

    The claims are limited to verifiable reasoning with checkable answers, the shared 120 fixed gsm_hard items, open-weight instruction-tuned backbones with thinking disabled, and one fault at one injection site.

    Source: §9 · p. 8

Abstract

from arXiv · show

One variable sets what an upstream fault costs a staged pipeline of language-model agents: re-derivability, how much of what a stage needs it can rebuild from the original problem. Grounding an inspector agent in that problem is worth +0.608 [+0.517, +0.700] to +0.358 over a blind one on four open-weight backbones served with thinking disabled, and on the two Qwen backbones the blind inspector changes no item at all. That head-to-head is exploratory. One deterministic fault enters the first stage, and we re-expose the original problem to $k = 0,\dots,3$ of the downstream stages with agents, items, fault and topology held fixed, on 120 gsm_hard items per arm at temperature zero. Accuracy under fault rises on four of four backbones, from +0.233 to +0.392, the largest Holm-adjusted $p$ being $2.1\times10^{-6}$. A registered kill test rules out tokens. Blanking every word holds the word slots fixed, and retention tracks the visible fraction on four of four, climbing from 0.221 to 0.692 on the primary. Those two families are confirmatory and everything else here is exploratory. The interaction excludes zero on two of four backbones under the registered pipeline, four of four under a three-stage pipeline, and three of four under full message history, the primary at +0.317. On Llama-3.1-8B the fault carries no detectable cost at any dose, so the other three carry every claim about what a fault costs. Re-derivability also sets what the architecture costs, and no decomposition we measured reliably beats one direct call. With no fault injected the registered pipeline loses to that call by -0.267, -0.125 and -0.317, and on Phi-4 reads +0.058 at $p = 0.118$, which the test fails to separate from zero. The repair that works is cheap and front-loaded: the first re-grounded stage buys +0.394 of matched retention for +59.8 tokens per item on Qwen3-14B, and the stages after it buy nothing.

1 INTRODUCTION

The introduction asks what determines whether an upstream mistake survives a staged pipeline and identifies re-derivability—the ability to rebuild needed information from the original problem—as the key variable. Re-grounding downstream stages improves retention under fault, while a content-blanking control distinguishes usable content from word slots.

1 INTRODUCTION

  • The strict staged pipeline loses to one direct call on three of four backbones without a fault, while the fourth difference is not separable from zero.With a fault at the first stage, strict-pipeline retention is 0.368, 0.289, 0.230, and 0.667 across the four backbones.Source: §1 · p. 1
  • The open question is which property determines whether an upstream mistake survives, since prior explanations do not vary what a stage can see.The cited lines of work explain closed-loop advantage, architectural vulnerability, and grounded inspection without varying access to the original problem.Source: §1 · p. 2
  • At k = 3, matched retention reaches 0.692, 0.711, 0.707, and 0.957 across the four backbones; the endpoint contrast rejects with adjusted p no larger than 2.1×10^-6.The switch re-injects the original problem into k downstream stages while holding the other conditions fixed.Source: §1 · p. 2
  • Replacing every problem word with a blank preserves word slots but leaves no content; retention falls to 0.221 on the primary and rises with visible fraction on all four backbones.The registered kill test for the risk that token presence explains recovery did not fire.Source: §1 · p. 2

2 SETUP

The setup compares fixed staged pipelines under a single deterministic first-stage fault, varying whether downstream stages receive the original problem. It defines separate matched, deployed, and occlusion ratios and evaluates four open-weight instruction-tuned backbones on a fixed gsm_hard subset.

2 SETUP

  • Pipeline A has four sequential stages that receive only their predecessor’s output; one wrong_intermediate fault is injected at the first stage with probability 1.0 and severity 1.0.The re-grounding switch re-injects the original problem into the k downstream stages nearest the fault; k = 1 reaches the stage that directly receives the faulted message.Source: §2 · p. 3
  • PRRmatched divides faulted accuracy by the no-fault cell at the same depth and re-grounded stage set, and every dose claim rests on this moving-ceiling ratio.PRRdeployed uses the strict pipeline at k = 0 as denominator, while PRRocc uses a fixed no-fault denominator at kmax.Source: §2 · p. 3
  • The blanking control replaces nested, hash-seeded fractions of problem words with blanks, preserving word count but not tokenizer count.The fully masked arm carries 0.964, 0.904, 1.032, and 0.942 times the fully visible prompt tokens across the four backbones.Source: §2 · p. 3
  • The evaluation uses four open-weight instruction-tuned backbones with thinking disabled and the same fixed 120 gsm_hard items per arm at temperature zero.Qwen3-14B is the primary backbone; MATH500 is used for an exploratory topology bank, while no result is computed on the MMLU bank.Source: §2 · p. 3
  • Table 1 reports per-backbone clean ceilings, matched and deployed PRRs, paired accuracy differences with exact conditional intervals, and Family A Holm-adjusted p-values.The deployed PRR is operational only; its denominator is the strict pipeline at k = 0.Source: Table 1 · p. 4

3 THE PLAN PROTECTS THE PROCEDURE, NOT THE THRESHOLDS

The analysis plan protects specified inferential procedures, but not thresholds or other choices, and was fixed only after dose-curve point estimates were available. Two registered confirmatory families use one-sided paired tests with within-family Holm correction; the kill rule did not fire.

3 THE PLAN PROTECTS THE PROCEDURE, NOT THE THRESHOLDS

  • The analysis plan was fixed after all four dose-curve point estimates were on disk; tests, corrections, bootstraps, trend tests, thresholds, sidedness, family membership, and backbone set were not protected.The authors explicitly distinguish protecting the inferential procedure from protecting thresholds.Source: §3 · p. 4
  • The two confirmatory families are the four k = 0 versus k = 3 endpoint contrasts and the four occlusion endpoints, tested with one-sided exact paired McNemar tests and within-family Holm correction at α = 0.05.There is no correction across the two families, and all four dose curves were already on disk when the plan was pinned.Source: §3 · p. 4
  • None of the four pre-result kill-rule clauses fired, and the authors simulated what it would have taken for the rule to fire.Each clause would have killed the pipeline on at least two backbones if triggered.Source: §3 · p. 4

4 NEITHER DECOMPOSITION RELIABLY BEATS ONE CALL

The registered strict pipeline does not reliably beat one direct call: it loses on three of four backbones, with the remaining comparison unresolved. A three-stage decomposition is at parity with one call in exploratory results, while the measured starting performance varies across configurations.

4 NEITHER DECOMPOSITION RELIABLY BEATS ONE CALL

  • The strict pipeline trails one direct call by −0.267, −0.125, and −0.317 on three backbones, while Phi-4’s +0.058 difference is not separated from zero.The fully re-grounded pipeline separates from the direct solve only on Llama, where it is −0.133 below it.Source: §4 · p. 4
  • Pipeline B’s four no-fault differences from one call are +0.017, +0.025, +0.033, and −0.050, with every interval covering zero; these exploratory results indicate parity, not a win.On the primary, the −0.267 deficit becomes a contrast of four discordant items.Source: §4 · p. 4
  • Figure 2 compares each faulted dose row with its same-depth no-fault twin; its saturated deficit block narrows as k rises on all four backbones, while Llama has no block to narrow.Panel (c) shows PRRmatched with 95% paired-item bootstraps; k = 0 versus k = 3 is confirmatory, while intermediate doses are exploratory.Source: Figure 2 · p. 5
  • The registered pipeline is the worst of four measured configurations on two backbones and third of four on another; its smallest interactions occur where it starts lowest.The largest interaction is on Phi-4, where the registered pipeline starts highest.Source: §4 · p. 5

5 THE DOSE-RESPONSE HOLDS ON FOUR OF FOUR

Re-grounding improves accuracy under fault across all four backbones, although Llama-3.1-8B shows no detectable fault cost at any dose. The matched-retention curve can dip even as accuracy under fault does not fall.

5 THE DOSE-RESPONSE HOLDS ON FOUR OF FOUR

  • The paired accuracy-under-fault difference acc(F, kmax) − acc(F, kmin) was +0.392 on Qwen3-14B and Phi-4, +0.375 on Qwen3-8B, and +0.233 on Llama-3.1-8B.Family A holds on four of four, with Holm-adjusted p from 1.1×10^-13 to 2.1×10^-6.Source: §5 · p. 5
  • On Qwen3-14B, matched retention is 0.368, 0.762, 0.692, and 0.692 across k = 0 to 3, while the other three curves share the front-loaded shape.Qwen3-8B’s k = 2 and k = 3 arms have identical correctness vectors despite different raw completions.Source: §5 · p. 5
  • Accuracy under fault, not matched retention, is claimed to be monotonic; on Qwen3-14B the matched ratio dips as its no-fault ceiling rises from 0.700 to 0.867.No adjacent decrease counts across the twelve contrasts under the registered rule; the largest counted drop is +0.0 items against a tolerance of five.Source: §5 · p. 5
  • Llama-3.1-8B has no detectable fault cost at any dose, while its pipeline loses to a single call by −0.317, separating decomposition loss from fault propagation.Claims that require a costly fault therefore apply only to the other three backbones.Source: §5 · pp. 5–6

6 THE PRICE IS RE-DERIVABILITY, NOT TOKENS

The registered occlusion control supports re-derivable content, rather than token count, as the relevant factor: retention rises with visible content across all four backbones. Neither registered kill criterion fires.

6 THE PRICE IS RE-DERIVABILITY, NOT TOKENS

  • 0.221 to 0.692: on the primary backbone, occlusion retention rises across visible fractions while every word slot remains present but blanked content supplies no information.The curve is nondecreasing on every backbone and strictly rising at every step except Llama’s tie at 0.370.Source: §6 · p. 6
  • No clause of the registered kill rule fires; the second-smallest deployed and matched gains clear their margins by +28.4 and +13.0 items, respectively.Both margins exceed the measured four-item run-to-run jitter.Source: §6 · p. 6

7 RE-GROUNDING WORKS BY RETURNING THE PROBLEM

Replacing the faulty upstream message with an uninformative line yields different outcomes across backbones, and fault-specific benefits depend on pipeline configuration. Grounding an inspector outperforms a blind one, but can harm a healthy pipeline.

7 RE-GROUNDING WORKS BY RETURNING THE PROBLEM

  • +0.208 on Phi-4 and +0.125 on Llama: the uninformative upstream message beats the faulty one, while the two Qwen contrasts cover zero without establishing equivalence.The Qwen intervals still admit ±0.117 and ±0.108, and no equivalence margin was registered.Source: §7 · p. 7
  • On the registered predecessor-only pipeline, the re-grounding interaction covers zero on Qwen3-14B and Llama-3.1-8B; that result does not generalize to other configurations.The same estimand excludes zero on four of four under pipeline B and on the primary under full history.Source: §7 · p. 7
  • +0.608 to +0.358: grounding the inspector beats a blind inspector on all four backbones, but on the Qwens the blind inspector changes no item from the strict pipeline.On a healthy pipeline, the two significant inspector differences are costs rather than deficits against one direct call.Source: §7 · p. 7
  • 0.980 [0.931, 1.030] against the same-depth no-fault cell contrasts with up to 6.250 [3.500, 16.667] against a different-stage-count cell.The apparent ratio depends on which ceiling supplies its denominator.Source: §7 · p. 7

8 THE EFFECT SURVIVES BOTH OTHER CONFIGURATIONS

The re-grounding effect persists under a three-stage pipeline and full message history, though its interaction with fault varies by configuration. The first re-grounded stage captures nearly all the matched-retention gain for a modest token increase.

8 THE EFFECT SURVIVES BOTH OTHER CONFIGURATIONS

  • +0.433 [+0.342, +0.525] on Qwen3-14B: pipeline B’s interaction excludes zero on all four backbones, compared with two of four under pipeline A.On the primary, pipeline B’s no-fault gain is exactly 0.000, making its interaction entirely fault-specific in that configuration.Source: §8 · p. 7
  • +0.317 [+0.200, +0.433] is the full-history interaction on Qwen3-14B; the interaction excludes zero on three of four backbones overall.Full history does not distinguishably change the faulted arm on the first three backbones and is worse on Llama by −0.075 [−0.133, −0.017].Source: §8 · pp. 7–8
  • +0.394 matched retention for +59.8 tokens per item comes from the first re-grounded stage on Qwen3-14B; the next two add −0.070 and +0.000.The first-stage pattern holds on the other three backbones, while tokens rise monotonically with k.Source: §8 · p. 8

9 WHAT THE CONTROLS DECIDE, AND WHERE THE CLAIMS STOP

Length-matched controls show that content removal, not simply a shorter message, drives the primary result, while outcomes vary across backbones and reasoning families. Claims remain bounded by the fixed benchmark and exploratory status of most analyses.

9 WHAT THE CONTROLS DECIDE, AND WHERE THE CLAIMS STOP

  • Across six non-mathematical reasoning families, state-tracking families collapse and recover, while binary-answer families barely move.The authors attribute the latter pattern to the two-valued answer space bounding how far one wrong intermediate can push the result.Source: §9 · p. 8
  • 0.408 on the primary backbone for the equal-length filler, below both the one-line control (−0.167 [−0.250, −0.083]) and the faulty message itself (−0.192 [−0.308, −0.067]).This post-pin exploratory control refutes the distraction account on the primary backbone: removing content at fixed length costs accuracy.Source: §9 · p. 8
  • The length-matched control detects dependence on the primary, none on Qwen3-8B (+0.025 [−0.083, +0.133]), and an anomaly-direction effect on Phi-4 (+0.242 [+0.150, +0.333]).On Llama, the one-line anomaly disappears once length matches (+0.058 [−0.033, +0.150]).Source: §9 · p. 8
  • The item-level inferences apply only to 120 fixed gsm_hard items, and every task is verifiable reasoning with a checkable answer.All backbones are open-weight, instruction-tuned, and served with thinking disabled; the single-site fault is not a severity sweep, and claims outside two registered families are exploratory.Source: §9 · p. 8
  • Redundancy and topology search both fail to improve the measured outcome in the exploratory analyses.The passage reports these nulls without further results.Source: §9 · p. 8

10 RELATED WORK

Related work studies agent failures, observability, memory, and communication topology, but prior fault-injection work did not manipulate downstream access to the original problem. This paper frames re-derivability as a pipeline-level intervention under matched ceilings and an occlusion control.

Fault injection and failure taxonomies

  • Prior fault-injection work tested multiple fault types and attributed closed-loop resilience to a shared message pool, but did not test that explanation.This paper manipulates the shared-information hypothesis; the prior study covers many fault types, whereas this paper uses one.Source: §10 · p. 8

The closest prior measurement

  • Huang et al. (2025) passed chat history to an Inspector by construction, so their study could not separate adding an inspector from giving it the problem.They did not vary what the inspector could see.Source: §10 · p. 8

Re-derivability as a named variable elsewhere

  • Kwon (2026) named re-derivability for lossy memory in a single agent; this paper manipulates it between pipeline stages with matched ceilings and an occlusion control.Neighboring studies examine isolated context loss, long-context position, decomposed prompts, or skill-library reconstruction.Source: §10 · p. 9

No widely used framework defaults to strict

  • Strict predecessor-only visibility isolates the variable, but no widely used framework defaults to that setting.AutoGen carries message history, MetaGPT routes through a publish-subscribe pool, and ChatDev forwards more than the preceding artefact.Source: §10 · p. 9

Byzantine and adversarial framings

  • This paper inverts Byzantine and adversarial framings, where faulty components are adversarial and agreement is the remedy.The cited neighboring work also covers self-correction, redundancy as reliability, and error propagation.Source: §10 · p. 9

11 CONCLUSION: GROUND THE STAGE THAT LOST THE INFORMATION

Re-derivability moves fault retention across four backbones, and re-grounding still helps under full message history. The authors recommend grounding the stage that lost information, while emphasizing that the pipeline itself often trails a single direct call and that the evidence has narrow scope.

11 CONCLUSION: GROUND THE STAGE THAT LOST THE INFORMATION

  • One manipulated variable moves fault retention on four of four backbones, with a matched ceiling at every dose and a registered control separating derivable content from token presence.Full message history reproduces the effect on four of four backbones.Source: §11 · p. 9
  • The registered transfer target of 0.900 was missed: among three eligible backbones, the third-largest matched retention is 0.692.The interaction covers zero on two of four backbones under the registered predecessor-only pipeline; Llama has no detectable fault cost at any dose.Source: §11 · p. 9
  • Full message history is not re-grounding: when the first stage is faulty, passing its history also passes the contamination, while re-grounding still lifts accuracy under fault on four of four backbones.The result indicates that the registered setting does not manufacture the remedy.Source: §11 · p. 9
  • Teams using a pipeline should ground the stage that lost information, and ground it first, though the pipeline loses to a single direct call on three of four backbones and never reliably wins.Full history narrows the deficit on one of those three without closing it; open-ended generation, multi-hop retrieval, and tasks without checkable answers remain untested.Source: §11 · p. 9
  • Generative AI tools assisted only with language editing; the authors state that they developed and verified the scientific content and take responsibility for it.Source: AI USE STATEMENT · p. 10
  • The paper measures injected-fault recovery on public reasoning benchmarks with open-weight models served locally.The fault is deterministic, single-site, and benign by construction, so the paper does not address adversarially chosen faults.Source: ETHICS STATEMENT · p. 10
  • Appendix T identifies the result files, analyser, gate suite, and command for rebuilding every table and figure.The reproducibility materials also document analysis-plan deviations, cache replays, replica-lane jitter, fixed items and settings, and per-item correctness vectors available on request.Source: REPRODUCIBILITY STATEMENT · p. 10

A THE REGISTRATION, AND EVERY DEVIATION FROM IT

The analysis plan was fixed after the four dose curves were on disk, protecting the inferential procedure but not the thresholds or confirmatory choices. Across the section’s checks, the kill rule did not fire, while the transfer target was missed and item-level gains were concentrated in earlier re-grounding doses.

A THE REGISTRATION, AND EVERY DEVIATION FROM IT

  • The plan was fixed after all four dose curves were tabulated, so the inferential procedure was protected but thresholds, sidedness, family membership and backbone set were not.The authors explicitly do not call the analysis pre-registered.Source: A THE REGISTRATION, AND EVERY… · p. 16

B PER-ARM REPLAY STATUS, AND THE MEASURED RUN-TO-RUN JITTER

  • Four primary-backbone arms shifted by −0.017 on re-score, a two-item change below the measured four-item run-to-run jitter.Qwen3-8B’s eight recomputed arms did not move; the re-score is distinct from a re-measurement.Source: B PER-ARM REPLAY STATUS, AND THE… · p. 17

C WHICH ITEMS EACH DOSE RECOVERS

  • 25 items were already right at k = 0, 43 more first turned right at k = 1 and 7 at k = 2; none first turned right at k = 3.These counts describe Qwen3-14B’s 120 items, ordered by the first dose that answered each item.Source: C WHICH ITEMS EACH DOSE RECOVERS · p. 18

D FAMILIES, THE KILL RULE, THE BREAKDOWN POINTS AND THE RULE’S

  • 0.999 is the kill rule’s firing probability against no dose response, yet it fires with probability 0.000 at the gains measured in this campaign.At the registered margin, firing probability is 0.705; the largest true gain detected at 80% power is 0.150.Source: D FAMILIES, THE KILL RULE, THE… · p. 21
  • The registered transfer threshold was 0.692 against a target of 0.900, using three eligible backbones because Llama-3.1-8B’s PRRmatched(kmin) was 0.667.The eligible-set shortfall was disclosed after analysis; the registered formula and threshold did not change.Source: A THE REGISTRATION, AND EVERY… · pp. 16–17, D FAMILIES, THE KILL RULE, THE… · p. 21

E TWO DESCRIPTIVE ANCHORS

  • The preflight anchors were exploratory: leaking the original problem at the injection site scored 0.600, while fault damage varied by injection site rather than increasing with depth.The same fault at stages one through four scored 0.208, 0.200, 0.325 and 0.017.Source: E TWO DESCRIPTIVE ANCHORS · p. 21

F SEED-LEVEL TESTS

  • At temperature 0.7, endpoint, slope and Page trend tests rejected on all four backbones, but trend tests do not establish monotonicity.The main-text monotonicity claim instead rests on the item-level adjacent-decrease rule.Source: F SEED-LEVEL TESTS · p. 21

H THE TWO MATCHED DENOMINATORS, AND THE TOKEN PREMISE

  • 0.221 to 0.692 is the primary backbone’s occlusion ratio across visible fractions; blanks hold word count fixed while removing problem content.The fully masked arm has 0.964, 0.904, 1.032 and 0.942 times the fully visible prompt tokens across the four backbones.Source: H THE TWO MATCHED DENOMINATORS, AND… · p. 22

I CROSS-FAMILY RESULTS

The cross-family results require a moving no-fault ceiling, while the mechanism and architecture comparisons show that re-grounding’s benefits depend on configuration and do not establish that staged pipelines outperform one direct call. The blind inspector changes no items on the two Qwen backbones, so its comparison with a grounded inspector is not independent evidence there.

I CROSS-FAMILY RESULTS

  • The matched ratio uses the no-fault ceiling at the same dose; Llama-3.1-8B’s ceilings move by up to 39 of 120 items, and the injected fault is weaker on non-numeric families.The paper does not claim one fault applies across families.Source: I CROSS-FAMILY RESULTS · p. 23, Table 5 · p. 24

J THE MECHANISM TABLE, AND THE LENGTH-MATCHED CONTROL

  • On Qwen3-14B, D(k=1) = +0.192 [+0.075, +0.308] excludes zero, while D(k=2) and D(k=3) do not; Qwen3-8B and Phi-4 exclude zero at every dose, and Llama at none.The registered interaction is at kmax; interior-dose results are exploratory.Source: J THE MECHANISM TABLE, AND THE… · p. 23, Table 6 · p. 25

K THE STRICT PIPELINE AGAINST ONE CALL, AND WHAT THE RIGGING

  • The strict four-stage pipeline trails one direct call on three backbones (−0.267, −0.125, and −0.317) and is indistinguishable on Phi-4 (+0.058 [+0.000, +0.125], p = 0.118).The fully re-grounded no-fault pipeline is a different, more favorable comparison against the direct solve.Source: K THE STRICT PIPELINE AGAINST ONE… · pp. 24–25

L THE DEFENCE HEAD-TO-HEAD, AND THE CEILING IT IS MEASURED

  • The blind inspector matches the strict pipeline on 0 of 120 items on both Qwen backbones; the grounded-versus-blind and grounded-versus-strict contrasts are therefore not independent evidence there.The arms differ on only 3 and 9 items on Phi-4 and Llama-3.1-8B, respectively.Source: L THE DEFENCE HEAD-TO-HEAD, AND THE… · pp. 25–26
  • The grounded inspector’s ratio is 0.980 [0.931, 1.030] against its same-stage no-fault ceiling, but 6.250 [3.500, 16.667] against a different-stage-count ceiling.These ratios use different denominators.Source: L THE DEFENCE HEAD-TO-HEAD, AND THE… · p. 26, Figure 5 · p. 26

M THE TWO PIPELINES SIDE BY SIDE

Across these sections, re-grounding’s measured effects depend on the pipeline configuration and comparison baseline; the cost curve is front-loaded, while topology-search results are limited and exploratory. The paper also distinguishes operational ratios from matched retention and documents what its reproduction path can rebuild.

M THE TWO PIPELINES SIDE BY SIDE

  • On Phi-4, the registered pipeline’s no-fault gain is −0.008 and its interaction D is +0.400, the largest reported; where it starts lowest, interactions are +0.092 and +0.050.Pipeline B is measured but unregistered, so its results are exploratory.Source: M THE TWO PIPELINES SIDE BY SIDE · pp. 26–27

N FULL MESSAGE HISTORY AGAINST PREDECESSOR-ONLY VISIBILITY

  • At n = 120, full-history contrasts cover zero on three backbones, but item-level disagreement means this is failure to detect a difference, not evidence of equivalence.On Llama, full history is worse by −0.075 [−0.133, −0.017], a boundary case rather than a fourth replication.Source: N FULL MESSAGE HISTORY AGAINST… · pp. 28–29, Table 10 · p. 29

O COST AT THE HEADLINE STANDARD

P TOPOLOGY SEARCH AS A NEGATIVE CONTROL

Q LEVERS THAT ARE NOT LEVERS

  • Under the re-run fault, a blind aggregator’s one-replica retention is 1.000, 1.022 and 1.011 on the first three backbones, versus grounded values of 0.980, 1.000 and 1.000.On Llama, the corresponding values are 0.538 blind and 0.717 grounded.Source: Q LEVERS THAT ARE NOT LEVERS · p. 30

R THE FLAT REGIME IN FULL

  • On 30 topologies, structural-predictor correlation is −0.503 [−0.756, −0.166] for reasoning-error faults, but intervals cover zero for injected noise and role drift.The bank is near a plateau, and the headline-matching fault cell was not run (n = 0).Source: R THE FLAT REGIME IN FULL · p. 31, Table 13 · p. 32

S THE DEPLOYED RATIO

  • PRRdeployed uses the strict pipeline at k = 0 as its fixed denominator; nine deployed ratios exceed 1.0, while the matched ratio resolves seven.The remaining two are Phi-4 boolean-evaluation cases where both ratios read 1.008.Source: S THE DEPLOYED RATIO · p. 32, Figure 8 · p. 34

T REPRODUCIBILITY

  • One command rebuilds every table and figure from result files, but rebuilding those files requires the inference server and GPU allocation.Code and per-run logs are available from the corresponding author on request.Source: T REPRODUCIBILITY · pp. 32–34

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