Faithful, Not Corrective: Message-Format Effects in Multi-Hop Agent Relays Are Tier-Dependent

# Message-Format Effects in Multi-Hop Agent Relays Are Tier-Dependent
Source: [https://arxiv.org/html/2607.09678](https://arxiv.org/html/2607.09678)
## Faithful, Not Corrective: Message\-Format Effects in Multi\-Hop Agent Relays Are Tier\-Dependent

###### Abstract

When LLM agents hand information to one another, does the message format matter? Two literatures give contradictory answers: format\-optimization work reports that structured messages cut cost without hurting accuracy, while format\-restriction studies find that imposing structure degrades generation—and neither line has measured what happens when messages traverse*multiple*hops, where copy fidelity rather than one\-shot generation quality dominates\. We introduce a controlled relay testbed: task briefs containing twelve programmatically generated atomic facts are re\-encoded hop\-by\-hop in five formats \(free natural language, precision\-instructed NL, JSON, triples, key–value\) over six hops, scored by a fixed strong grader against programmatic ground truth, across two relay\-capability tiers, a cognitive\-load condition, and a paired\-fork error injection\. In short, in this two\-tier case study: format effects depend on the relay model—and, at the strong tier, not on how busy the relay is—while structure preserves content without repairing it\. Specifically, \(i\) under faithful\-relay instructions a strong relay is nearly lossless: the documented “telephone\-game” collapse does not occur, and for all but free NL the residual loss concentrates in the first encoding step; \(ii\) at the strong tier, adding per\-hop cognitive load raises generation cost by 24–53% while format\-level fidelity changes are bounded within±\\pm1\.8 points \(simultaneous bound\)\. Under a weak \(1\.5B\) relay, \(iii\) the dispersion of hop\-6 recall across formats grows by a factor of8\.78\.7by QA \(2\.2×2\.2\\timesjudge\-free\) on matched items \(SD across format means, 95% CI5\.35\.3–15\.515\.5; the spread grows from 2\.3 to 20\.5 points\), driven by two opposing mechanisms—an encoding toll paid by both rigid formats and drift resistance associated specifically with the fixed\-key JSON schema—that flip the format ranking in transit; and \(iv\) in a paired\-fork injection at the weak tier, a redundancy\-free wrong value, once present, persists to the final hop in 83–100% of chains in every format \(surface presence; grader\-level 76–86%\), while collateral damage to neighboring facts is undetectable \(per\-format upper bounds 0–13 points; JSON’s bound is≤0\\leq 0\)\. Structure buys a faithful, error\-localizing channel—not an error\-correcting code—and format choice should follow the weakest relay in the pipeline\.

Faithful, Not Corrective: Message\-Format Effects in Multi\-Hop Agent Relays Are Tier\-Dependent

Zayx ShawnIndependent Researcher

## 1Introduction

Multi\-agent LLM systems are, at bottom, relay systems\. A planner summarizes a task for an executor, the executor hands findings to a reviewer, an orchestrator re\-briefs a sub\-agent: at every boundary, task\-critical information is re\-encoded by one model for consumption by anotherHonget al\.\([2024](https://arxiv.org/html/2607.09678#bib.bib2)\); Qianet al\.\([2024](https://arxiv.org/html/2607.09678#bib.bib3)\); Duet al\.\([2024](https://arxiv.org/html/2607.09678#bib.bib1)\)\. Production pipelines increasingly place*small*models at these boundaries for cost reasonsNarayanet al\.\([2025](https://arxiv.org/html/2607.09678#bib.bib4)\); Żywotet al\.\([2026](https://arxiv.org/html/2607.09678#bib.bib5)\), and empirical failure analyses attribute over a third of multi\-agent failures to inter\-agent misalignment rather than to base\-model capabilityCemriet al\.\([2025](https://arxiv.org/html/2607.09678#bib.bib6)\)\. What gets lost at each handoff—and what the message*format*does to that loss—is therefore a load\-bearing design question\.

Two adjacent literatures answer it in opposite directions\. On one side, format\-optimization work shows that letting agents communicate in structured, non\-natural\-language formats preserves accuracy at a fraction of the token costChenet al\.\([2024](https://arxiv.org/html/2607.09678#bib.bib7)\), and protocol and safety guidelines recommend schema\-constrained messages specifically to prevent semantic driftWibowo and Polyzos \([2025](https://arxiv.org/html/2607.09678#bib.bib8)\)\. On the other, format\-restriction studies find the opposite sign: forcing models to generate inside rigid schemas measurably degrades reasoningTamet al\.\([2024](https://arxiv.org/html/2607.09678#bib.bib9)\), and natural\-language tool interfaces outperform structured schemasJohnsonet al\.\([2025](https://arxiv.org/html/2607.09678#bib.bib10)\)\. Meanwhile, a separate distortion literature documents that information passed through chains of LLM generations degrades progressively—the “broken telephone” effectMohamedet al\.\([2025](https://arxiv.org/html/2607.09678#bib.bib11)\); Perezet al\.\([2024](https://arxiv.org/html/2607.09678#bib.bib12)\); Ghafouri and Ferrara \([2026](https://arxiv.org/html/2607.09678#bib.bib13)\)—with delegation accuracy collapsing from 90\.7% to 22\.5% over five stages in one recent studyAoet al\.\([2026](https://arxiv.org/html/2607.09678#bib.bib14)\), and theory bounding the accumulation of relay errorFanet al\.\([2026](https://arxiv.org/html/2607.09678#bib.bib15)\)\.

These lines have never met: distortion studies fix the format and vary the chain; format studies vary the format over shallow, fixed\-depth exchanges without per\-hop fidelity measurement\. The missing cell matters because multi\-hop relay changes which mechanism dominates\. At one hop, the question is whether structure helps a model*generate*; across many hops, it is whether structure helps a model*re\-encode*content it did not author—and a format that hurts generation might still anchor content against cumulative drift, or vice versa\. The sign of the format effect in the relay regime is genuinely unknown\.

We resolve it with a controlled testbed in which everything that threatens validity is pinned down\. Ground truth is*programmatic*: briefs are rendered from twelve synthetic atomic facts \(owners, quantities, deadlines, constraints, dependencies, prohibitions\), so fidelity is measured against the generator, never against another model’s output\. Each relay agent sees only the previous hop’s message and must re\-issue the complete handoff in the same format\. Fidelity is scored two ways: a paraphrase\-tolerant QA recall \(a fixed strong grader at temperature 0 answers twelve closed\-form questions, exact\-matched programmatically\) and a judge\-free verbatim string recall; the grader is held fixed across all conditions so relay capability is never conflated with grader capability\. On this testbed we cross five formats with six hops, two relay\-capability tiers \(a strong API model versus a 1\.5B local model—a bundled contrast in family, scale, quantization, and serving stack\), a cognitive\-load condition at the strong tier, and a paired\-fork causal error injection at the weak tier\.

#### Contributions\.

\(1\) We complete the format×\\timeshops×\\timescapability design space with, to our knowledge, the first format\-controlled relay study, and find that for a strong relay the telephone\-game collapse simply does not occur: QA recall stays at or above0\.9730\.973for every format after six hops, and for all but free NL the residual loss concentrates at the first encoding step rather than accumulating \(§[4\.1](https://arxiv.org/html/2607.09678#S4.SS1)\)\. \(2\) At the strong tier, per\-hop cognitive load raises generation cost by 24–53% while any fidelity effect is bounded within±1\.4\\pm 1\.4points per format \(pointwise;±1\.8\\pm 1\.8simultaneous\) \(§[4\.2](https://arxiv.org/html/2607.09678#S4.SS2)\)\. \(3\) We show the format effect is a*capability regime*: on matched items, the across\-format dispersion of hop\-6 recall grows8\.7×8\.7\\timesunder the weak relay \(SD ratio, CI5\.35\.3–15\.515\.5; range2\.3→20\.52\.3\\to 20\.5points\), with every format degrading significantly \(paired weak−\-strong differences of1818–3737points\)\. The effect decomposes into two opposing mechanisms: an encoding toll paid by the rigid formats \(hop\-1 recall0\.7650\.765–0\.8000\.800forKv/Json, statistically indistinguishable from each other, vs\.0\.9620\.962forConstr\) versus drift resistance associated specifically with the fixed\-key schema:Jsonloses only4\.74\.7raw points over hops 1–6, retains0\.940\.94of its hop\-1\-correct facts to hop 6 under a survivor\-bias\-controlled measure \(vs\.0\.740\.74–0\.850\.85for all others\), and its paired drift advantage over every other format excludes zero even under Bonferroni adjustment—flipping the ranking in transit \(§[4\.3](https://arxiv.org/html/2607.09678#S4.SS3)\)\. \(4\) With a paired\-fork injection we give the folklore claim “schemas prevent drift” a causal adjudication: once an injected error is present in a message, every format propagates it faithfully \(surface persistence 83–100% at the final hop, closely matching each format’s retention of the*true*value, 86–100%\), and no format exhibits a detectable collateral cascade onto neighboring facts\. Structure is a faithful, error\-localizing channel, not an error\-correcting code \(§[4\.4](https://arxiv.org/html/2607.09678#S4.SS4)\)\.

## 2Related Work

#### Iterated distortion in LLM chains\.

Mohamedet al\.\([2025](https://arxiv.org/html/2607.09678#bib.bib11)\)establish that iterative LLM generation distorts information, using translation chains as the instrument;Perezet al\.\([2024](https://arxiv.org/html/2607.09678#bib.bib12)\)characterize attractor dynamics over repeated transmission, andGhafouri and Ferrara \([2026](https://arxiv.org/html/2607.09678#bib.bib13)\)track which social information survives AI–AI relay\. Closest to us in machinery,Fanet al\.\([2026](https://arxiv.org/html/2607.09678#bib.bib15)\)bound error accumulation across sequential tool calls, andAoet al\.\([2026](https://arxiv.org/html/2607.09678#bib.bib14)\)derive mutual\-information limits for delegated multi\-stage pipelines and observe accuracy collapsing within five stages\. All of these hold the message format fixed; none treats format as the experimental variable, and most rely on translation or social\-content proxies rather than task\-grounded facts with programmatic ground truth\.

#### Format effects at a single exchange\.

Chenet al\.\([2024](https://arxiv.org/html/2607.09678#bib.bib7)\)show agents can adopt compact non\-NL formats with comparable accuracy at up to 72\.7% fewer tokens; structured inter\-agent protocols are standard in deployed frameworksWanget al\.\([2025](https://arxiv.org/html/2607.09678#bib.bib16)\); Marroet al\.\([2024](https://arxiv.org/html/2607.09678#bib.bib17)\); Ehteshamet al\.\([2025](https://arxiv.org/html/2607.09678#bib.bib18)\)\. The opposing pole reports that format*restrictions*degrade reasoningTamet al\.\([2024](https://arxiv.org/html/2607.09678#bib.bib9)\)—a contested finding whose size depends on prompt engineering, and on which our strong\-tier ceiling result itself bears—and that natural\-language interfaces beat structured schemas for tool useJohnsonet al\.\([2025](https://arxiv.org/html/2607.09678#bib.bib10)\); prompt\-format sensitivity is itself largeSclaret al\.\([2024](https://arxiv.org/html/2607.09678#bib.bib27)\)\. These single\-exchange results cannot be extrapolated to relays, where per\-hop copy fidelity, not generation quality, dominates—the regime we measure\.

#### Multi\-agent communication and its failures\.

Topology shapes how errors and insights propagateShenet al\.\([2025](https://arxiv.org/html/2607.09678#bib.bib19)\), seeded errors can solidify into false consensusXieet al\.\([2026](https://arxiv.org/html/2607.09678#bib.bib20)\), and failure taxonomies place inter\-agent misalignment among the leading causes of system failureCemriet al\.\([2025](https://arxiv.org/html/2607.09678#bib.bib6)\)\. Capability is an emerging moderator across this literature: architecture–task fit governs when coordination helpsKimet al\.\([2025](https://arxiv.org/html/2607.09678#bib.bib21)\), and compute\-matched comparisons reverse headline multi\-agent gainsTran and Kiela \([2026](https://arxiv.org/html/2607.09678#bib.bib22)\)\. Orthogonal work replaces the text channel altogether with activations, latents, or KV cachesRamesh and Li \([2025](https://arxiv.org/html/2607.09678#bib.bib23)\); Duet al\.\([2026](https://arxiv.org/html/2607.09678#bib.bib24)\); Shiet al\.\([2026](https://arxiv.org/html/2607.09678#bib.bib25)\); we instead characterize the text channel that black\-box, cross\-vendor pipelines actually use\. Our experimental hygiene follows recent methodological guidance for collective\-LLM experimentsZhouet al\.\([2025](https://arxiv.org/html/2607.09678#bib.bib26)\)\.

## 3The Relay Testbed

### 3\.1Corpus with programmatic ground truth

Each item is a task\-handoff brief rendered by deterministic templates from twelve atomic facts in three domains \(software migration, incident response, logistics\), four fact types: person–role bindings, quantities \(ports, budgets, percentages, versions\), constraints/deadlines, and dependencies/prohibitions, with values drawn randomly from synthetic pools \(names, codes, numbers\)\. Ground truth is the generating fact tuple itself—never any model output—and a self\-check verifies that every fact’s surface form appears verbatim in the hop\-0 brief \(string recall=1\.0=1\.0by construction\)\. Synthetic values also block a grader from answering out of world knowledge\.

### 3\.2Relay protocol

Hop 1 receives the original brief and must re\-issue the complete handoff in the assigned format; hopi\>1i\{\>\}1receives*only*hop\(i−1\)\(i\{\-\}1\)’s message\. Relay temperature is0\.70\.7throughout \(re\-encoding under realistic sampling\)\. In the*process\-relay*condition, each hop must first answer, under anAnalysisheading, which element of the handoff is most time\-critical and why, before re\-issuing the handoff—adding the per\-hop cognitive load characteristic of real pipelines; the analysis section is stripped programmatically before forwarding, so only the handoff travels\.

### 3\.3Formats

Five format specifications span the structure spectrum:Free\(free prose, no constraints\);Constr\(natural language plus a precision instruction: convey every fact, keep numbers/names/codes verbatim\);Json\(a fixed six\-key schema: title, people, quantities, constraints, dependencies, prohibitions\);Triples\(subject\|\|predicate\|\|object lines\);Kv\(flat snake\_case key–value lines\)\. JSON messages are checked for syntactic validity at every hop; invalid messages \(1% under the weak relay, none under the strong\) are passed downstream and scored as\-is, mirroring deployed pipelines without validators\.

### 3\.4Measurement

QA recall\(primary\): a fixed grader—the strong model at temperature0—reads only the hop message and answers the twelve closed\-form questions in JSON; answers are exact\-matched programmatically \(whole\-token numeric matching; yes/no normalization\) against ground truth\. The grader never sees the ground truth or the original brief, and grader parse failures trigger one retry and are otherwise excluded rather than scored as zero \(parse\-fail rate0\.0%0\.0\\%in all grids\)\.String recall\(secondary, judge\-free\): normalized verbatim containment of each fact’s surface form\. String recall under\-counts formats that legitimately re\-render surface forms while preserving content—in the strong grid the hop\-6 QA−\-string gap is\+8\.3\+8\.3points forKvand\+4\.0\+4\.0forTriples—which is why a paraphrase\-tolerant primary metric is required\. In the weak grid the gap reverses sign for three formats \(QA33–55points*below*string recall\), consistent with degraded messages preserving surface strings while corrupting relations, though grader loss on degraded text cannot be fully excluded; we therefore verify all weak\-tier orderings under both metrics \(Appendix[C](https://arxiv.org/html/2607.09678#A3)\)\. Token accounting excludes hidden reasoning tokens, which would otherwise inflate message\-length comparisons by up to4×4\\times\(Appendix[D](https://arxiv.org/html/2607.09678#A4)\)\.

### 3\.5Capability tiers and grader separation

Strong\-tier grids use DeepSeek\-v4\-flash \(henceforth*strong*\) as the relay; the weak\-tier grid uses Qwen2\.5\-1\.5B\-InstructQwen Team \([2024](https://arxiv.org/html/2607.09678#bib.bib28)\)\(4\-bit quantized, served locally; henceforth*weak*\)\. Crucially, the*grader is the strong model in every condition*, so weak\-relay distortion is never conflated with weak grading\. Two facts argue against a grader artifact behind the weak\-tier spread: first and decisively, the judge\-free string metric—no LLM grader at all—independently reproduces the weak\-tier separation \(22\.222\.2\-point hop\-6 spread\) and the flat\-Jsonsignature \(Appendix[C](https://arxiv.org/html/2607.09678#A3)\); second, on well\-formed messages the grader reads every format at≥0\.973\\geq 0\.973\(§[4\.1](https://arxiv.org/html/2607.09678#S4.SS1)\), bounding format\-specific reading loss at≈\\approx2\.7 points there \(a clean\-message bound whose transfer to degraded text is exactly why the judge\-free replication is the primary defense\)\. A partial replication of the strong grid on a second strong model \(string metric\) reproduces the format ordering \(Appendix[C](https://arxiv.org/html/2607.09678#A3)\)\.

### 3\.6Causal error injection

To separate “structure prevents change” from “structure repairs errors,” we use a paired fork: hops 1–3 run normally; at hop 3’s output we programmatically replace one owner name \(all surface occurrences\) with a plausible name that appears nowhere in the item; the chain then forks into a clean arm and an injected arm for hops 4–6\. Both arms share the identical prefix, so any downstream difference is the causal effect of the single injected error\. Injection is only possible when the target name is still present in the hop\-3 message; this held in 164 of 200 chains \(82%\), and the per\-format injection\-opportunity rates themselves mirror overall fidelity \(Constr37/40,Free34/40,Json35/40,Kv30/40,Triples28/40\)\. All injection analyses condition on successful injection\. We track*persistence*\(does the wrong value survive to hop 6?\) and*containment*\(paired difference in recall over the eleven uninjected facts\)\.

Table 1:Design matrix \(items×\\timesformats×\\timeshops; “Scored” counts graded messages\)\. The Inject grid scores40×540\\times 5chains×\\times9 messages each \(3 shared prefix \+ 3 clean\-arm \+ 3 injected\-arm hops\); the 36 chains where the target was already lost by hop 3 still fork \(their two arms coincide\) but are excluded from all conditioned analyses\. Every grid is graded by the same fixed strong grader att=0t\{=\}0\.

## 4Experiments

Table[1](https://arxiv.org/html/2607.09678#S3.T1)summarizes the four grids\. All uncertainty is reported as percentile\-bootstrap 95% CIs over items \(2,000–4,000 resamples; pointwise unless stated\); proportions carry Wilson 95% CIs; throughout, one “point” is0\.010\.01recall\. Multiplicity policy: within each analysis family we either report a Bonferroni\-adjusted simultaneous bound \(load, §[4\.2](https://arxiv.org/html/2607.09678#S4.SS2); drift advantages, §[4\.3](https://arxiv.org/html/2607.09678#S4.SS3)\) or explicitly flag the comparisons as uncorrected \(containment, §[4\.4](https://arxiv.org/html/2607.09678#S4.SS4)\); tier\-gap effects of1818–3737points survive any correction trivially\. Decay slopes are obtained by fitting a line to logit\-transformed per\-hop mean recall over hops 1–6 \(means clipped to\[10−3,1−10−3\]\[10^\{\-3\},1\-10^\{\-3\}\]before the transform\), with CIs from a bootstrap over items; because the logit amplifies movement near the ceiling, we report raw hop\-1→\\to6 point losses alongside every slope we interpret\.

### 4\.1A strong relay barely distorts—and the loss lives at the encoding step

![Refer to caption](https://arxiv.org/html/2607.09678v1/x1.png)Figure 1:Fact recall \(QA recall\) over six relay hops for five message formats \(color, marker, and line style jointly encode the format\)\. Bands are bootstrap 95% CIs over items \(n=100n\{=\}100strong;n=50n\{=\}50weak\)\. \(a\) A strong relay is nearly lossless in every format \(inset: zoomed view; free NL’s slow drift is the only sustained decay\)\. \(b\) A 1\.5B relay breaks the ceiling: on matched items the across\-format dispersion \(SD\) of hop\-6 recall grows8\.7×8\.7\\times\(CI5\.35\.3–15\.515\.5\); as a range,2\.3→20\.52\.3\\to 20\.5points\.Json\(green triangles\) is the only format whose curve stays nearly flat after the first hop\. Panels share the y\-axis \(the inset has its own zoomed scale\); pairwise inference uses within\-item paired contrasts, not the marginal bands shown\.Figure[1](https://arxiv.org/html/2607.09678#S4.F1)a shows the strong\-tier grid\. After six hops, every format retains QA recall≥0\.973\\geq 0\.973; the multi\-stage collapse documented for delegation and translation chainsAoet al\.\([2026](https://arxiv.org/html/2607.09678#bib.bib14)\); Mohamedet al\.\([2025](https://arxiv.org/html/2607.09678#bib.bib11)\)does not materialize at this tier under faithful\-relay instructions\. We read this as a boundary condition rather than a refutation: those collapses arise in pipelines whose stages*transform*content \(delegation, translation\), whereas our duty is faithful re\-encoding—so collapse is not intrinsic to multi\-hop text relay; it requires transformation duty or, as §[4\.3](https://arxiv.org/html/2607.09678#S4.SS3)shows, a weak relay\. What little loss exists has a precise location: it is incurred when the brief is first*encoded*into the format, not while the encoded message is relayed\.Kv’s curve is flat from hop 1 onward at≈0\.973\\approx 0\.973\(a2\.72\.7\-point encode\-then\-hold deficit, the only real content loss at this tier; the deficit also appears under a second relay model by the string metric, Appendix[C](https://arxiv.org/html/2607.09678#A3)\), andJson/Triples/Constrcurves are statistically flat throughout \(all per\-format slopes and CIs for both tiers are tabulated in Appendix[E](https://arxiv.org/html/2607.09678#A5)\)\.Freeis the lone exception, drifting slowly but consistently: its strong\-grid slope is−0\.295\-0\.295\(CI\[−0\.379,−0\.045\]\[\-0\.379,\-0\.045\]; raw loss just0\.40\.4points over six hops at this tier—statistically detectable, materially tiny\), and the same chronic drift appears in a separate run on the load grid \(−0\.243\-0\.243, CI\[−0\.374,−0\.028\]\[\-0\.374,\-0\.028\]; same first\-60 items, different condition; §[4\.2](https://arxiv.org/html/2607.09678#S4.SS2)\): free prose re\-statement drifts where structured and instruction\-constrained formats lock\.

Two cost\-relevant observations follow\. First,Constrachieves perfect hop\-6 recall \(1\.0001\.000\) at143143tokens per message versusJson’s0\.9980\.998at194194tokens—a single precision instruction buys schema\-grade fidelity 26% cheaper in message tokens \(and more in billed tokens; §[5](https://arxiv.org/html/2607.09678#S5)\)\. Second, the fidelity–cost trade\-off is real but small at this tier:Kvis the cheapest format \(135135tokens\) and pays for it with the only measurable content loss\.

### 4\.2Cognitive load raises cost, not distortion \(strong tier\)

Table 2:Process relay vs\. pure relay at the strong tier: paired hop\-6 differences on the samen=60n\{=\}60items \(the seeded generator makes the load grid’s items the first 60 of the strong grid’s 100\), bootstrap 95% CIs, and token change of the full per\-hop output \(the analysis section is stripped programmatically before forwarding\)\.†All 60 paired differences are exactly zero \(both conditions at ceiling\), so the interval is degenerate and uninformative\. Every format\-level effect is bounded within±1\.4\\pm 1\.4points \(pointwise CIs; descriptive family bound\)\.A natural objection to pure relay is that real agents process while they relay\. The process\-relay grid adds an explicit per\-hop analysis duty at the strong tier\. Table[2](https://arxiv.org/html/2607.09678#S4.T2)shows the result: messages grow 24–53% longer, yet every format’s paired hop\-6 difference is small and its CI contains zero\. Rather than merely accepting the null, we read the CIs as equivalence bounds: any load effect on hop\-6 fidelity is bounded within±1\.4\\pm 1\.4points per format \(pointwise\), or±1\.8\\pm 1\.8points under a Bonferroni\-adjusted simultaneous bound across the four non\-degenerate formats\. The format ordering andFree’s chronic drift \(slope−0\.243\-0\.243, CI\[−0\.374,−0\.028\]\[\-0\.374,\-0\.028\]\) replicate under load\. At this tier, distortion is a property of the*format and the relay model*, not of how busy the relaying agent is—which licenses reading the cheaper pure\-relay grids as representative for strong relays\. Whether load interacts with format*under weak relays*—where fidelity has 20\+ points of headroom to move—is untested here \(a ceiling\-protected null is cheap; see Limitations\)\.

### 4\.3The format effect is tier\-dependent

![Refer to caption](https://arxiv.org/html/2607.09678v1/x2.png)Figure 2:The two opposing mechanisms under the weak relay \(bootstrap 95% CIs;n=50n\{=\}50\)\. x\-axis: encoding fidelity \(hop\-1 recall\); y\-axis: drift as raw points lost over hops 1–6, inverted so up = less drift\. The rigid formats pay the largest encoding tolls \(Kv0\.7650\.765,Json0\.8000\.800, indistinguishable from each other\) butJsonthen drifts least \(4\.74\.7points\);Constrencodes best \(0\.9620\.962\) yet keeps drifting \(14\.514\.5points\);FreeandTriplesdrift most \(21\.821\.8/20\.720\.7\);Kvis weakly dominated byJson\(strictly on drift, within noise on encoding\)\. The encode–drift trade\-off flips the ranking in transit \(Json: fourth at hop 1, second at hop 6 in98%98\\%of item\-bootstrap resamples\)\.Figure[1](https://arxiv.org/html/2607.09678#S4.F1)b repeats the pure\-relay grid with the weak relay \(same corpus seed, same grader\)\. The ceiling breaks: every format now decays significantly \(all slope CIs exclude zero\), and every format degrades significantly relative to the strong tier \(paired weak−\-strong hop\-6 differences on matched items:−18\-18points forConstrup to−37\-37forTriples, all CIs excluding zero\)\. The across\-format dispersion of hop\-6 recall grows8\.7×8\.7\\times\(SD over format means, bootstrap CI5\.35\.3–15\.515\.5\); as a descriptive range, the spread grows from2\.32\.3to20\.520\.5points\. Recall at hop 6 runs from0\.8170\.817\(Constr\) down to0\.6120\.612\(Triples\)\. Notably, the weak model*keeps*format syntax \(invalid\-Jsonrate 1%, §[3\.3](https://arxiv.org/html/2607.09678#S3.SS3)\) while losing content, so the effect is informational, not a parsing artifact\. The judge\-free counterpart of the dispersion ratio is2\.2×2\.2\\times\(CI1\.71\.7–3\.03\.0\): smaller because the string metric inflates the strong\-tier denominator by penalizing legitimate re\-rendering \(§[3\.4](https://arxiv.org/html/2607.09678#S3.SS4)\), so attacks on the QA denominator push the true ratio*up*; orderings and the per\-format tier gaps \(1818–3030points by string\) replicate under both metrics\. Here “capability” denotes a bundled tier contrast \(model family, scale, quantization, and serving stack all change\); corpus, prompts, protocol, and grader are held fixed\.

The decomposition in Figure[2](https://arxiv.org/html/2607.09678#S4.F2)explains*how*the tier governs the effect: format acts through two mechanisms with opposite signs\.Encoding fidelity: converting a prose brief into a rigid scheme is itself hard for a weak model—the two rigid formats pay statistically indistinguishable hop\-1 tolls \(Kv0\.7650\.765,Json0\.8000\.800; pairedΔ\\DeltaCI\[−0\.03,\+0\.10\]\[\-0\.03,\+0\.10\]\), both far belowConstr\(0\.9620\.962;Constr−\-JsonΔ=0\.162\\Delta=0\.162, CI\[0\.120,0\.205\]\[0\.120,0\.205\]\)\.Drift rate: once encoded, the fixed\-key schema anchors content—Jsondrifts least by a wide margin \(per\-item paired drift advantage:9\.59\.5points overKv,9\.89\.8overConstr,16\.016\.0overTriples,17\.217\.2overFree; all four CIs exclude zero, and all four still do under a Bonferroni\-4 adjustment, theKvcontrast marginally\), losing4\.74\.7raw points over hops 1–6 whileFreeandTripleslose21\.821\.8and20\.720\.7\(Constr14\.514\.5;Kv14\.214\.2\)\. Two checks rule out survivor bias \(formats that lose fragile facts at hop 1 having less left to lose\): first,Kvis a toll\-matched control—it pays the same hop\-1 toll asJsonyet drifts three times as much; second, a survivor\-conditioned measure \(among facts correct at hop 1, the fraction still correct at hop 6\) givesJson0\.940\.94\(CI0\.890\.89–0\.980\.98\) versus0\.740\.74–0\.850\.85for every other format, with all paired contrasts excluding zero \(e\.g\.,Json−\-Kv\+11\.0\+11\.0points, CI\[2\.9,18\.8\]\[2\.9,18\.8\]\)\. Notably, drift resistance is*not*a property of structure per se: line\-orientedTriplesdrifts like free prose, andKvlike constrained prose\. The pattern is consistent with the*closed, fixed key set*giving every fact a stable address that survives re\-encoding \(Kv’s open per\-fact keys lack this\), though with one fixed\-schema format instantiated we cannot separate the closed key set from nesting or from pretraining familiarity with JSON\. The two mechanisms flip the ranking in transit:Jsonstarts fourth of five at hop 1 and finishes second at hop 6 in98%98\\%of item\-bootstrap resamples \(marginal probability of the hop\-6 rank event, computed on format means;Json−\-Triplesat hop 6:\+0\.142\+0\.142, CI\[0\.055,0\.222\]\[0\.055,0\.222\]\); the bottom pair \(Triples,Kv\) is statistically indistinguishable \(−0\.012\-0\.012, CI\[−0\.090,\+0\.065\]\[\-0\.090,\+0\.065\]\)\. Under a strong relay both mechanisms are saturated, which is exactly why the format choice looks free at the frontier \(Fig\.[1](https://arxiv.org/html/2607.09678#S4.F1)a\) and decisive below it\.

### 4\.4Causal adjudication: faithful, not corrective

![Refer to caption](https://arxiv.org/html/2607.09678v1/x3.png)Figure 3:Paired\-fork injection under the weak relay, conditional on successful injection \(target name present at hop 3; per\-formatnn:Constr37,Free34,Json35,Triples28,Kv30\)\. \(a\) Persistence of the injected error at hop 6: solid bars = wrong value present in the message \(surface\); hatched bars = grader answers the wrong value \(QA\); whiskers are Wilson 95% CIs\. Once present, the error survives in 83–100% of chains in every format\. \(b\) Collateral damage to the eleven uninjected facts \(clean−\-injected, paired bootstrap 95% CI\): no format shows a detectable cascade;Jsonis the only nominally significant cell \(1 of 5 uncorrected comparisons\) and its sign is mildly protective\.The drift results invite a tempting reading: rigid schemas act as error\-correcting codes for relayed content\. That phrase hides two distinct claims—*resisting change*and*repairing corruption*—and the paired fork separates them\. One honesty note first: a wrong owner name is a*redundancy\-free leaf error*—no other fact in the item entails the correct value—so no channel, however capable, could “correct” it from in\-message evidence alone\. The informative questions are therefore \(a\) whether formats differ in how faithfully they carry a present error, and \(b\) whether one corrupted value drags down its neighbors\.

Persistence is near\-universal and direction\-blind\.Once injected, the wrong name survives all three subsequent hops in 83–100% of chains depending on format \(Json97%, Wilson CI 85–99;Constr100%, CI 91–100;Kvlowest at 83%, CI 66–93; Fig\.[3](https://arxiv.org/html/2607.09678#S4.F3)a\)\. At the grader level \(does the grader now answer the wrong name?\), persistence is 76–86%\. Because injection conditions on a format\-dependent event \(the name surviving to hop 3\), cross\-format comparisons select different item subsets, plausibly the easier items for each format; restricting to the 17 items injectable in*all five*formats, persistence is 82–100% \(Wilson CI atn=17n\{=\}17reaching down to 59% forKv\), so the near\-universality is not a selection artifact, though per\-format precision is limited there\. Faithfulness is direction\-blind, and now quantifiably so: in the clean arms of the same conditioned chains, the*true*name survives to hop 6 at 86–100% by format—format\-by\-format within a few points of the wrong name’s 83–100%\. The lossiest format \(Kv\) is also the one most likely to lose the error\. Where format fidelity*does*matter is upstream, in whether the target fact was still intact at hop 3 to be corrupted at all \(injection\-opportunity rates above\)\.

No detectable cascade\.Across all five formats, injecting one wrong value causes no detectable collateral loss on the other eleven facts \(Fig\.[3](https://arxiv.org/html/2607.09678#S4.F3)b\): every paired CI either contains zero or, in the single nominally significant cell \(Json,−0\.031\-0\.031, CI\[−0\.075,−0\.003\]\[\-0\.075,\-0\.003\]\), shows a mildly*protective*sign\. With five uncorrected comparisons, we read that cell as consistent with multiplicity noise rather than a mechanism; the robust statement is a set of per\-format upper bounds on damage \(pointwise 95%\):Json≤0\\leq 0,Triples≤3\\leq 3points,Constr≤6\\leq 6,Kv≤10\\leq 10,Free≤13\\leq 13\. These bounds are post\-hoc, pointwise, and loosest forFree\(n=34n\{=\}34\); on the 17\-item all\-format core the estimates are direction\-consistent \(all CIs cross zero\)\. Within these bounds, the feared error cascadeXieet al\.\([2026](https://arxiv.org/html/2607.09678#bib.bib20)\)does not ignite from a single corrupted leaf value in any format\.

The folklore is thus adjudicated with precision: “schemas prevent drift” is true in the narrow sense that rigid structure resists*change of any kind*—it neither amplifies nor repairs errors, it preserves whatever it is given\. The correct mental model is a faithful, error\-localizing channel, not an error\-correcting code\.

## 5Analysis and Practical Guidance

#### One phenomenon, four results\.

The four grids compose a single picture\. Format effects on relay fidelity operate through encoding cost and drift resistance; both mechanisms vary with relay tier; at the strong tier both saturate \(ceiling\), under weakness both bind \(gradient\), workload moves neither at the tier where this was testable \(robustness\), and the drift resistance that the fixed\-key schema buys is direction\-blind \(injection\)\. This also reconciles the single\-hop contradiction in prior work: anti\-structure resultsTamet al\.\([2024](https://arxiv.org/html/2607.09678#bib.bib9)\); Johnsonet al\.\([2025](https://arxiv.org/html/2607.09678#bib.bib10)\)measure the encoding mechanism, pro\-structure resultsChenet al\.\([2024](https://arxiv.org/html/2607.09678#bib.bib7)\)measure cost at saturated fidelity, and only the relay regime exposes the second, drift\-side mechanism that rewards structure\.

#### Guidance\.

\(1\)*Choose the format for the weakest relay in the pipeline*, not the strongest: at the frontier the choice is nearly free, so the weak link sets the requirement\. \(2\)*Short chains or strong relays: precision\-instructed NL\.*It matches schema fidelity at 26% fewer message tokens—and the gap widens to∼63%\{\\sim\}63\\%on billed completion tokens, because the strong relay spends4×4\\timesmore hidden reasoning tokens emittingJsonthanConstr\(Appendix[D](https://arxiv.org/html/2607.09678#A4)\)—with no schema engineering needed\. \(3\)*Long chains through weak relays: a fixed\-key schema \(Json\)—and budget for the entry toll\.*Jsonpays∼\\sim0\.160\.16recall relative toConstrat encoding but loses only0\.050\.05over five further hops\. Within the measured six hopsConstrstays ahead on point estimates \(hop\-6Constr−\-Json:\+0\.063\+0\.063, CI\[−0\.010,\+0\.130\]\[\-0\.010,\+0\.130\]\); the implied crossover near hops 9–10 is an out\-of\-range extrapolation of the measured loss rates, which we flag as such\. A hybrid design—encode once with a strong model, relay in schema through weak links—inherits both advantages; we flag it as a prediction of the mechanism decomposition, not a tested configuration\. \(4\)*Do not expect structure to repair anything*: validation and re\-groundingFanet al\.\([2026](https://arxiv.org/html/2607.09678#bib.bib15)\)remain necessary; structure only keeps damage local\.

#### Relation to theory\.

Per\-format decay parameters give empirical content to relay\-fidelity theory: martingale\-style accumulation boundsFanet al\.\([2026](https://arxiv.org/html/2607.09678#bib.bib15)\)and information\-loss limitsAoet al\.\([2026](https://arxiv.org/html/2607.09678#bib.bib14)\)are format\-agnostic; our slopes \(−0\.060\-0\.060forJsonto−0\.331\-0\.331forConstr, logit/hop under weakness\) show the constants those theories abstract over vary several\-fold with a design choice as mundane as the message format\.

## 6Conclusion

We completed the missing format×\\timeshops×\\timescapability cell in the study of LLM information relay, with programmatic ground truth and a causal injection\. When faithful re\-encoding is the instructed objective, the telephone game is not a law of LLM pipelines—it is tier\-dependent, absent at our strong tier and nearly an order of magnitude larger in across\-format dispersion \(8\.7×8\.7\\timesby QA;2\.2×2\.2\\timesby the judge\-free metric\) under our weak relay; we read this as a capability regime, with the bundled\-contrast caveat stated throughout\. What the fixed\-key schema provides is faithful, error\-localizing transmission rather than error correction\. As pipelines push cost\-driven small models into relay positions, message format stops being a style choice and becomes a reliability parameter\.

## Limitations

Synthetic, templated corpus\.Programmatic ground truth buys exact measurement at the price of distributional realism; briefs are information\-dense, English\-only, and template\-rendered with a fixed 12\-fact density\. Effects on naturalistic documents may differ in magnitude, though the mechanism decomposition does not depend on the template\.Two capability points, bundled tier contrast\.“Capability governs” rests on one strong API model versus one 1\.5B model that differ jointly in family, scale,*quantization*\(4\-bit\), and serving stack; intermediate scales would map the transition, and other small\-model families may differ\.Preservation is the instructed objective\.Every hop is told to re\-issue the*complete*handoff; pipelines whose handoffs intentionally compress or transform content face a different objective, and collapse there may be driven by the task rather than capability\. Our no\-collapse finding is scoped to faithful\-relay duty\.The load condition was run only at the strong tier, where ceiling effects protect the null; a weak×\\timesload cell remains untested\.Single\-leaf injection bounds cascades from below—and correction from above\.We injected an independent fact \(an owner name\), which is uncorrectable by construction and minimally entangled; errors in facts with dependents could cascade where leaf values do not, and conversely, redundancy\-bearing errors that a format*could*expose and repair are untested, so “not corrective” is established only for the redundancy\-free class\.Grader reuse and other constants\.The strong grader also serves as the strong relay \(separate calls att=0t\{=\}0with programmatic exact\-match scoring\); a fully independent grader family would remove residual self\-preference concerns—our judge\-free string metric replicates the structured\-vs\-free separation and theKvdeficit \(Appendix[C](https://arxiv.org/html/2607.09678#A3)\), though near the ceiling its fine ordering differs within noise\. Relay temperature \(0\.70\.7\) and chain length \(6\) were fixed, and other sampling parameters follow each serving stack’s defaults \(pinned in released configs\); each item×\\timesformat chain is a single stochastic realization, so item\-level CIs cover item and sampling variance jointly\. The injection position \(hop 3\) and horizon \(three downstream hops\) were also fixed\. QA recall was not calibrated on the pristine hop\-0 brief \(the hop\-0 self\-check is string\-based\), so hop\-1 “encoding tolls” are upper bounds that may include format\-specific grader reading loss; the judge\-free replication of the tolls bounds this concern\.

## Ethics Statement

The corpus is fully synthetic; no human subjects or personal data are involved\. The findings inform reliability engineering of multi\-agent systems; we do not foresee direct dual\-use risk beyond general agent\-pipeline capability improvements\.

## References

- R\. Ao, S\. Gao, and D\. Simchi\-Levi \(2026\)On the reliability limits of LLM\-based multi\-agent planning\.External Links:2603\.26993Cited by:[§1](https://arxiv.org/html/2607.09678#S1.p2.1),[§2](https://arxiv.org/html/2607.09678#S2.SS0.SSS0.Px1.p1.1),[§4\.1](https://arxiv.org/html/2607.09678#S4.SS1.p1.8),[§5](https://arxiv.org/html/2607.09678#S5.SS0.SSS0.Px3.p1.2)\.
- M\. Cemri, M\. Z\. Pan, S\. Yang, L\. A\. Agrawal, B\. Chopra, R\. Tiwari, K\. Keutzer, A\. Parameswaran, D\. Klein, K\. Ramchandran, M\. Zaharia, J\. E\. Gonzalez, and I\. Stoica \(2025\)Why do multi\-agent LLM systems fail?\.External Links:2503\.13657Cited by:[§1](https://arxiv.org/html/2607.09678#S1.p1.1),[§2](https://arxiv.org/html/2607.09678#S2.SS0.SSS0.Px3.p1.1)\.
- W\. Chen, C\. Yuan, J\. Yuan, Y\. Su, C\. Qian, C\. Yang, R\. Xie, Z\. Liu, and M\. Sun \(2024\)Beyond natural language: LLMs leveraging alternative formats for enhanced reasoning and communication\.InFindings of EMNLP,External Links:2402\.18439Cited by:[§1](https://arxiv.org/html/2607.09678#S1.p2.1),[§2](https://arxiv.org/html/2607.09678#S2.SS0.SSS0.Px2.p1.1),[§5](https://arxiv.org/html/2607.09678#S5.SS0.SSS0.Px1.p1.1)\.
- Y\. Du, S\. Li, A\. Torralba, J\. B\. Tenenbaum, and I\. Mordatch \(2024\)Improving factuality and reasoning in language models through multiagent debate\.InProceedings of ICML,External Links:2305\.14325Cited by:[§1](https://arxiv.org/html/2607.09678#S1.p1.1)\.
- Z\. Du, R\. Wang, H\. Bai, Z\. Cao, X\. Zhu, Y\. Cheng, B\. Zheng, W\. Chen, and H\. Ying \(2026\)Enabling agents to communicate entirely in latent space\.InProceedings of ACL,External Links:2511\.09149Cited by:[§2](https://arxiv.org/html/2607.09678#S2.SS0.SSS0.Px3.p1.1)\.
- A\. Ehtesham, A\. Singh, G\. K\. Gupta, and S\. Kumar \(2025\)A survey of agent interoperability protocols: model context protocol \(MCP\), agent communication protocol \(ACP\), agent\-to\-agent protocol \(A2A\), and agent network protocol \(ANP\)\.External Links:2505\.02279Cited by:[§2](https://arxiv.org/html/2607.09678#S2.SS0.SSS0.Px2.p1.1)\.
- F\. X\. Fan, C\. Tan, R\. Wattenhofer, and Y\. Ong \(2026\)Information fidelity in tool\-using LLM agents: a martingale analysis of the model context protocol\.External Links:2602\.13320Cited by:[§1](https://arxiv.org/html/2607.09678#S1.p2.1),[§2](https://arxiv.org/html/2607.09678#S2.SS0.SSS0.Px1.p1.1),[§5](https://arxiv.org/html/2607.09678#S5.SS0.SSS0.Px2.p1.8),[§5](https://arxiv.org/html/2607.09678#S5.SS0.SSS0.Px3.p1.2)\.
- B\. Ghafouri and E\. Ferrara \(2026\)Lost before translation: social information transmission and survival in AI–AI communication\.External Links:2602\.17674Cited by:[§1](https://arxiv.org/html/2607.09678#S1.p2.1),[§2](https://arxiv.org/html/2607.09678#S2.SS0.SSS0.Px1.p1.1)\.
- S\. Hong, M\. Zhuge, J\. Chen, X\. Zheng, Y\. Cheng, C\. Zhang, J\. Wang, Z\. Wang, S\. K\. S\. Yau, Z\. Lin, L\. Zhou, C\. Ran, L\. Xiao, C\. Wu, and J\. Schmidhuber \(2024\)MetaGPT: meta programming for a multi\-agent collaborative framework\.InProceedings of ICLR,External Links:2308\.00352Cited by:[§1](https://arxiv.org/html/2607.09678#S1.p1.1)\.
- R\. T\. Johnson, M\. D\. Pain, and J\. D\. West \(2025\)Natural language tools: a natural language approach to tool calling in large language agents\.External Links:2510\.14453Cited by:[§1](https://arxiv.org/html/2607.09678#S1.p2.1),[§2](https://arxiv.org/html/2607.09678#S2.SS0.SSS0.Px2.p1.1),[§5](https://arxiv.org/html/2607.09678#S5.SS0.SSS0.Px1.p1.1)\.
- Y\. Kim, K\. Gu, C\. Park, C\. Park, S\. Schmidgall, A\. A\. Heydari, Y\. Yan, Z\. Zhang, Y\. Zhuang, Y\. Liu, M\. Malhotra, P\. P\. Liang, H\. W\. Park, Y\. Yang, X\. Xu, Y\. Du, S\. Patel, T\. Althoff, D\. McDuff, and X\. Liu \(2025\)Towards a science of scaling agent systems\.External Links:2512\.08296Cited by:[§2](https://arxiv.org/html/2607.09678#S2.SS0.SSS0.Px3.p1.1)\.
- S\. Marro, E\. La Malfa, J\. Wright, G\. Li, N\. Shadbolt, M\. Wooldridge, and P\. Torr \(2024\)A scalable communication protocol for networks of large language models\.External Links:2410\.11905Cited by:[§2](https://arxiv.org/html/2607.09678#S2.SS0.SSS0.Px2.p1.1)\.
- A\. Mohamed, M\. Geng, M\. Vazirgiannis, and G\. Shang \(2025\)LLM as a broken telephone: iterative generation distorts information\.InProceedings of ACL,External Links:2502\.20258Cited by:[§1](https://arxiv.org/html/2607.09678#S1.p2.1),[§2](https://arxiv.org/html/2607.09678#S2.SS0.SSS0.Px1.p1.1),[§4\.1](https://arxiv.org/html/2607.09678#S4.SS1.p1.8)\.
- A\. Narayan, D\. Biderman, S\. Eyuboglu, A\. May, S\. Linderman, J\. Zou, and C\. Ré \(2025\)Minions: cost\-efficient collaboration between on\-device and cloud language models\.InProceedings of ICML,External Links:2502\.15964Cited by:[§1](https://arxiv.org/html/2607.09678#S1.p1.1)\.
- J\. Perez, C\. Léger, M\. Ovando\-Tellez, C\. Foulon, J\. Dussauld, P\. Oudeyer, and C\. Moulin\-Frier \(2024\)When LLMs play the telephone game: cumulative changes and attractors in iterated cultural transmissions\.External Links:2407\.04503Cited by:[§1](https://arxiv.org/html/2607.09678#S1.p2.1),[§2](https://arxiv.org/html/2607.09678#S2.SS0.SSS0.Px1.p1.1)\.
- C\. Qian, W\. Liu, H\. Liu, N\. Chen, Y\. Dang, J\. Li, C\. Yang, W\. Chen, Y\. Su, X\. Cong, J\. Xu, D\. Li, Z\. Liu, and M\. Sun \(2024\)ChatDev: communicative agents for software development\.InProceedings of ACL,External Links:2307\.07924Cited by:[§1](https://arxiv.org/html/2607.09678#S1.p1.1)\.
- Qwen Team \(2024\)Qwen2\.5 technical report\.External Links:2412\.15115Cited by:[§3\.5](https://arxiv.org/html/2607.09678#S3.SS5.p1.3)\.
- V\. Ramesh and K\. Li \(2025\)Communicating activations between language model agents\.InProceedings of ICML,External Links:2501\.14082Cited by:[§2](https://arxiv.org/html/2607.09678#S2.SS0.SSS0.Px3.p1.1)\.
- M\. Sclar, Y\. Choi, Y\. Tsvetkov, and A\. Suhr \(2024\)Quantifying language models’ sensitivity to spurious features in prompt design\.InProceedings of ICLR,External Links:2310\.11324Cited by:[§2](https://arxiv.org/html/2607.09678#S2.SS0.SSS0.Px2.p1.1)\.
- X\. Shen, Y\. Liu, Y\. Dai, Y\. Wang, R\. Miao, Y\. Tan, S\. Pan, and X\. Wang \(2025\)Understanding the information propagation effects of communication topologies in LLM\-based multi\-agent systems\.InProceedings of EMNLP,External Links:2505\.23352Cited by:[§2](https://arxiv.org/html/2607.09678#S2.SS0.SSS0.Px3.p1.1)\.
- X\. Shi, M\. Chiesa, G\. Q\. Maguire, and D\. Kostic \(2026\)KVComm: enabling efficient LLM communication through selective KV sharing\.InProceedings of ICLR,External Links:2510\.03346Cited by:[§2](https://arxiv.org/html/2607.09678#S2.SS0.SSS0.Px3.p1.1)\.
- Z\. R\. Tam, C\. Wu, Y\. Tsai, C\. Lin, H\. Lee, and Y\. Chen \(2024\)Let me speak freely? A study on the impact of format restrictions on performance of large language models\.InProceedings of EMNLP: Industry Track,External Links:2408\.02442Cited by:[§1](https://arxiv.org/html/2607.09678#S1.p2.1),[§2](https://arxiv.org/html/2607.09678#S2.SS0.SSS0.Px2.p1.1),[§5](https://arxiv.org/html/2607.09678#S5.SS0.SSS0.Px1.p1.1)\.
- D\. Tran and D\. Kiela \(2026\)Single\-agent LLMs outperform multi\-agent systems on multi\-hop reasoning under equal thinking token budgets\.External Links:2604\.02460Cited by:[§2](https://arxiv.org/html/2607.09678#S2.SS0.SSS0.Px3.p1.1)\.
- Z\. Wang, S\. Moriyama, W\. Wang, B\. Gangopadhyay, and S\. Takamatsu \(2025\)Talk structurally, act hierarchically: a collaborative framework for LLM multi\-agent systems\.External Links:2502\.11098Cited by:[§2](https://arxiv.org/html/2607.09678#S2.SS0.SSS0.Px2.p1.1)\.
- J\. A\. Wibowo and G\. C\. Polyzos \(2025\)Toward a safe internet of agents\.External Links:2512\.00520Cited by:[§1](https://arxiv.org/html/2607.09678#S1.p2.1)\.
- Y\. Xie, C\. Zhu, X\. Zhang, T\. Zhu, D\. Ye, M\. Qi, H\. Chen, and W\. Zhou \(2026\)From spark to fire: modeling and mitigating error cascades in LLM\-based multi\-agent collaboration\.External Links:2603\.04474Cited by:[§2](https://arxiv.org/html/2607.09678#S2.SS0.SSS0.Px3.p1.1),[§4\.4](https://arxiv.org/html/2607.09678#S4.SS4.p3.8)\.
- J\. Zhou, J\. Huang, X\. Zhou, M\. H\. Lam, X\. Wang, H\. Zhu, W\. Wang, and M\. Sap \(2025\)The PIMMUR principles: ensuring validity in collective behavior of LLM societies\.External Links:2509\.18052Cited by:[§2](https://arxiv.org/html/2607.09678#S2.SS0.SSS0.Px3.p1.1)\.
- A\. Żywot, X\. Chen, Y\. Yuan, A\. Søgaard, and M\. de Rijke \(2026\)Can small agents collaborate to beat a single large language model?\.External Links:2601\.11327Cited by:[§1](https://arxiv.org/html/2607.09678#S1.p1.1)\.

## Appendix ACorpus Item and Format Renderings

A software\-domain brief contains facts such as: ticket owner, reviewer, on\-call contact \(person–role\); deadline in days, old/new port, canary percentage, pinned version, budget \(quantities\); migration\-order dependency; deploy\-window constraint; and a schema\-rollback prohibition\. The hop\-0 self\-check requires every fact’s surface form verbatim in the brief \(string recall=1\.0=1\.0on all items in all grids\)\. Format specifications are reproduced verbatim in the released code \(fmtrelay/formats\.py\)\.

## Appendix BGrader Protocol and Matching Rules

The grader receives only the hop message and twelve questions, must answer in JSON, and is instructed to outputUnknownwhen the document lacks the answer\. Matching normalizes Unicode, case, and number formatting; pure numbers must match as whole tokens \(“17” does not match “170”\); percentages match on the numeric part; yes/no answers are normalized over a small synonym set\. Parse failures trigger one retry and are otherwise excluded from QA recall \(rate0\.0%0\.0\\%in all grids, including the weak grid\)\.

## Appendix CCross\-Model Replication \(String Metric\)

A partial strong\-tier replication on a second strong model \(mimo\-v2\.5\-pro\) covers 2,841 of 3,000 relay messages; the run was interrupted by an API budget pause mid\-grid, leaving 66–76 complete chains per format \(truncation spread across formats, not concentrated in any one\)\. By the judge\-free string metric \(hop\-6 values computed on complete chains only\), hops 1→\\to6:Constr0\.999→0\.9950\.999\{\\to\}0\.995,Json0\.999→1\.0000\.999\{\\to\}1\.000,Triples0\.987→0\.9880\.987\{\\to\}0\.988,Free0\.964→0\.9510\.964\{\\to\}0\.951\(the only sustained decay\),Kv0\.906→0\.9070\.906\{\\to\}0\.907\(encode\-then\-hold\)\. The replication reproduces the qualitative structure—encode\-step loss,Freedrift, theKvdeficit—while the near\-ceiling ordering ofConstr/Jsondiffers within noise\. For the weak grid, the same judge\-free metric gives hops 1→\\to6:Constr0\.947→0\.8150\.947\{\\to\}0\.815,Free0\.873→0\.7070\.873\{\\to\}0\.707,Json0\.842→0\.8000\.842\{\\to\}0\.800,Triples0\.830→0\.6450\.830\{\\to\}0\.645,Kv0\.725→0\.5930\.725\{\\to\}0\.593\(hop\-6 spread22\.222\.2points\)—reproducing the top\-three QA ordering and the flat\-Jsonsignature without any LLM judge; the bottom pair swaps relative to QA \(Kv/Triples\), consistent with their statistical indistinguishability \(§[4\.3](https://arxiv.org/html/2607.09678#S4.SS3)\)\. For reference, the matched\-50\-item strong\-grid hop\-6 QA means behind the dispersion ratio are:Constr1\.0001\.000,Free0\.9980\.998,Json0\.9970\.997,Triples0\.9850\.985,Kv0\.9770\.977\.

## Appendix DToken–Fidelity Trade\-off

![Refer to caption](https://arxiv.org/html/2607.09678v1/x4.png)Figure 4:Hop\-6 QA recall \(bootstrap 95% CIs\) vs\. mean message tokens per hop \(hidden reasoning tokens excluded\), both relay tiers \(circles: strong; triangles: weak; colors as in Fig\.[1](https://arxiv.org/html/2607.09678#S4.F1)\)\. At the strong tier formats trade only cost \(CIs smaller than the markers\); under weakness they trade both\. Hidden reasoning tokens differ sharply by format at the strong tier \(means per hop:Json574,Triples355,Kv329,Constr139,Free86\), so billed completion cost favors the NL formats even more than message\-token cost does\.Figure[4](https://arxiv.org/html/2607.09678#A4.F4)plots the cost–fidelity plane for both capability tiers\.

## Appendix EPer\-Format Decay Slopes

Table 3:Logit\-slope estimates per format and tier \(bootstrap 95% CIs over items; fit and clipping as in §4\)\. Raw hop\-1→\\to6 losses appear in §[4\.1](https://arxiv.org/html/2607.09678#S4.SS1)and §[4\.3](https://arxiv.org/html/2607.09678#S4.SS3); weak\-tier hop\-6 item\-level SDs range0\.190\.19–0\.290\.29across formats\.
## Appendix FInjection Example

For itemsw\-000, the hop\-3 message’s owner “Felix Okafor” is replaced by “Hassan Petrov” \(a name absent from the item\); the clean and injected arms then relay hops 4–6 independently\. Per\-arm, per\-hop messages and scores are released with the code \(anonymized archive accompanies the submission\)\. Model specifics: strong relay/grader DeepSeek\-v4\-flash \(API, accessed June 2026;t=0\.7t\{=\}0\.7relay,t=0t\{=\}0grading\); replication model mimo\-v2\.5\-pro \(API, June 2026\); weak relay Qwen2\.5\-1\.5B\-Instruct, Q4\_K\_M quantization, served via Ollama 0\.30\.7 on a single RTX 3060\.