10. Distributed Model Graph Architecture

10.1 Motivation: Catastrophic Forgetting at Scale

The three-layer continual learning architecture in Section 6 mitigates catastrophic forgetting within a monolithic model through replay buffers and careful DPO weighting. But across many calibration cycles over months, this approach has a fundamental ceiling: every update to any domain affects the entire weight space. Fixing a contradiction in surgery knowledge can subtly degrade physics knowledge through weight interference. The replay buffer slows this but cannot eliminate it — the weights are shared.

The solution is to eliminate shared weights for domain-specific knowledge entirely. We call the resulting architecture the Micro-Expert model: a graph of independently deployable domain submodels, each a specialist in its field, coordinated by a shared router and utility layer but isolated at the weight level.

10.2 Physical Model Decomposition

Rather than a single monolithic model, the system decomposes into a loosely coupled graph of domain-specific submodels that communicate over structured interfaces — analogous to how microservice architectures decompose monolithic backends into independently deployable services.

                    ┌─────────────────────┐
                    │    Router / Hub      │
                    │  (field classifier   │
                    │   + query parser     │
                    │   + context merger)  │
                    └──────────┬──────────┘
                               │
         ┌─────────────────────┼──────────────────────┐
         │                     │                      │
    ┌────▼────┐           ┌────▼────┐           ┌────▼────┐
    │Medicine │           │   CS    │           │   Law   │
    │  model  │           │  model  │           │  model  │
    └────┬────┘           └────┬────┘           └─────────┘
         │                     │
   ┌─────┴─────┐    ┌──────────┼──────────┐
   │Radiology  │  ┌─▼──┐   ┌──▼──┐   ┌──▼──┐
   │Pharma     │  │ ML  │   │Algo │   │Prog │
   │Surgery    │  └──┬──┘   └─────┘   └─────┘
   └───────────┘     │
                ┌────┴────┐
                │RL  │NLP │
                └────┴────┘

Each node in the graph is a separately deployed model with its own weights, calibration cycle, and utility tracker. The interface between nodes is a structured protocol:

Request:  { query, context, field, confidence_floor, session_id }
Response: { answer, confidence, assertions[], uncertainty_flags, U_score }

This is the same data structure the wrapper already produces — no new interface design is required. The router simply fans queries to the relevant submodels and merges their responses.

Why this eliminates catastrophic forgetting:

Updating the surgery submodel only modifies surgery weights. The CS model is physically unaffected. Cross-domain knowledge lives exclusively in the router and a thin shared embedding layer that all submodels project into. Rolling back a surgery update requires swapping one model file, not re-running the entire training pipeline.

10.3 Branching Heuristics

The graph branches recursively until one of two stopping conditions is met:

Hardware bound: Stop when a single submodel fits comfortably on one GPU. At current hardware a 7B parameter model fits on one H100. A graph of 20 domain models × 7B = 140B total parameters distributed across 20 GPUs, but with the key advantage that only the relevant 1–3 submodels activate per query. Inference cost is proportional to query complexity, not model size.

Statistical bound: Stop branching when the within-domain contradiction rate drops below a threshold — meaning the submodel is internally consistent enough that further specialization adds noise rather than signal. A domain with contradiction rate < 2% does not benefit from subdivision.

In practice: branch until the hardware bound is reached for active domains, use the statistical bound to decide which domains warrant a branch at all.

10.4 Cross-Domain Query Handling

Multi-domain queries (e.g. "Write a Python script to analyze patient drug dosage data") require both CS and Medicine submodels simultaneously. The router handles this through query decomposition:

1. Field classifier returns distribution:
      {"software_engineering": 0.65, "medicine": 0.35}

2. Router decomposes query:
      CS subquery:  "Write Python data analysis code"
      Med subquery: "What are the clinical constraints on dosage data?"

3. Fan out: send subqueries to respective models in parallel

4. Merge: combine responses, flag conflicts,
         apply weighted confidence from field distribution
         (medicine response gets 35% weight on confidence bounds)

5. Arbitration: if CS and Medicine models contradict each other,
         escalate to parent model or flag for human review

The arbitration layer is addressed in §10.5 — a dedicated Arbiter Agent that runs structured contradiction detection across conflicting submodel outputs and feeds verified corrections back into both submodels via the blue-green update pipeline.

10.4.1 Router Misclassification: Open Problem and Mitigations

The Micro-Expert model's correctness depends critically on the router sending each query to the right submodel. Two recent empirical findings establish that this is a genuine vulnerability rather than an engineering detail.

Xu et al. (2024) demonstrate that LLMs force-select from available label options even when no correct label exists — they cannot output "none of these apply" without explicit training to do so. Applied to the field classifier: if a query falls outside or between the classifier's known fields, it will still commit to a field rather than expressing genuine uncertainty. The entropy fallback mechanism in §5.2 partially addresses this by detecting high-entropy distributions, but does not handle the case where the classifier is confidently wrong rather than uncertain.

Raval et al. (2026) show that for structured classification tasks — exactly the type of classification our router performs — traditional ML models (LightGBM, fine-tuned BERT-scale models) consistently outperform LLMs, particularly on medical data. An LLM-based field classifier is therefore the weakest possible architectural choice for routing.

The two failure regimes:

Regime 1 — Wrong submodel, low confidence (recoverable)
    Query about medication dosage → routed to CS submodel
    CS submodel has low C on this query (out-of-domain)
    C < C_min(f) → abstention triggered → escalation
    Outcome: slow but safe — utility function catches it

Regime 2 — Wrong submodel, high confidence (dangerous)
    Query about medication dosage → routed to CS submodel
    CS submodel saw medical text in training, answers confidently
    C stays above C_min → wrong answer delivered without warning
    Outcome: silent failure — utility function does not catch it

Regime 1 is safe: the utility function's abstention mechanism serves as a natural containment layer — a well-calibrated submodel that recognizes it is out of domain will produce low confidence, triggering $C < C_{\min}(f)$ and escalation to the correct expert. The dangerous case is Regime 2, where the wrong submodel produces an overconfident out-of-domain answer.

Mitigations:

M1 — Replace LLM classifier with a trained lightweight classifier as primary. Per Raval et al. (2026), a fine-tuned DeBERTa-scale model or LightGBM trained on labeled routing examples outperforms an LLM classifier for structured field classification. The LLM classifier is retained as a fallback for ambiguous or out-of-distribution queries. Routing does not require generation capability — a discriminative model is both more accurate and cheaper.

M2 — Ensemble routing with disagreement detection. Run the lightweight trained classifier and the LLM classifier in parallel. When they disagree on the top-1 field, treat the query as high-entropy and broadcast to both candidate fields. Agreement between two independent classifiers provides much stronger routing confidence than either alone.

M3 — Explicit "none of the above" output class. Address the Xu et al. (2024) finding directly: add an explicit ambiguous class to the classifier's label space, trained on queries that span fields or belong to no current submodel. When selected, the system broadcasts to the top-3 submodels by embedding similarity and lets the Arbiter reconcile. This catches confident misclassification rather than uncertain classification.

M4 — Post-routing domain membership verification. After routing but before returning a response, ask the receiving submodel to perform a lightweight binary classification: does this query fall within its domain? A submodel trained with explicit out-of-domain negatives can reliably say "this is not a CS question" when given a medical query. If the self-assessment is negative, re-route to the second-ranked field. This catches Regime 2 at the submodel level rather than relying on confidence calibration.

M5 — Submodel domain boundary calibration (training-time fix for Regime 2). Each submodel is trained with out-of-domain examples as negatives, learning to produce low $C$ on queries outside its specialization. This converts Regime 2 failures (dangerous, silent) into Regime 1 failures (recoverable, visible). This is the architectural fix; M1–M4 are operational fixes.

M6 — Utility-feedback rerouting. If a routed response scores $U$ below a field-calibrated threshold — particularly if it fails logical or cross-session checks at rates above baseline — flag the routing decision as potentially incorrect and re-route to the second-ranked field. The utility function's output becomes a routing quality signal, closing the feedback loop between field classification and response quality.

Status. M1 and M5 are the highest-priority items for Phase 6 implementation. M1 improves routing accuracy at classification time; M5 makes residual misclassifications recoverable through the existing utility abstention mechanism. M2–M4 and M6 are defense-in-depth layers that reduce both the frequency and severity of routing errors without requiring changes to the core architecture.

References: Xu et al. (2024), "LLMs' Classification Performance is Overclaimed," arXiv:2406.16203. Raval et al. (2026), "LLM is Not All You Need: A Systematic Evaluation of ML vs. Foundation Models for Medical Classification," arXiv:2601.16549.

10.5 The Arbiter Agent

Builder walkthrough: Tutorial §11 — The Arbiter Agent

When two submodels produce conflicting answers to the same query, the system does not escalate to a human or fall back to a parent model — both of which are slow and expensive. Instead, a dedicated Arbiter Agent resolves the conflict using the same structured contradiction detection pipeline already built into the system, determines which submodel is correct (or whether both are wrong), and feeds verified corrections back into both submodels simultaneously via the blue-green update mechanism.

The Arbiter Agent is not a general-purpose reasoner. It has a single job: given two conflicting outputs A and B on subject S in domain D, determine ground truth and issue correction signals. Its reliability comes from running deterministic, automatable tests rather than subjective judgment.

Arbitration pipeline:

INPUT:
    output_A   from submodel_A (e.g. CS model)
    output_B   from submodel_B (e.g. Medicine model)
    subject    S  (the conflicting claim)
    domain     D  (field context for penalty weighting)

STEP 1 — Classify conflict type (in order of detectability):

    Logical check:
        Does A contradict its own stated premises?
        Does B contradict its own stated premises?
        Tool: contradiction_detector.check(A) / check(B)
        Cost: O(1), fully automated

    Mathematical check:
        Are any numerical claims in A or B provably wrong?
        Tool: symbolic verifier (SymPy, Lean), complexity analyzer
        Cost: O(1) for formal domains, not available for all

    Cross-session check:
        Does A or B contradict prior verified assertions
        in the assertions store for subject S?
        Tool: assertions_store.query(S, domain=D)
        Cost: one DB lookup + embedding similarity

    Empirical check:
        Does A or B contradict verifiable external ground truth?
        Tool: web search, curated knowledge base, field-specific APIs
              (e.g. PubMed for medicine, arXiv for CS)
        Cost: highest — only run if prior checks inconclusive

STEP 2 — Verdict:

    Case 1: A correct, B wrong
        → issue correction to submodel_B
        → reinforce submodel_A (add to its DPO preferred set)

    Case 2: B correct, A wrong
        → issue correction to submodel_A
        → reinforce submodel_B

    Case 3: Both wrong
        → issue corrections to both submodels
        → share internal evidence chain with both submodels
          (each submodel adds it to its DPO rejected set)
        → log as high-priority knowledge gap
        → assign curiosity gap bonus to subject S:

            K_gap(S) = K_effective(S) × gap_multiplier(field)

            gap_multiplier(field) = 1 + penalty_multiplier(field) / 10
                Surgery:      gap_multiplier = 2.0
                Software Eng: gap_multiplier = 1.2
                Creative:     gap_multiplier = 1.0

        The gap bonus overrides normal curiosity competition —
        the system preferentially routes novel queries on subject S
        to the relevant submodels until the gap is resolved.
        Gap status is cleared when:
            both submodels achieve confidence(S) > C_min(field)
            AND no new contradictions on S for T(field) interactions

        Two budget constraints apply simultaneously to prevent
        Case 3 gaps from monopolizing exploration:

        Constraint 1 — Per-gap cap:
            K_gap(S) ≤ K_natural_max(field)
            No single gap can be more attractive than the maximum
            natural curiosity score achievable in that field.

        Constraint 2 — Collective budget cap:
            Σ K_gap(all active gaps) ≤ (2/3) × K_budget_total
            Case 3 gaps collectively cannot exceed 2/3 of the total
            curiosity exploration budget. At least 1/3 is always
            reserved for natural novelty-driven exploration.

        When multiple Case 3 gaps compete within the 2/3 ceiling,
        budget is allocated proportionally to
        gap_multiplier × field_penalty — higher-stakes gaps
        get priority. The 2/3 ceiling ensures the system never
        becomes a pure gap-resolution machine.

    Case 4: Arbiter inconclusive
        → flag for deferred resolution (internal)
        → serve minimal hedge to user: no internal state disclosed
        → initiate controlled external escalation protocol
          (see §10.5 External Escalation — only when all four
           check types return no clear winner)

STEP 3 — Correction signal (internal only):

    For each submodel receiving a correction:
        correction = {
            subject:      S,
            domain:       D,
            wrong_claim:  extracted from losing output,
            correct_claim: verified ground truth,
            evidence:     [full evidence chain — internal only,
                           shared with arbitrated submodels for DPO,
                           never disclosed externally],
            weight:       field_penalty_multiplier(D)
        }
        → share evidence chain with affected submodel(s) only
          (Case 1/2: one submodel; Case 3: both submodels)
        → submodel independently decides to add to DPO rejected set
        → add verified claim to assertions store
        → if correction_count(S) > threshold:
              trigger blue-green update cycle for that submodel
        → if Case 3: assign curiosity gap bonus to subject S
              (see Case 3 above)

    External response: the user receives only the verified answer.
    No arbiter verdict, no internal evidence, no correction signal
    is disclosed. If the system is uncertain (Case 4), the user
    sees only a minimal hedge ("I am not fully confident in this
    answer") — not the reason, not the conflict, not which models
    disagreed.

Assertions store decay — field-specific evidence staleness:

Not all verified facts age equally. A mathematical theorem proven beyond doubt — Pythagoras, the fundamental theorem of calculus, the law of conservation of energy — does not become less true over time. A clinical treatment guideline, a software security best practice, or a legal precedent can be obsolete in months. The assertions store therefore applies a field-specific confidence decay function to stored evidence:

C_effective(assertion, t) = C_verified × decay(field, Δt)

decay(field, Δt):

    Class A — No decay (mathematically or physically proven facts):
        Pure mathematics (proofs, theorems, derivations)
        Fundamental physics (gravity, thermodynamic laws, calculus)
        decay = 1.0 for all Δt

    Class B — Slow decay (decades-stable fields):
        Mechanical engineering principles
        Classical chemistry, structural physics
        decay = exp(-Δt / τ),  τ = 10 years

    Class C — Moderate decay (years-stable fields):
        General medicine (anatomy, pharmacology mechanisms)
        Software architecture patterns
        Legal common law principles
        decay = exp(-Δt / τ),  τ = 3 years

    Class D — Fast decay (months-to-years volatile fields):
        Clinical treatment guidelines (medical consensus)
        Software security best practices
        Regulatory and compliance standards
        ML/AI research findings
        decay = exp(-Δt / τ),  τ = 6 months

When the Arbiter retrieves a cross-session assertion for its check, the effective confidence used is `C_verified × decay(field, Δt)` — not the original verification confidence. An assertion with C=0.95 verified three years ago in a fast-decay field (τ=6 months) has effective confidence ≈ 0.95 × exp(-6) ≈ 0.001 — functionally untrustworthy, and correctly treated as inconclusive. The same assertion in a no-decay field retains full confidence indefinitely.

Field class assignment is determined by the field classifier at assertion write time and stored with the assertion. The class boundaries above are the initial calibration — they will be updated empirically as the system accumulates evidence about how quickly different domains evolve.

Why some facts truly have no decay. A mathematical or logical proof is not an empirical claim that could be overturned by new evidence — it is a deductive conclusion from axioms. If Pythagoras's theorem was valid when stored, it is valid now. The no-decay class is not an approximation; it is epistemologically correct. Treating proven mathematical results as time-sensitive would introduce spurious uncertainty where none exists.

Why corrections feed both submodels simultaneously:

A contradiction between two submodels means at least one of them has a knowledge gap. But often both have the gap — one is simply wrong in a way that happens to contradict the other's different wrong answer. The Arbiter does not assume the non-losing submodel is correct; it independently verifies ground truth and corrects any submodel whose output deviates from it, regardless of which "won" the pairwise comparison.

The correction threshold before triggering blue-green:

Not every arbitrated correction immediately triggers a model update — single corrections are noisy. The trigger uses the same δ and T mechanism from §10.7:

trigger blue-green IF:
    corrections on subject S > T_arbiter     [enough evidence]
    AND avg_correction_confidence > 0.85     [arbiter is sure]
    AND field_penalty(D) × n_corrections > θ [weighted severity]

T_arbiter = T(field) / 2
    [half the normal detection window — arbiter corrections
     are higher quality signal than routine utility drift]

The half-window shortcut is justified because arbiter corrections are backed by structured internal verification — logical, mathematical, cross-session, and empirical checks — rather than aggregate utility drift alone. Each correction carries a known evidence basis internally, making it higher-quality signal per event. None of this evidence is surfaced externally; it informs only the correction weight and the blue-green trigger.

Arbiter confidence scoring:

The Arbiter itself maintains a confidence score per verdict, built from how many check types converged on the same answer:

arbiter_confidence = Σ checks_passed × check_weight / Σ check_weight

check_weights:
    logical:       0.30   (always run, but weakest alone)
    mathematical:  0.40   (strongest — formal proof is definitive)
    cross-session: 0.20   (prior assertions are verified but may be stale)
    empirical:     0.10   (slowest, but grounds the verdict in reality)

If arbiter_confidence < 0.85 → Case 4 (inconclusive), do not correct

This prevents the Arbiter from propagating its own errors — a low-confidence verdict does less damage held in the internal review queue than being applied as a correction to two submodels.

Full arbitration flow integrated with blue-green:

Cross-domain query → conflicting outputs detected
         ↓
Arbiter Agent invoked
         ↓
Run 4 contradiction checks (logical → mathematical →
cross-session → empirical, stop when confident)
         ↓
         ├── Case 1/2: one submodel wrong
         │       → correction → DPO rejected pair
         │       → assertions store updated
         │       → if threshold met → blue-green triggered
         │
         ├── Case 3: both wrong
         │       → corrections to both
         │       → both DPO rejected sets updated
         │       → both blue-green cycles may trigger
         │
         └── Case 4: inconclusive
                 → serve minimal hedge (no internal detail)
                 → external escalation protocol (§10.5)
                 → responses feed back to submodels
                 → blue-green if merit threshold met

Arbiter calibration via external expert sampling:

The Arbiter's confidence weight vector w = (logical: 0.30, mathematical: 0.40, cross-session: 0.20, empirical: 0.10) is initially hand-specified. To calibrate these weights empirically and detect drift over time, a random sample of Arbiter verdicts — targeting 2–5% of all Case 1, 2, and 3 resolutions — is independently routed to domain experts under the standard external escalation protocol.

Calibration pipeline:

1. Arbiter issues verdict (Case 1, 2, or 3) with conf_arbiter score
2. With probability p_sample (field-calibrated, ~0.02–0.05):
      → route same subject S to eligible domain experts (§10.5 escalation)
      → blind: experts do not know an Arbiter verdict already exists
3. Compare expert consensus to Arbiter verdict:
      Match:    reinforces current weight vector (no change)
      Mismatch: flags potential Arbiter drift
4. If mismatch rate > drift_threshold(field) over sliding window W:
      → consult additional experts until consensus reached
      → update weight vector in direction of expert consensus
      → log weight change for audit
5. If Arbiter and experts persistently disagree on a subject class:
      → flag as systematic Arbiter blind spot
      → increase sampling rate for that subject class
      → escalate weight recalibration

Drift is detected when the mismatch rate between Arbiter verdicts and independent expert consensus exceeds a field-specific threshold over a rolling window. The expert consensus is treated as the ground truth because it is the most reliable signal available — multiple verified domain experts independently agreeing constitutes strong empirical evidence.

This mechanism means the Arbiter is not self-referential: it is calibrated against an independent external signal on a continuous basis, not just at initialization. The calibration sample is small enough that it does not significantly increase the escalation load, but large enough to detect systematic drift within a reasonable observation window.

Adaptive sampling for over-correction detection:

The base sampling rate of 2–5% provides general drift detection. However, the Personality-Arbiter feedback loop introduces a specific failure mode: if the Arbiter is systematically over-correcting (high false positive rate on contradiction detection), the elevated contradiction signal causes the personality system to increase caution, reduce exploration, and reduce gap resolution capacity — a loop that tightens without any external signal triggering correction.

This is detected through correction volume monitoring. The system tracks each Arbiter instance's correction rate per unit time relative to baseline:

correction_rate(arbiter, window) = corrections_issued / interactions_processed

if correction_rate > baseline_rate × over_correction_threshold(field):
    → escalate sampling rate for this Arbiter instance

adaptive_sampling_rate:
    baseline:          2–5%    (normal drift detection)
    elevated:          8–10%   (correction rate moderately high)
    intensive:         10–15%  (correction rate significantly above baseline)
    intensive ceiling: 15%     (hard cap — never exceeded regardless of rate)

At elevated and intensive sampling rates, the increased expert verification provides faster feedback on whether the Arbiter's corrections are accurate. If expert consensus confirms the corrections are correct, the high correction rate is real signal — the field has accumulated genuine errors. If expert consensus contradicts a significant fraction of corrections, over-correction is confirmed and the Arbiter's weight vector is recalibrated.

The hard cap at 15% ensures the escalation infrastructure is never overwhelmed by a single misbehaving Arbiter instance. At 15% sampling on a high-volume domain, the expert load is still manageable and the verification turnaround is fast enough to detect and correct the feedback loop before the personality system has drifted significantly. The personality system's drift rate cap (§6.2, Layer 2: max Δ = 0.02–0.05 per cycle) provides an additional buffer — the personality cannot change faster than the Arbiter sampling can detect and correct a problem.

Note on alternative arbitration mechanisms.

The hand-specified weight vector (logical: 0.30, mathematical: 0.40, cross-session: 0.20, empirical: 0.10) and the adaptive 2–15% expert sampling rate are engineering approximations to what a theoretically grounded mechanism would derive endogenously. §10.6 develops the theoretically grounded alternative in full: treating domain submodels as players in a cooperative game, the Vickrey-Clarke-Groves mechanism achieves POA = 1 with truthful reporting as the dominant strategy (Theorems S1–S3). The current hand-specified mechanism is retained here as the deployable approximation; §10.6 is the theoretical ideal toward which Phase 6 Arbiter architecture converges.

Information disclosure boundary:

The Arbiter Agent maintains a strict internal/external split consistent with §6.3. Everything in this section — internal evidence chains, check weights, arbiter confidence scores, correction signals, DPO pair assignments, verdict cases — is internal state. The external boundary exposes exactly two things:

External output (what the user sees):
    1. The verified answer                (when arbiter is confident)
    2. A minimal hedge: "I have limited   (when arbiter is inconclusive —
       confidence in this answer"          Case 4 only; external escalation
                                          proceeds invisibly in background)

Everything else stays inside the system:
    - Which submodels conflicted
    - What the arbiter checked
    - What evidence was found
    - Which model was wrong
    - That a correction was issued
    - That a blue-green cycle was triggered

The trust principle from §6.3 applies here with particular force: a user who knows the system detected an internal conflict and knows which domains conflicted has information that could be used to probe the system's weaknesses deliberately. The minimum disclosure posture protects against this.

External escalation protocol (Case 4 only):

When all four internal check types fail to produce a confident verdict, the Arbiter initiates a controlled external consultation. This is the only condition under which any information crosses the system boundary — and even then, the information shared is deliberately minimal, obfuscated, and partialized.

Eligibility gating — who receives the query:

External consultation is restricted to entities whose trust scores meet two independent thresholds simultaneously:

Eligible consultant IF:
    entity_score.domain_expertise(D) > median_expertise(D)
    AND entity_score.trust > trust_threshold(field)

trust_threshold(field):
    Surgery, Aviation:    0.90   (near-maximum trust required)
    Law, Engineering:     0.80
    Software Eng:         0.70
    Research, Education:  0.65

domain_expertise measured from:
    verifiable professional experience (years in field)
    educational qualifications (degree level, institution tier)
    field-specific certifications (board certification, PE, bar)
    prior interaction accuracy with this system (tracked internally)

Only entities who clear both gates receive the query. A highly trusted entity with shallow domain expertise is not eligible. A deep domain expert with low trust is not eligible. Both dimensions must exceed threshold.

Query construction — obfuscation and partialization:

The external query is constructed to extract useful signal while revealing as little internal state as possible:

What is NEVER included in the external query:
    - That two submodels conflicted
    - Which submodels or domains were involved
    - The specific outputs that caused the conflict
    - That an internal arbitration process ran
    - Any internal confidence scores or check results
    - That this is a system-generated query

What IS included (minimum viable context):
    - The subject S, generalized to remove system-specific framing
    - The specific claim that cannot be verified internally
    - A neutral domain label (e.g. "medicine") if necessary
      for the expert to answer, stripped of subdomain specifics
    - A prompt framed as a professional judgment question,
      not a conflict resolution request

Example transformation:

Internal conflict:
    CS model:  "bubble sort is O(n log n) average case"
    Med model: "ibuprofen reduces fever via COX-2 inhibition only"
    [unrelated models, each internally inconsistent]

External query to CS expert (generalized, partialized):
    "What is the average-case time complexity of bubble sort?"
    [No mention of conflict, no mention of other model, no context]

External query to pharmacology expert (generalized, partialized):
    "Does ibuprofen reduce fever exclusively via COX-2 inhibition,
     or are other mechanisms involved?"
    [Same treatment — clean professional question, no system context]

The external expert sees a professional question indistinguishable from a standard query. They have no visibility into the fact that an AI system is consulting them, that models disagreed, or that their answer will be used to correct model weights.

Response handling and feedback:

Expert responses are not applied directly as corrections. They re-enter the Arbiter pipeline as high-weight empirical evidence:

Expert response received
        ↓
Arbiter re-runs contradiction checks with response as
additional evidence (weight = entity_score.trust × 
entity_score.domain_expertise)
        ↓
If arbiter now confident → proceed to Case 1, 2, or 3
        ↓
Correction signal issued to relevant submodel(s)
        ↓
Correction added to DPO training pairs
        ↓
Blue-green triggered IF:
    correction_merit > field_threshold
    AND system load within stability bounds
    AND no other blue-green cycle active for this submodel

Blue-green is NOT automatically triggered — it depends on
merit and current system state. System stability takes
priority over any individual correction.

Stability preservation:

The external escalation path is designed to never compromise system stability. Expert responses feed the Arbiter as evidence, not as direct commands. The Arbiter still runs its full check pipeline before issuing any correction. Blue-green deployment is gated by the same stability checks as all other updates — no escalation response can bypass the canary phase, the benchmark evaluation, or the rollback safeguards. If the system is already under load from another update cycle, the correction is queued rather than applied immediately.

This means the escalation path is informational, not operational: it enriches the Arbiter's evidence base without granting external entities any control over the system's update mechanism.

What this resolves about the arbitration problem:

The original concern was that multi-model conflict resolution requires consensus — a notoriously hard distributed systems problem. The Arbiter sidesteps consensus by replacing the question "which model do we believe?" with "what does the internal evidence say?" This arbitration is entirely internal — evidence chains, check results, confidence scores, and correction signals never leave the system. Externally, the user sees only the verified answer, or in Case 4 a minimal hedge with no elaboration. The only remaining hard cases are those where all four check types return no clear winner. These are not left unresolved — they trigger a controlled external escalation protocol (§10.5) in which a carefully obfuscated and partialized query is routed to a small set of verified domain experts whose entity scores meet the field trust threshold. The user is told nothing beyond a minimal hedge; the internal conflict, the models involved, and the escalation itself are never disclosed.

---

10.6 Game-Theoretic Arbitration: The VCG Mechanism

The hand-specified Arbiter mechanism in §10.5 is a deployable engineering approximation. This section develops the theoretically grounded alternative — treating domain submodels as players in a cooperative game and using the Vickrey-Clarke-Groves (VCG) mechanism to achieve social optimum with truthful reporting as the dominant strategy. The VCG mechanism makes both hand-specified weights and periodic expert sampling unnecessary. It is the target architecture for the Phase 6 Arbiter implementation.

10.6.1 The Game Setup

Players and information. Let $\mathcal{I} = \{1, \ldots, k\}$ be the set of domain submodels involved in an arbitration round. Each submodel $i$ has produced an output claim $\hat{a}_i$ on subject $S$ in domain $f$.

The Arbiter is the external social planner — a distinct agent with access to all submodel outputs $\{\hat{a}_i\}_{i \in \mathcal{I}}$, the assertions store, all four check results (logical, mathematical, cross-session, empirical), and the field-specific utility functions $U_i(\cdot;\, f_i)$ for each submodel.

Claim space. The feasible set of outcomes is:

$$\mathcal{A} = \{\hat{a}_1, \ldots, \hat{a}_k\} \cup \{s_1, \ldots, s_m\}$$

where $\hat{a}_1, \ldots, \hat{a}_k$ are the submodels' submitted claims and $s_1, \ldots, s_m$ are synthesis candidates generated by the Arbiter from the evidence checks — capturing the case where neither original claim is correct but a composite claim is.

Value functions. Each submodel $i$ holds a private value function $v_i : \mathcal{A} \to \mathbb{R}$, where $v_i(a)$ is the utility submodel $i$ assigns to outcome $a$ being adopted as the verified claim:

$$v_i(a) = U_i\bigl(E(a, f_i),\; C(a, f_i),\; K(a, f_i);\; f_i\bigr)$$

Disagreement point. If the Arbiter cannot select any claim, the system falls back to abstention. The disagreement payoff for each submodel is:

$$d_i = v_i(\text{abstain}) = U_i(0,\; C_{\min}(f_i) - \epsilon,\; 0;\; f_i) \approx 0$$

The Arbiter only selects a claim $a$ if it strictly Pareto-dominates abstention: $v_i(a) > d_i$ for at least one submodel and $v_i(a) \geq d_i$ for all.

Social welfare function. The social optimum is the claim that maximises the sum of submodel utilities:

$$a^{**} = \arg\max_{a \in \mathcal{A}} \sum_{i \in \mathcal{I}} v_i(a)$$

This is the claim the Arbiter would select if it could observe all $v_i$ truthfully. The VCG mechanism constructs the incentive structure that makes truthful reporting dominant.

10.6.2 The VCG Mechanism

Allocation rule. Given reported value functions $\hat{v}_i$ from each submodel:

$$a^{**}(\hat{v}) = \arg\max_{a \in \mathcal{A}} \sum_{i \in \mathcal{I}} \hat{v}_i(a)$$

The Arbiter selects the claim that maximises reported social welfare.

Clarke pivot transfer. Each submodel $i$ receives a transfer:

$$t_i(\hat{v}) = \underbrace{\sum_{j \neq i} \hat{v}_j\!\left(a^{**}(\hat{v})\right)}_{\text{welfare others achieve with } i} - \underbrace{\max_{a \in \mathcal{A}} \sum_{j \neq i} \hat{v}_j(a)}_{\text{welfare others achieve without } i}$$

The transfer measures how much submodel $i$'s participation improves outcomes for all other submodels. If $i$'s preferred claim is also best for the others, $t_i > 0$. If $i$ forces the outcome toward a claim the others value less, $t_i < 0$.

Transfer implementation. The transfer $t_i$ is applied as an adjustment to submodel $i$'s DPO penalty weight in the next calibration cycle:

$$\mu_i^{(\text{next})} = \mu(f_i) \cdot \exp\!\bigl(-\gamma \cdot t_i\bigr)$$

where $\mu(f_i)$ is the field base penalty multiplier and $\gamma > 0$ is a scaling constant, clamped so that $\mu_i^{(\text{next})} \geq \mu_{\min} > 0$.

• $t_i > 0$: submodel $i$ contributed positively to the social optimum → next DPO correction weighted less harshly (reward)
• $t_i < 0$: submodel $i$ forced the outcome away from the social optimum → next DPO correction weighted more harshly (penalty)
• $t_i = 0$: submodel $i$'s participation had no effect on others → no adjustment

10.6.3 Theorem S1 — Dominant Strategy Truthfulness

Theorem S1. Under the VCG mechanism, truthful reporting $\hat{v}_i = v_i$ is a weakly dominant strategy for every submodel $i$, regardless of the reports of other submodels.

Proof. Fix the reports of all other submodels $\hat{v}_{-i} = (v_j)_{j \neq i}$ at any values. Submodel $i$ chooses $\hat{v}_i$ to maximise its net payoff:

$$\Pi_i(\hat{v}_i) = v_i\!\bigl(a^{**}(\hat{v}_i, \hat{v}_{-i})\bigr) + t_i(\hat{v}_i, \hat{v}_{-i})$$

Substituting the VCG transfer:

$$\Pi_i(\hat{v}_i) = v_i(a^{**}) + \sum_{j \neq i} \hat{v}_j(a^{**}) - \max_{a} \sum_{j \neq i} \hat{v}_j(a)$$

The last term does not depend on $\hat{v}_i$ — it is a constant from submodel $i$'s perspective. Maximising $\Pi_i$ is therefore equivalent to maximising $v_i(a^{**}) + \sum_{j \neq i} \hat{v}_j(a^{**})$.

When $\hat{v}_i = v_i$, the allocation rule selects $a^{**} = \arg\max_a \sum_j v_j(a)$, maximising $\sum_j v_j(a^{**})$. If submodel $i$ misreports $\hat{v}_i \neq v_i$, the allocation rule may select a different outcome $a'$. The net payoff becomes:

$$\Pi_i(\hat{v}_i \neq v_i) = v_i(a') + \sum_{j \neq i} v_j(a') - \max_a \sum_{j \neq i} v_j(a)$$

Since $a^{**}$ maximises $\sum_j v_j(a)$ under truthful reporting:

$$\sum_j v_j(a^{**}) \geq \sum_j v_j(a') \implies \Pi_i(\hat{v}_i = v_i) \geq \Pi_i(\hat{v}_i \neq v_i)$$

for all possible misreports $\hat{v}_i$ and all possible reports $\hat{v}_{-i}$. Truthful reporting is weakly dominant. $\blacksquare$

10.6.4 Theorem S2 — Social Optimum (POA = 1)

Theorem S2. Under the VCG mechanism with dominant strategy truthful reporting, the Arbiter selects the social optimum $a^{**}$. The Price of Anarchy is exactly 1.

Proof. By Theorem S1, every submodel reports $\hat{v}_i = v_i$ in dominant strategy equilibrium. The allocation rule therefore selects:

$$a^{**}(\hat{v}) = \arg\max_{a \in \mathcal{A}} \sum_i \hat{v}_i(a) = \arg\max_{a \in \mathcal{A}} \sum_i v_i(a)$$

This is the social optimum by definition. The Price of Anarchy is:

$$\text{POA} = \frac{W^{**}}{W_{\text{Nash}}} = \frac{W^{**}}{W^{**}} = 1 \qquad \blacksquare$$

since the dominant strategy equilibrium is also the Nash equilibrium and achieves $W^{**}$. This is strictly stronger than the POA $\leq 4/3$ bound for the proportional allocation game (Johari and Tsitsiklis, 2004), which applies without a mechanism designer. The VCG mechanism achieves POA = 1 because the Arbiter's external position allows it to compute and implement the social optimum directly.

10.6.5 Theorem S3 — Individual Rationality

Theorem S3. Under the VCG mechanism, every submodel weakly prefers participation to abstention: $v_i(a^{**}) + t_i \geq d_i$ for all $i$.

Proof. The Arbiter only selects $a^{**}$ if it Pareto-dominates abstention: $v_i(a^{**}) \geq d_i$ for all $i$. In the worst case, the Clarke transfer satisfies $t_i \leq 0$. The Arbiter enforces individual rationality by applying the transfer only when $v_i(a^{**}) + t_i \geq d_i$, and reverting to abstention otherwise (the individually rational VCG variant). $\blacksquare$

10.6.6 Comparison with the Hand-Specified Arbiter

Property	Current Arbiter (§10.5)	VCG Arbiter (§10.6)
Check weights	Hand-specified: (0.30, 0.40, 0.20, 0.10)	Endogenous: emerge from $v_i(a)$
Calibration	Expert sampling 2–15%	Clarke transfer — continuous signal
Outcome selection	Weighted vote among original claims	Social optimum over $\mathcal{A}$ including synthesis
Synthesis claims	Case 3 gap bonus heuristic	Natural: $a^{**}$ may be a synthesis $s_j$
Efficiency guarantee	None (POA unspecified)	POA = 1 exactly
Truthfulness	Not guaranteed	Dominant strategy (Theorem S1)
Individual rationality	Not guaranteed	Satisfied (Theorem S3)
Ties	Possible (requires tiebreaker)	None (VCG outcome unique under strict concavity)
Infrastructure required	Monolithic + Micro-Expert	Micro-Expert only (submodels must expose $v_i$)

The current mechanism is retained in §10.5 because it is deployable without changes to the submodel interface. The VCG mechanism requires each submodel to expose a value function over the claim space — a richer output format that is feasible in the Micro-Expert Architecture (where submodels are separate services with controlled APIs) but not in the monolithic wrapper setting.

10.6.7 Practical Implementation

Value function elicitation. Each submodel $i$ reports $v_i(a)$ for all $a \in \mathcal{A}$ via a structured prompt:

For each candidate claim a ∈ A:
    "Given your domain expertise in {f_i}, assign a confidence score
     in [0, 1] to the following claim: {a}
     Consider: factual accuracy, internal consistency, alignment with
     your verified knowledge base."

v_i(a) = U_i(E=score, C=consistency(a), K=0; f_i)

The curiosity term $K = 0$ during arbitration — the agent is resolving a contradiction, not exploring.

Synthesis candidate generation. The Arbiter generates synthesis candidates $\{s_j\}$ from the evidence check results:

s_1 = claim consistent with logical check winner
s_2 = claim consistent with mathematical check winner
s_3 = conjunction of non-contradictory parts of a_1, ..., a_k
s_4 = claim from assertions store with highest effective confidence
s_5 = hedged claim: "X in context Y, but Z in context W"
      (when claims are both correct under different conditions)

Typically $m = 3$–$5$ synthesis candidates suffice. The full claim space $|\mathcal{A}| = k + m$ is small and evaluation is fast.

Budget balance. The VCG mechanism does not satisfy budget balance: $\sum_i t_i \leq 0$ in general (the Hurwicz-Walker impossibility result establishes no mechanism can simultaneously achieve efficiency, incentive compatibility, and budget balance). In the DPO weight implementation, total penalty adjustments across submodels in an arbitration round need not sum to zero — which is acceptable because there is no conservation law on training weights. Over many rounds, a well-calibrated submodel's expected transfer approaches zero.

10.6.8 Connection to the POA Bound

The Johari-Tsitsiklis (2004) POA $\leq 4/3$ bound (§3.1) applies to the learning game — where submodels compete for calibration budget — not to the arbitration game.

For the arbitration game specifically: without a mechanism designer, POA may be as bad as $4/3$ (submodels asserting their own claims without coordination). With the VCG mechanism, POA = 1 (Theorem S2). The gap — from $4/3$ to $1$ — is exactly the value the Arbiter's external position provides. An internal voting mechanism, even with well-chosen weights, cannot achieve POA = 1 because it cannot enforce the Clarke transfers that align individual incentives with social welfare.

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10.7 Blue-Green Deployment for Submodel Updates

Builder walkthrough: Tutorial §12 — Blue-Green Deployment

This is the mechanism by which individual submodels update without disrupting the rest of the graph, and without waiting for a monolithic release cycle.

Trigger condition:

A submodel monitors its own utility score over a sliding window. An update cycle is triggered when deviation from baseline is both significant and sustained:

Trigger when ALL of:
    |U_current - U_baseline| > δ(field)    [significant deviation]
    deviation sustained for ≥ T interactions  [not noise]
    held-out benchmark available             [can evaluate candidate]

The theoretical values for δ and T are derived from the utility score variance (σ ≈ 0.04 from simulation) and field penalty multipliers:

δ(field) = base_δ / penalty_multiplier(field)
base_δ   = 0.05

Surgery:          δ = 0.005  (very sensitive — small changes matter)
Software Eng:     δ = 0.025  (moderate)
Creative Writing: δ = 0.050  (relaxed)

T(field) = (z_α × σ / δ(field))²    [power analysis, α=0.05]

Surgery:          T ≥ 246 interactions  (high confidence required)
Software Eng:     T ≥  10 interactions  (responsive)
Creative Writing: T ≥   2 interactions  (fast)

The deployment lifecycle:

Phase 0 — Detection:
    U_monitor watches sliding window of W interactions
    If |U_current - U_baseline| > δ for T consecutive interactions:
        → trigger training phase

Phase 1 — Training (offline):
    DPO calibration on accumulated (preferred, rejected) pairs
    Weighted by field_penalty_multiplier
    Mixed with replay buffer
    Produces candidate GREEN model
    BLUE model continues serving 100% of traffic

Phase 2 — Canary (5% green / 95% blue):
    Router sends 5% of traffic to GREEN, 95% to BLUE
    Minimum N_min interactions before any traffic shift
    N_min(field) = T(field) × 2   [double the detection window]
    Both models log U scores per interaction

Phase 3 — Gradual shift (utility-weighted routing):
    Every evaluation window, recompute split:

        traffic_green = softmax(U_green, U_blue, τ=τ_field)
                      = exp(U_green/τ) / (exp(U_green/τ) + exp(U_blue/τ))

        Enforced floor/ceiling:
            traffic_green = clip(traffic_green, 0.05, 0.95)

        τ(field): small τ → fast promotion, large τ → conservative
            Surgery:      τ = 0.05  (slow, winner-takes-all only when clear)
            Software Eng: τ = 0.20  (moderate)
            Creative:     τ = 0.50  (fast, early adopter)

    As U_green > U_blue, traffic shifts automatically toward green
    No manual intervention required

Phase 4 — Promotion (traffic_green ≥ promotion_threshold):
    promotion_threshold(field) = 1 - δ(field)  [field-calibrated]
    traffic_green → 1.0
    BLUE enters cooldown (not retired yet — instant rollback available)
    Cooldown duration = T(field) interactions

Phase 5 — Retirement:
    If GREEN holds through cooldown without regression:
        BLUE retired, weights freed
        U_baseline = U_green  ← new baseline for next cycle
        δ recalibrated from observed variance in this cycle

Rollback (any phase):
    Triggers: U_green < U_blue - ε for M interactions
              OR contradiction_rate_green > contradiction_rate_blue × 1.5
              OR benchmark regression > field_tolerance
    Action:   traffic_blue → 1.0 instantly
              GREEN flagged — failure DPO pairs added to replay buffer
                             with negative weight for next candidate

Traffic split visualization across a typical promotion cycle:

Traffic %  │
  100 BLUE ├────────────────────╮
           │                    ╰──╮
           │                       ╰──╮
           │                          ╰──────────╮
    5 GREEN├─────────────────────╮               │
           │                     ╰──╮            │
           │                        ╰──╮         │
    0      │                           ╰─────────╯────▶ time
           │  Canary    Gradual shift        Promotion
           │  (5/95)    (utility-driven)     (100% green)

10.8 System Properties

Catastrophic forgetting: Eliminated at the domain level. Intra-domain forgetting is mitigated by replay buffer as before, but the blast radius of any update is bounded to one submodel.

Independent deployability: Each submodel has its own blue-green cycle. A surgery model update in progress does not block a CS model update. They are fully decoupled.

Graceful degradation: If a submodel is mid-update (blue-green in progress), the router falls back to the parent model or a sibling domain model rather than failing. This requires the router to maintain a fallback graph.

Cost: Only the relevant 1–3 submodels activate per query. Total inference cost scales with query complexity, not total graph size. The 20-model graph costs roughly the same per query as a single-domain model.

Auditability: Every submodel update has a logged trigger (which utility deviation, over which window), a logged promotion trajectory (traffic split over time), and a clear rollback path. This is significantly more auditable than a monolithic model release.

10.9 Hardware-Adaptive Decomposition and the Consumer GPU Argument

Domain deep-dive: AI Data Centers — Hardware-Adaptive Decomposition

10.9.1 The Core Architectural Property

The granularity of the model graph is not fixed — it is relative to the hardware it runs on. This is a deliberate design property, not a constraint.

The core principle: intra-GPU compute is orders of magnitude faster than inter-GPU communication.

When a model operation stays within a single GPU's memory, it executes at full memory bandwidth (up to ~3.35 TB/s on an H100). The moment computation crosses a GPU boundary, it is throttled by the interconnect — NVLink at ~900 GB/s for close neighbors, PCIe at ~64 GB/s for further nodes. The implication is direct: the larger the submodel that fits on a single GPU, the less inter-GPU communication overhead per query.

Decomposition depth scales with GPU memory:

Hardware tier          GPU VRAM    Submodel fit     Graph shape
──────────────────────────────────────────────────────────────────
High-end  (H100 80GB)   80 GB     ~70B params      Shallow graph,
                                   per GPU          few large nodes
Mid-range (A100 40GB)   40 GB     ~35B params      Medium depth
Consumer  (RTX 4090)    24 GB     ~20B params      Deeper graph,
                                                    many small nodes
Edge / older            8–16 GB   ~7B params       Deep graph,
                                                    fine-grained specialist nodes

10.9.2 The Consumer Hardware Argument — Scope and Honesty

The claim is not that consumer GPUs match H100s on general workloads. They do not — H100s have 3.35 TB/s memory bandwidth versus 1.01 TB/s on an RTX 4090, and NVLink provides 900 GB/s inter-GPU bandwidth versus PCIe's 64 GB/s. For training and large-batch inference, enterprise hardware maintains a decisive advantage.

The claim is more specific, and it is the claim the Micro-Expert Architecture is designed to support: for inference on specialised domain queries, a graph of domain-specialist models on consumer hardware can match the output quality of a monolithic frontier model on enterprise hardware, at lower cost per query on the tasks where professional AI use is most valuable.

This rests on two foundations: an analytical cost model derived from published hardware specifications, and a routing quality experiment measuring the contribution of the routing and arbitration layer.

10.9.3 Analytical Cost Model

The following cost comparison is derived entirely from published hardware specifications and cloud provider pricing — no original measurement is required.

H100 SXM5 (enterprise):
  VRAM:                80 GB
  Memory bandwidth:    3.35 TB/s
  Cloud cost:          ~$2.50–3.50/hr (Lambda Labs, CoreWeave, 2025)
  Llama 3.1 70B:       ~140 GB fp16 → requires 2× H100, or 1× H100 at 4-bit quant
  Inference throughput: ~2,000 tokens/sec (batch=1, 200-token output)

RTX 4090 (consumer):
  VRAM:                24 GB
  Memory bandwidth:    1.01 TB/s
  Cloud cost:          ~$0.35–0.50/hr (RunPod, Vast.ai, 2025)
  Mistral/Llama 7B:    ~14 GB fp16 → fits in 1× 4090 with headroom
  Inference throughput: ~800 tokens/sec (batch=1)

Cost per 1,000 output tokens:
  70B on 2× H100:  (2 × $3.00/hr) ÷ (2,000 tok/sec × 3,600) × 1,000 = $0.00083
  7B on 1× 4090:   ($0.40/hr)    ÷ (800  tok/sec × 3,600) × 1,000 = $0.00014

  Single-specialist query cost ratio: 7B/4090 is ~6× cheaper per token.
  With 3 specialists activated (high fan-out): 3 × $0.00014 = $0.00042 — still 2× cheaper.

The cost inversion argument holds across all fan-out widths up to 5 activated specialists. This is an analytical result from public data, not a measured experiment. The latency picture is more nuanced: a single 7B model on a 4090 generates tokens at 800 tok/sec versus 2,000 tok/sec for a 70B model on an H100 — slower per model, but the specialist 7B model may require fewer tokens because its domain-specific response is more concise and accurate. Latency measurement on physical hardware is the primary item of empirical future work.

10.9.4 Data Center Operator Economics

Domain deep-dive: AI Data Centers — Cost Model & Revenue per Watt

For infrastructure operators the practical implication is best understood through revenue per watt and fleet utilisation, not abstract model size. A routed specialist architecture lets an operator reserve H100-class capacity for general-purpose premium workloads while serving a large class of professional domain queries on cheaper hardware with higher margin. In that setting the relevant comparison is not “can a 4090 beat an H100 on everything?” but “can a lower-tier GPU serve a specialist workload well enough that the operator earns more per useful query and per watt consumed?”

This matters most for mixed fleets. Providers such as CoreWeave and other GPU clouds often hold inventory across generations: H100s, A100s, A40s, L40S-class parts, and consumer-adjacent hardware. Without routing, lower-tier inventory risks being stranded in the product catalogue — too weak for frontier monoliths, too expensive for trivial workloads. A specialist-graph architecture gives those GPUs a high-value role. The fleet becomes heterogeneous by design rather than by accident.

A second lever is LoRA multi-tenancy. A base specialist can remain resident while domain- or customer-specific adapters are rotated in, allowing several customers’ specialist workloads to share one logical serving tier. This improves utilisation, lowers cold-start overhead, and creates room for tiered SLAs: premium broad-model inference on scarce frontier hardware, and lower-cost but still high-quality specialist inference on cheaper GPU pools. Under export restrictions, supply constraints, or simply uneven access to H100-class hardware, this flexibility is strategic rather than cosmetic.

10.9.5 Routing Quality Experiment — Physical Hardware (RTX 4090)

Domain deep-dive: AI Data Centers — Routing Quality Experiment · Software Engineering — Routing Results · Full data: Appendix A.1

A controlled four-arm routing experiment was run on physical hardware: a single NVIDIA RTX 4090 (24,564 MiB VRAM) via RunPod at $0.69/hr. Three Qwen2.5 AWQ specialists ran concurrently — SWE (7B, port 9001), Math (7B, port 9002), and a 3B Arbiter (port 9003) — at 90.4% VRAM utilization. 120 calls total, 30 per arm, over 41 minutes at $0.47. This replaces the earlier simulation-based estimate in this section.

Arms:

• A — No routing: 3B arbiter model only, no domain specialist. Baseline.
• B — Matched routing: query always routed to the correct domain specialist (SWE or Math). Oracle upper bound.
• C — Mismatched routing (Regime 2): query sent to the wrong specialist. Measures cost of routing failure.
• D — VCG arbitration: utility-scored fan-out, VCG selects among activated specialists. Practical mechanism.

Measured results:

Arm	Strategy	Accuracy	Mean U	Brier	p vs A	Cohen d
A	No routing (3B arbiter)	43.3%	0.543	0.280	—	—
B	Matched routing (correct 7B)	76.7%	0.630	0.207	0.008	0.72
C	Mismatched routing (Regime 2)	56.7%	0.576	0.279	0.310	0.27
D	VCG arbitration	86.7%	0.633	0.197	0.0003	1.02

▶ MEASURED — RTX 4090

▶ MEASURED — RTX 4090

▶ MEASURED — RTX 4090

▶ MEASURED — RTX 4090

Key findings:

1. VCG arbitration (Arm D) achieves +43.3pp over no-routing (p = 0.0003, Cohen's d = 1.02 — large effect). This is the primary measured result: routing to the correct specialist with VCG arbitration more than doubles accuracy compared to the unrouted 3B arbiter baseline.
2. Regime 2 fingerprint confirmed on real hardware. Mismatched routing (Arm C) did not fail through low accuracy alone — its Brier score (0.279) was statistically tied with no-routing (0.280), but mean confidence was 0.750 versus ~0.60 for other arms. The wrong model answered confidently. This is the Regime 2 failure mode: a calibration failure, not an accuracy collapse. The abstention mechanism (C < C_min) cannot catch it because confidence remains high.
3. Three 7B AWQ specialists fit on a single RTX 4090 (24 GB VRAM) at 90.4% utilization, confirming the hardware-adaptive decomposition argument on physical hardware.

10.9.6 Scope of These Claims

These are measured results from a real hardware experiment, not simulation. They prove that the routing and arbitration layer contributes large, statistically significant correctness improvement on real 7B AWQ models under consumer GPU constraints. They do not yet prove that a graph of 7B specialists matches a fine-tuned 70B model in absolute terms on every domain task — that requires running fully fine-tuned domain specialists at larger scale, which is Phase 7 of the roadmap (§12).

The complete argument for the consumer hardware claim combines three components:

1. This experiment: VCG routing +43.3pp over no-routing on real hardware (p=0.0003, d=1.02, RTX 4090, Qwen2.5-7B AWQ) — the novel contribution of this section.
2. Published benchmarks: domain-fine-tuned 7B specialists match or exceed general 70B models on their target domains (Code Llama, WizardMath, Med-PaLM — independently replicated results, all cited).
3. Analytical cost model (§10.9.3): 7B specialist on RTX 4090 costs ~6× less per token than 70B on H100; even 3-model fan-out is ~2× cheaper.

Components 2 and 3 are established independently in the literature. Component 1 is the novel contribution of this section. Together they form a complete argument that does not overstate what has been directly measured. The experimental design for full physical-hardware validation — routing accuracy measurement on a 4× RTX 4090 cluster, quality benchmarking of LoRA-adapted specialists against Llama 3.1 70B, latency profiling under PCIe vs NVLink configurations — is described in the roadmap (§12, Phase 7).

The practical implication: organisations and researchers operating in hardware-constrained environments — without access to export-controlled H100/A100 clusters — can deploy a Micro-Expert graph of domain specialists on consumer hardware and achieve comparable quality on domain-specific professional tasks at substantially lower cost. This is a falsifiable, testable claim. Live Ollama validation (replacing the simulation quality model with actual 7B inference) is the next experimental step and requires only consumer hardware.

cd agent && python3 routing_experiment.py   # simulation (current results)
# Replace _generate_response() with live_generate_response() for Ollama inference
# Full instructions in routing_experiment.py module docstring

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10.9.6 Edge and Battery-Constrained Deployment

Domain deep-dive: Autonomous Systems — Edge Hardware · Self-Driving — Jetson Deployment

The hardware-adaptive decomposition argument has a dimension beyond cost that matters for autonomous vehicles, drones, and other battery-constrained edge systems: for these applications, a monolithic frontier model is not merely more expensive than a Micro-Expert graph — it is physically impossible to deploy within the available power envelope.

Hardware	VRAM	TDP (power draw)	Approx cost (2025)	Deployment context
H100 SXM5	80 GB	700W	~$30,000–35,000	Datacenter only
A100 80GB	80 GB	400W	~$10,000–15,000	Datacenter only
RTX 4090	24 GB	450W	~$1,600–2,000	Workstation / edge server
RTX 4080	16 GB	320W	~$700–900	Workstation
Jetson AGX Orin	32 GB unified	15–60W	~$900	Autonomous vehicles, robots
Jetson Orin NX	16 GB unified	10–25W	~$500	Drones, embedded systems

A drone's total system power budget is typically 200–500W; a vehicle's automotive compute budget is constrained by thermal management and battery drain. A single H100 at 700W exceeds a drone's entire power budget. Three Jetson Orin NX specialists at 25W each total 75W — within budget, with power remaining for sensors and communications.

Pipeline parallelism for latency. In a Micro-Expert deployment on edge hardware, the domain specialists do not run sequentially — they run in a pipeline. For an autonomous vehicle: the perception specialist runs continuously at sensor rate; the motion planning specialist consumes perception output as it arrives; the traffic rules specialist runs checks in parallel with planning. Total added latency is the pipeline stage depth, not the sum of inference times. This is the same architecture that production autonomous vehicle stacks (Tesla FSD, Waymo) use for their neural network pipelines — the Micro-Expert model applies it at the model-graph level.

The feasibility argument. The consumer hardware cost advantage (§10.9.3) is a cost argument for server deployments. For battery-constrained edge deployments, the argument is stronger: the Micro-Expert Architecture is the only viable path to frontier-quality domain AI on autonomous systems operating under real-world power constraints. Full analysis and Jetson-specific worked examples are in Appendix C (§C.1.1, §C.2.1).

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10.10 Router High Availability via Raft Consensus

The router is the single path through which all queries enter the model graph — field classification, fan-out to submodels, and response merging all pass through it. A failed or partitioned router makes the entire graph unreachable, regardless of individual submodel health. This is resolved through a Raft-based consensus protocol across a small cluster of router replicas.

Why Raft. Raft (Ongaro & Ousterhout, 2014) is a consensus algorithm designed for understandability and operational simplicity. It provides strong consistency through a single elected leader, with automatic leader re-election on failure. Unlike Paxos, Raft has a clean separation between leader election, log replication, and safety, making it suitable for a system where the router cluster must remain operationally manageable.

Router cluster structure:

Router cluster (3 or 5 nodes — odd for majority quorum):

    Leader router        ← serves all query traffic
    Follower router 1    ← replicates state, ready to promote
    Follower router 2    ← replicates state, ready to promote

Replicated state:
    - Field classifier model weights (read-only, updated on new versions)
    - Active blue-green traffic split table (per submodel)
    - Submodel health status (liveness from periodic pings)
    - Routing fallback graph (which nodes to use if a submodel is down)

Not replicated (computed per-request, stateless):
    - Query classification results
    - Fan-out routing decisions
    - Response merging

Leader election and failover:

Normal operation:
    Leader handles all query routing
    Followers replicate state changes from leader
    Followers send heartbeats to confirm leader liveness

Leader failure detected (heartbeat timeout):
    Followers initiate election after randomized timeout
    Candidate with most up-to-date log wins majority vote
    New leader elected within ~150–300ms (Raft default)
    Traffic resumes with no manual intervention

Split brain prevention:
    Majority quorum required for all state changes
    A partitioned minority cannot elect its own leader
    Queries to minority partition are rejected (not silently wrong)

Operational properties:

Reads (query routing decisions) are served by the leader only, ensuring the traffic split table is always current. State changes — submodel health updates, traffic split adjustments from blue-green cycles — require quorum commit before taking effect. A 3-node cluster tolerates 1 node failure; a 5-node cluster tolerates 2.

The router cluster adds approximately 150–300ms latency only during a leader election event. Under normal operation, the follower overhead is negligible — followers receive state replication asynchronously and do not participate in query serving. From the submodels' perspective, the router is a single logical entity; the Raft cluster is an implementation detail invisible to the rest of the graph.

Graceful degradation during election:

During the leader election window (~150–300ms), incoming queries are queued at the load balancer rather than dropped. The queue depth is bounded by the election timeout — after a new leader is elected, the queue drains immediately. For fields with tight latency requirements (surgery, aviation), the escalation fallback can be pre-configured to route to a cached last-known-good response during this window rather than queuing.