Interpretation, External-Validity Limits, and Unmeasured Extensions

The connected GUM comparison in sec. 5.1 evaluates a fixed message schedule on a locally specified population. Its character-loss result does not remove closed-vocabulary word failure or identify the contribution of each channel. The historical component gates answer a different question.

For those gates, fig. 26 places every built level between its own trivial baseline and its own ceiling comparator on a single normalized axis, so a reader who has followed six level-specific results in six units can see in one place how far each shipped model went and what kind of comparator bounds that placement.

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Limitations that follow from deliberate architectural choices

Several limitations follow from deliberate architectural choices; stating them plainly is the price of those choices.

Not a competitive language model, and not comparable to subword perplexities

AILM has no embeddings, no attention, no learned continuous representations, and no capacity to generalize beyond discrete conditional tables. The perplexities in tbl. 9 and tbl. 12 are order-1 numbers over small inventories — not comparable to word-level or subword-level perplexities. Its named arrays make parameter roles accessible to inspection (sec. 7); the recursion, encoder and message schedule still determine how those roles combine into behavior. The experiments characterize this architecture’s limits, without estimating a general tradeoff between interpretability and language capability.

Historical component composition and current conditional coupling

The historical standalone levels compose by sharing an alphabet rather than passing beliefs. The current connected runtime does pass explicitly scheduled messages; its global posterior is not asserted to be exact, and its aggregate GUM comparison does not estimate individual channel effects. update_empirical_prior is within-level temporal recursion at every call site. Inter-level coupling was built and measured (L1→L2B, src/ailm/levels/coupling.py): accuracy fell monotonically as the mixing weight rose, with a significant harmful margin of -0.2639 points at the best positive weight on the recorded grid, alpha = 0.1 (paired McNemar p = 1.547e-06). Because the decline is monotone, that figure is the smallest harm the sweep contains rather than a summary of it. The harm is not marginal under exact uncertainty: the uncoupled decoder wins a 0.603291 share of the 547 discordant pairs, exact 95% interval [0.560912, 0.644548] (tbl. 36). The cause is structural: at position t the letter-to-phone level already observes letter t, while the message is a function of letters 0 to t-1 only.

First-order limits on orthographic and syllabic structure

The letter and phoneme levels are both first-order Markov. The letter level cannot represent orthographic constraints spanning >2 characters, and the phoneme level cannot represent syllable structure. The 89.9% figure is a large fraction of a small quantity.

The length-matched subset is not English

Results are measured on the length-matched subset of CMUdict (74.3% of pronunciations discarded), biased toward transparent orthography. No comparison with published G2P systems is made. The thin margin follows from the subset’s transparency — where the letter nearly determines the phone, context adds little. Two external-validity bounds follow. First, the family-disjoint arm of sec. 4.4 removes shared-prefix transfer but not lexically or morphologically grouped leakage more broadly. The existing held-out family-group analysis already measures heterogeneity within those prefix-defined groups (sec. 5). The remaining sensitivity check would assign train/test membership using independently defined morphological families, rather than treating shared prefixes as the family definition. Second, the task itself — equal-length position-aligned letter-to-phone decoding under a pairing the evaluation imposes — stops short of many-to-many grapheme-to-phoneme conversion over a full dictionary, the setting in which the classical G2P literature evaluates (e.g. Jiampojamarn et al. (2007)); no result here transfers to that setting without the alignment being learned rather than stipulated.

Filtering rather than smoothing, and what whole-word methods gain by it

The model’s online algorithm is forward filtering; its canonical full-set score is computed by the NumPy implementation after the bounded live-Agent check. Whole-word methods do substantially better on the same parameters — 75.642% for forward-backward smoothing and 75.306% for Viterbi, against 70.801% for filtering. The gap is reported rather than hidden precisely because the architecture forgoes it by construction.

Part A’s dictionary perplexity is in-sample, defended only by its parameter ratio

The dictionary perplexity in tbl. 12 is a descriptive in-sample protocol: the same primary pronunciations supply the counts that fit the transition matrix and the sufficient statistics that are scored. Its defense is the parameter-to-data ratio — 39 × 39 parameters from 800,198 positions, with the recorded protocol’s add-1 smoothing — not a holdout, so on its own it is not a generalization claim and is not comparable with Level 1’s held-out number as one.

The held-out word split converts that defense into a measurement. The Part A unigram and bigram are re-fit — inside the analysis code, from the pinned CMUdict snapshot, with the same recorded add-1 smoothing and per-word prior reset — on the 100,841 dictionary words that remain when a seedless stride holds out every 5th sorted word, the same interleave construction the letter-to-phone split uses one level down, and the identical closed-form path is scored on the disjoint 25,211 held-out words over 160,196 phone positions. The context-free bar is re-fit on the same training words, so model and bar share one fit and one denominator. Held out, the bigram agent scores 16.7665 against the bar’s 27.6027 — a margin of 0.4985 nats per position, essentially the whole in-sample advantage — at a generalization penalty of only 0.022 perplexity units above the in-sample 16.7445. The reading is bounded by a control on each side. A model fit on training phones re-dealt across word boundaries — the corpus unigram and word lengths preserved, every trace of order destroyed — does not beat the bar; its gap is -0.0013 nats, so the held-out margin is not available to a structure-free fit. And a model fit on the training words with each word’s phone order shuffled within the word still clears the bar, at 0.1443 nats against the honest margin’s 0.4985 — which says that a substantial part of the margin is available from which phones merely co-occur in a word, before any adjacency is used. The in-sample table remains the descriptive dictionary protocol; the held-out arm is the measurement behind the claim that Part A’s margin survives generalization.

Historical fast score paths and current live inference have different evidence

At Level 2B, infer_states is one call per observation. Its full-set statistics are computed by the NumPy oracle and attributed to pymdp through the bounded decoder-equivalence result (eq. 16). This is a constraint on that evaluation path, not a license to attribute every later exact or NumPy score to live inference. L3 uses an exact path identity, L4 a NumPy filter that the live recursion reproduces at every held-out position, L5 a closed-form mixture with a live posterior-agreement check that is not score equivalence, and L6 separates its registered observed-position score from a descriptive live sequential score. The connected GUM evaluation instead executes live agents on its full declared population using compiled calls. That later execution does not retroactively extend the historical decoder-equivalence checks or equate their estimands with the normalized-character result.

Decoder equivalence is bounded, and licenses nothing outside its subset

Decoder equivalence is tested on a bounded subset (13,224 of 42,820 held-out positions; 0 disagreements on the checked positions); the recorder refuses to proceed if nonzero. A finite test cannot establish that two implementations are the same function, so the result licenses no statement about positions outside the subset, and full-set attribution to pymdp remains an extrapolation from the checked ones. Proving equality would take an algebraic derivation over the two call sequences or a full-population comparison; neither is done (sec. 4.11).

The UD case oracle is a research claim, not ground truth

Only NOM, ACC and GEN carry morphological marking in English EWT — 3 of the 8 roles. The remaining 5 — DAT, INS, LOC, ABL and VOC — are derived from dependency relations, a principled heuristic that this project has not validated. Agreement with it is agreement, not accuracy.

Unresolved component verdicts and the speech interface boundary

The clause level’s case-only ablation is non-passing at bigram order over punctuation-typed sentences (decision 83). Its privileged-label reference has a negative point estimate, its paired whole-document-bootstrap interval spans zero, and no equivalence margin was declared. The canonical clause level, on the widened observation alphabet, clears its registered bar. But what it clears is a development-session specification with no held-back replication, so it does not close the question that ablation leaves open. The document-position (tercile) level — narrative in code — has a positive point estimate, in its preregistered direction, of 0.0051 nats per sentence, whose primary document-clustered log-loss interval spans zero on the development population. The same estimand, registered separately and carried to the held-back split, gives 0.008288 nats with an interval that excludes zero (sec. 5.8.2). So the level is no longer a case of a positive point estimate with nothing behind it. Three limits keep it from being more than that. The two populations disagree. The development one is not retracted. At the family-corrected coverage the held-back interval spans zero too. So the resolution is a claim at the level the development analysis was read at, not at the stricter one. The held-back population’s own resolution, 0.005726 nats, is coarser than the development-sized effect. So what was demonstrated is that a larger effect is present there, not that this effect size generalizes. A null there would not establish absence of the development-sized effect. The development-population sentence-sign statistic remains secondary: it crosses neither the fixed Bonferroni threshold nor its Holm step-down threshold. Even reversed tercile columns with worse mean loss can yield a nominally favorable sign (sec. 15.2). That is exactly why the held-back sign test was not allowed to stand in for the interval. A separate live-Agent filter is descriptive, not a replacement for that primary analysis. The independent L6→L5 prior intervention moves the receiver’s D. The case-only clause arm’s privileged-label reference has an unresolved gain and is not a hard bound; that arm is the receiver the intervention was measured into. The speech level is deliberately not a model at all: the boundary contract (docs/design/speech_boundary.md) is tested, while everything acoustic remains someone else’s system.

The familywise survivor sets are smaller than the nominal set

The declared significance family (sec. 15.2) has 16 members and 7 survivors at the fixed Bonferroni threshold 0.000625, 7 under Holm’s step-down correction at the same familywise level. The four headline paired results — Stage 2B letter-to-phone, Stage 4 derived, the lexical channel, and the coupling harm — survive both. The secondary Stage 6 sentence-sign test crosses neither the fixed Bonferroni threshold nor its Holm step-down threshold (stat_stage6_familywise_confirmed = false, stat_holm_stage6_rejected = false), and one survivor, subsample_prefix_mcnemar_p, is significant only because it measures a biased subsample (sec. 10.1). Multiplicity correction bounds the survivor set; it does not rank the science. A further boundary none of these corrections touches: every gate here is a placement audit against a threshold. Each audited gate now declares a smallest effect size of interest, and the audit reads the gate’s margin against it (decision 123), so a hairline margin is displayed as such rather than silently certified. The declared margins are floors attached after the fact for the retrospective rows — they change no recorded verdict — and the uncertainty reporting remains what carries the finding where a recorded margin sits near its floor; a gate registered from now on must declare its margin before measurement (sec. 4.2).

Two conditions that bound every one of those verdicts are stated in sec. 15.2 rather than here, because they qualify the results before the reader reaches them rather than afterwards: the paired tests are computed at units nested inside the units their corpora sample, and the family was assembled retrospectively on the population this project developed against. This entry adds nothing to either. It records only the arithmetic consequence — that the survivor set is smaller than the nominal one, and that neither set is a set of confirmed effects.

The calibration gate was a proxy, and the proxy was not conservative

Calibration was the one axis on which AILM and the external probes looked directly commensurable (sec. 13), and it was originally reported only for a system whose answer-slot distribution was at least 0.5 observed rather than reconstructed. That captured-mass floor stood in for the quantity that actually matters — whether the completion rule rather than the model decides the reported number — and it was declared on an argument rather than measured. It has since been measured, offline and with no model call. Truncating AILM’s own letter columns to 96 target captured masses and reconstructing each under both completion rules, the shipped min-bound rule and observed-only renormalization, puts the smallest captured mass above which neither expected calibration error nor the Brier score again disagrees by more than 0.01 at 0.9913050462092039, which is 1.9826100924184078 times the declared floor. The declared floor is permissive, not conservative: at 0.5009002481860143 captured mass the two rules still report expected calibration errors 0.027279486311722168 apart, against AILM’s whole recorded value of 0.06525983583459523.

That located value depends on requiring a sustained crossing rather than a first one. Each metric’s divergence crosses zero exactly once on the way up, at 0.46163474055756576 and 0.4955158182362678 captured mass — essentially at the declared floor — while the two reconstructions are still 0.8852931589225496 apart in total variation. A locator that stopped at the first crossing would have confirmed the declared floor on a coincidence of opposite biases.

The conservative threshold is also unreachable through the API these probes are served by. Holding 0.9913050462092039 captured mass takes 19.205 of 30 candidates on average against a server cap of 20, and 0.395 of positions need more than the cap. It is out of reach in principle for any probe read through this endpoint, not an unmet bar that more positions would clear.

The gate is therefore no longer the proxy. It is the direct check of the two completion rules against each other on each probe’s own recorded distribution (decision 93): a system whose expected calibration error or Brier score moves by more than 0.01 between rules is withheld. Under that gate Qwen 2.5 3B reports and Gemma 3 4B is withheld — its recorded divergences are 0.012740862022979305 in expected calibration error and 0.012133730087630523 in Brier score — although the captured-mass floor had admitted it at 0.8610770659256101 captured mass; SmolLM 1.7B Base v0.2 is withheld by both rules. The withheld figures remain in the ledger, and the values in sec. 13 are the gate-admitted ones.

The case the proxy could not see is the one the direct check exists for: a probe whose reported distribution is as flat as AILM’s own could clear the declared floor and still sit where the two rules disagree materially, so that its reported calibration would be a property of the completion rule rather than of the model. The direct check flags exactly that, which is why the proxy was retired from gating. The floor constant is retained as provenance for the starved-fraction diagnostic and the floor-locating sweep above, not as an admission rule.

The gate-audit method generalizes only as a working hypothesis

sec. 9 expects the bracketing check to generalize past this project and past active inference, and names the method among the most transferable results here. That claim carries the working hypothesis label of sec. 2 and no stronger one: it organizes the design and is bounded by the evidence that produced it. That evidence is every declared gate of a single repository (tbl. 22, tbl. 27), declared and audited by the same author. The recorded failure modes are varied enough — unreachable, vacuous, both at once, mis-scoped, necessary-but-not-sufficient — to establish that the defect class is real and cheap to detect. They are not a sample from which a base rate follows, and nothing here tests whether the check catches defects in gates whose author did not also write them.

Corpus and language boundaries remain specific to each result

The letter and phoneme results use Brown and CMUdict statistics vendored as frozen JavaScript Object Notation (JSON) artifacts. The EWT experiments, exploratory Czech morphology arm and connected GUM comparison add distinct populations, not blanket evidence for other registers, languages or pronunciation dictionaries. The normalization choices — collapsing whitespace, keeping only the primary pronunciation, discarding stress digits — each bias the counts in ways that were chosen for defensible reasons and not independently validated. GUM’s multilayer corpus design provides a resource for examining linguistic structure (Zeldes 2017), but the present raw-text comparison does not evaluate its discourse annotations or establish transfer across genres. Its document average and interval describe the frozen scored population; they leave performance on unexamined registers and independently collected documents open.

Adaptive observation selection was measured, does not pay, and is not built

One extension this architecture invites is budgeted attention: given a budget of observations for a word, choose which letters to look at by expected free energy rather than on a fixed schedule. It was measured rather than assumed, and it does not pay, so it is not built.

This arm is the exact complement of the generation regime in sec. 4.9, and the two are best read together. There the information-gain term is identically zero and the preference term carries the whole policy; here there is no preference term and the information-gain term is the sole criterion, each candidate position scored by the posterior entropy it is expected to leave. So the two components of the expected free energy have each been measured in isolation in this project, in the only two places its architecture admits them, and the one that carries the work is the pragmatic one.

The bar is the exhaustively optimal fixed schedule per word length and budget, fitted on the training split — for each shape, the observation set maximizing training accuracy, searched over every subset rather than approximated. That bar uses no inference at decode time and is strictly less data-dependent than the policy it is bounding. Over the held-out letter-to-phone positions at a 50% budget it scores 50.0381% against the adaptive arm’s 48.9549%, a loss of 1.0832 points for adaptivity. The comparison the proposal originally invited, against a “uniform stride”, is not a comparison at all: the stride’s phase is an unstated free parameter worth up to 12.3129 points across phases at one word length, which is larger than any margin at issue.

Two details of how that number was obtained belong here rather than in a methods appendix, because both are ways the measurement could have come out wrong in this paper’s favor. A policy may only use what it has already observed, so a candidate position is scored by the entropy it is expected to leave, marginalizing over the letters it might reveal under the model’s own predictive distribution. Scoring it instead by the entropy left after conditioning on the letter actually present returns +3.90 points for adaptivity — but that is not a policy, since it consumes the observation to decide whether to pay for it, and the budget it operates under is fictional. That variant is retained in the probe as a declared upper bound; it sits 4.987 points above the policy that can actually be run.

Zero epistemic value in the deterministic letter generator

Policy selection at the letter level (sec. 4.9) is driven entirely by the pragmatic term of the expected free energy: the preference vector supplied top-down by the lexicon (sec. 4.9), combined with the habit prior from the learned bigram. The information-gain term is 0 nats — identically zero rather than approximately zero. The cause is structural: the generator’s transition is deterministic and controllable, so the policy-conditioned predictive distribution is a point mass and carries no residual uncertainty the next observation could resolve. A stochastic-transition control confirms the quantity can be nonzero; it reaches 3.401197 nats, the entropy of a uniform letter distribution. AILM’s letter generator therefore cannot trade off exploration against exploitation: it selects letters because the lexicon wants them and habit expects them, not because any letter would say more about the hidden state than another. Whether that is a limitation depends on what the hidden state is. If it is the emitted prefix — which is the case in the shipped generator — then no letter is more informative than another and the zero is correct. The alternative construction — a word-identity hidden state over the lexicon — was built and measured (sec. 4.9). Its information gain is 2.716363 nats at the empty prefix, yet because emitting a letter never changes which word is being spelled, every action induces the same predictive distribution: the per-action spread of \(G\) is exactly 0 and the policy posterior stays on the habit to a maximum deviation of 1.11e-16. Uncertainty in the hidden state is necessary but not sufficient; the epistemic term bears on action only where actions induce different predictives, which over a fixed word is interrogation, not generation. The budgeted-attention arm above is that regime, and it does not pay.

Stratificational alternatives beyond the widened arm

The widened arm produces the number that makes a choice informed; it does not make the choice, and the choice it forces is the load-bearing one. A stream containing verb and auxiliary symbols is no longer Level 4’s hidden states read one level down, unless Level 4’s own state space is widened to match — which would move every Stage 4 number and contradict the stratificational reading the hierarchy rests on. The alternative, letting Level 5 observe Level 4’s states plus material Level 4 does not represent, abandons the one-level-down claim outright. Both branches remain live after this measurement, and nothing here selects between them. Making the widened arm the canonical clause level does not select between them either. It settles which arm the paper describes, and it takes the second branch as a matter of description while leaving the stratificational reading unrepaired, which is why the alphabet seam from Level 4 to Level 5 is stated as a containment rather than an identity in sec. 4.1 and why the case-only arm, whose seam is a true identity, is retained rather than discarded. What the measurement establishes is the size of what is at stake: the positions occupied by verbs and auxiliaries carry a type signal that the case-only projection does not see, worth 54.95% of the available entropy against the case-only arm’s unresolved gain.

Two further limits. The arm shows that those positions carry the signal, not why. Auxiliary fronting is the obvious account and is untested here; the first-symbol-is-an-auxiliary comparator bounds how much a single fronting indicator reproduces on its own, at 0.7543 against the model’s 0.8908, which is a bound on one rival explanation rather than a test of the mechanism. And the arm is descriptive throughout. It was specified before its artifact was regenerated and its predictions were not revised afterwards, but the specification and the outcome share one development session, so it carries the weight of a well-run exploratory result and not that of a confirmed one.

Scope of the held-back replication

What the replication of sec. 10.6 changes is narrow and worth stating precisely. Two of the 16 family members rest on a population that was fixed before the prediction was written and scored once under a registered rule, and two more were put to that test and returned no discordance. That is the difference between a result and a corrected-threshold survivor of a retrospectively assembled family, and it is available for exactly 4 members because only those had a held-back partition left: the eight lexicon members were exhausted, since upstream CMUdict has not moved since the vendored pin, and the four split diagnostics are re-analyses of a shipped subsample with nothing to replicate on fresh data. The twelve unrescored members are unchanged, and calling the paper confirmed would misread this.

The two members that did cross also differ in what they buy. Stage 4’s derived comparison already survived the frozen correction on the development population; its replication supplies held-back evidence for that survivor. Stage 6’s crossing adds evidence where the development run did not cross. The registration predicted the crossing on sample size alone, but the observed effect estimates also differ across splits. The crossing corroborates the registered direction; it does not establish a stable effect size or identify how much of the smaller p-value comes from the larger population. The case-only clause arm’s replicated null is the most useful result of the four for a reader deciding what to build on: an observation alphabet that fails on its development split and fails again, with zero discordance, on several times the data, against a live instrument, is not an alphabet awaiting more data. It is the one that was awaiting a different alphabet, and the widened arm of sec. 5.7.3 is what happened when it got one. That contrast is also the sharpest available statement of what the promotion does and does not buy: the widened result rests on a registered bar, the null it displaced rests on a held-back partition, and no single arm here has both.

Future Tests of Model Scope, Human Auditability, and Hybrid Composition

Everything below is a proposal, not a result. Where an item is already partly built, registered, or measured, the text says so; no item here licenses a claim about what a future run would find. Where a design choice is already fixed by a principal decision or a rejected alternative, that fact is stated so a reader does not mistake an open question for a settled one.

Richer State Dynamics, Wider Linguistic Coverage, and Cross-Framework Checks

A separate next test concerns the reader, rather than the model’s predictive score. The human-evaluation proposal in sec. 7 would assess whether named parameters and a trace of the recursion help readers diagnose a defect or anticipate an intervention. Such a study would need its own participants, comparison interface and prospective success criterion. Conformance tests and a functioning dashboard do not supply that evidence (Doshi-Velez and Kim 2017).

The open Major items already carried in TODO.md are the nearest and most concrete of these: equal opportunity to fit the task, the aligned-pronunciation zero-shot arms, and the end-to-end top-down cascade’s performance claim. None of them is a fresh idea. Each has an unadopted design written down in docs/extension_protocols.md, and each design is partially landed rather than merely sketched. Protocol P1’s offline data and identity foundation — the streaming census objective, the diagnostic carve, the separate fitted-probe registry, the stride-aliasing refutation — is built and fixture-tested, and its warm-up compute gate has been measured and found not to clear the census budget at the observed rate (decision 122); what remains is the fit pipeline itself, gated on the external model infrastructure the protocol assigns to its own implementation grant. Protocol P2’s stipulated pair-structured artifact and offline evaluator are built, its comparator arm is recorded offline, and its zero-shot probe arms are recorded: both scoring arms fall far below the analytic contract floor and the third probe is recorded as a contract refusal, so the arm closes by refusal rather than ranking (sec. 13). Protocol P3’s label-construction and split account, its registry entries, and its L3 inlet and executor are built, and its influence sweep is recorded (decision 121, an exploratory prior-only sweep on the development population); what remains, by the protocol’s own three-layer separation, is a performance claim under its own population, comparator, controls, and uncertainty analysis — deliberately the last of the protocols to be attempted, because it is the one whose cost is largest and whose value is least certain.

The connected schedule is now executed and evaluated on the locally frozen GUM population in sec. 5.1. Its next empirical steps are independent replication, coverage expansion and attribution of the aggregate result to particular channels; those steps remain unmeasured. The channels this project has already run disagree in sign on that question, which is the whole point of running them rather than arguing for them: the L3→L2B lexical channel and the independent oracle→L3 word-prior intervention both help their receivers, the L1→L2B coupling channel harms its receiver, and the case-word bridge has exploratory prior-only sweep evidence on the development population, while its privileged-oracle diagnostic remains structural (sec. 5.10.4). Attributing the connected gain to a particular channel requires further registered receiver interventions, each with its own zero-weight anchor, negative control and accounting of whether the expected direction preceded the measurement. The existing whole-configuration comparison is not that attribution, and neither result would declare the hierarchy complete.

Learning of parameters within Active Inference has already been probed at its boundary rather than left untried, and the next step should be read against that boundary rather than around it. Observed-state conjugate counting under pymdp’s own parameter-learning machinery reproduces the shipped counted matrices exactly, which is a correctness anchor rather than a capability (decision 22). Continuing those same updates online, on a stream whose statistics are made to drift partway through, does recover a measured, predicted-in-advance improvement over a matrix frozen before the drift — the one regime in which online learning has been shown to earn its place over not learning (decision 28). But in the one place a hidden state had to be inferred before the parameter update could use it — the G2P emission, whose phone states are never observed — the learned matrix was measured to be worse than counting the same data, with an observed-state control confirming the learning machinery itself was sound and the harm traceable to the latent-state inference (decision 29). A future attempt at parameter learning within this architecture should say in advance which of those two regimes it is in, rather than repeating the optimism this project’s own earlier documentation stated before decision 22 first measured the boundary.

Larger lexica and other languages remain almost entirely untried. The one non-English population this project has scored is the exploratory Czech case arm, built by reusing the English case-level builders unmodified against UD Czech-PDTC and reporting raw accuracy against morphological ground truth rather than agreement with a derived oracle, because Czech is the one population where that ground truth exists. That arm is also where the boundary of the approach shows most plainly: Czech’s own case inventory omits a role English case grammar carries, and several of Czech’s roles are marked directly on the word in a way English morphology does not supply, so the arm is not a template that generalizes by relabeling — it is a demonstration that extending to a new language means building that language’s own oracle, vendoring and checksumming that language’s own corpus, and stating that language’s own boundary, not rescaling the English numbers. The fixed default vocabulary at the word level is a separate, already-declined axis of scaling: a principal decision keeps it at its shipped size because the scaling ladder already publishes every rung through a closed form exact at any vocabulary size, so raising it buys no science, only a re-record. A larger lexicon or a second language is future work exactly to the extent that it is willing to pay for its own oracle and its own disclosed boundary, not to the extent that it reuses this project’s counts under a new label.

Finally, every shipped level’s GNN declaration already carries the ontology-annotated structure that a conformance checker reads — the same declaration a hand-written builder and ailm.spec_agent.build_agent_from_spec both construct an agent from, checked to match in shape, dtype, and bytes. What this project has deliberately not done is run those same declarations through the upstream GeneralizedNotationNotation project’s own generation pipeline, which independently renders a spec to RxInfer and ActiveInference.jl in addition to PyMDP — AILM keeps its local construction paths and does not adopt that pipeline. Rendering the shipped specs through it and comparing the resulting agent’s filtering output against AILM’s own, on the same held-out positions, would be a cross-implementation check in the same spirit as the pymdp-versus-independent-oracle agreement checks that already license every exact and NumPy score path in this paper (sec. 4.11) — except across frameworks maintained by different people, rather than within the one repository this project controls.

Declared Parameters and Learned Representations as Distinct Evaluation Targets

AILM and a transformer-based large language model are not competing answers to the same question, and stating the differences precisely is what makes that claim more than a disclaimer.

AILM’s probability and preference arrays have declared roles and axes checked against the live agent by the GNN conformance guard; habits and policy precision have separately named settings (sec. 4.1); a transformer’s parameters are weights distributed across attention and feed-forward blocks learned end to end by gradient descent (Vaswani et al. 2017), with no declared role for any individual weight. The consequence is asymmetric epistemic access. AILM’s semantic addressability is designed in: the ontology block names what a matrix means before it is measured. A transformer’s internal structure is instead the subject of mechanistic interpretability, a field that exists precisely because that structure is not declared and must be reverse-engineered from a trained network after the fact, circuit by circuit (Olah et al. 2020; Elhage et al. 2021). AILM’s guard would have nothing to check without the declaration; interpretability’s methods would have nothing to interpret without a network that hides its own organization.

Each component uses first-order transitions over its hidden state. That does not limit a filtered belief to the preceding observed symbol: recursive beliefs summarize earlier observations, the word posterior carries a within-word prefix, and the connected schedule carries messages across its declared reset clocks. These fixed finite-state summaries differ from learned attention across an input context. Component HMM correspondences are scoped in sec. 7; no global HMM equivalence is asserted for the connected runtime. A single-writer claims ledger binds reported values to their runs (sec. 8). The external probes do align bounded next-symbol units and positions, but their unequal training opportunities, prompting contracts and contamination exposure prevent those contrasts from establishing general competitiveness (sec. 13). Parameter-level auditability and broad language capability are different evaluation targets. Recent theoretical work argues in the same direction from the side of prediction and action: a system optimized to passively predict the next token and a system whose inference is coupled to acting on the world answer different questions about meaning, and the productive move is treating them as complementary resources rather than substitutes for one another (Pezzulo et al. 2024). Nothing in this paper measures that argument; it is cited here as the framing the compositions below take for granted.

Proposed Tool and Observation Channels Between AILM and Language Models

Compositions in both directions are sketched below, plus the discipline either one would have to satisfy to be worth building rather than merely demonstrating. Neither direction has been built, and no result about either is claimed.

An LLM calling AILM as an auditable tool. An agent built in the style of self-taught tool use (Schick et al. 2023) or interleaved reasoning and acting (Yao et al. 2023) could delegate a bounded subtask — letter-to-phone decoding, case-role inference, or a run of the gate-audit method itself (sec. 4.2) — to AILM as a callable tool, and receive back not only an answer but the posterior and the provenance chain the claims ledger already attaches to every number in this paper (sec. 8). The point of the composition, if it is worth building, is that the tool’s output would be checkable by the same mechanism a human reader of this paper already uses, rather than trusted because a well-audited tool produced it. What would make this falsifiable rather than a demonstration: a target the calling model cannot see held out in advance, with the composed answer scored against that held-out target and not against AILM’s own prediction of it.

AILM calling an LLM. The designs below are proposals only. First, an LLM’s output could be declared as a new observation modality with its own explicitly measured likelihood matrix inside a GNN spec — the same kind of typed declaration every shipped level already carries and the conformance guard already checks (sec. 4.1), fit and audited like any other emission rather than assumed useful because the source is a large model. Second, an LLM’s output could be treated as a proposal distribution mixed into a receiving level’s prior or preference, registered and measured exactly as the existing channels are: a weighted mixture with a bit-identical zero-weight anchor, a scrambled or shuffled negative control, and a document-clustered interval, reusing the apparatus P3’s case-word bridge already specifies (Protocol P3 bridge account) rather than inventing a new one. Read against work that already translates natural language into a probabilistic substrate for inference (Wong et al. 2023), the second design is the same move made in the other direction: instead of a language model translating language into a program that a probabilistic system executes, a probabilistic system here would be treating a language model’s output as one more typed input whose influence on the receiver is measured, not assumed.

Either direction inherits a discipline this project already learned the hard way. It has already rejected one shape of this composition outright: supplying AILM’s own fitted column to an external probe as the probe’s input, then scoring the probe against a target AILM itself produced, so that AILM becomes the probe’s ceiling by construction and any reported margin certifies the leak instead of catching it (TODO.md, “Rejected, with reasons”). Every proposal above is written to avoid that shape by the same means Protocol P1 already draws the line for the fitted-probe design (Protocol P1 fit/evaluation boundary): the evaluation target is held out and independent of whichever system sent the message, the effect is measured at the receiver rather than assumed from the sender’s identity, and no arm scores a system against its own prediction. The channels already in this paper follow exactly that rule — the sign of a message is something this project has measured at the receiver in both directions, not something it has ever been willing to assume from the sender (sec. 4.10) — and either an LLM-to-AILM or an AILM-to-LLM channel would be required to earn its sign the same way.

The gate-audit method applied to LLM evaluation claims. This paper already states, as a working hypothesis rather than a demonstrated one, that the gate-audit method — measure what a trivial baseline scores and what an achievable ceiling allows before accepting any threshold in between — should generalize past this project and past active inference to any staged or gated build whose progress is defined by a numeric criterion. A published LLM benchmark claim is exactly that shape of object: an accuracy or a leaderboard score judged against a threshold whose own trivial floor and achievable ceiling are usually neither stated nor measured. The calibration gate in this paper is the nearest worked example of what that audit looks like in practice: a declared floor, defended by argument rather than measurement, was found — once actually measured — to sit well short of where the two completion rules it was meant to distinguish still disagreed materially (sec. 6.1). Applying the same discipline to a published LLM evaluation claim would mean measuring, rather than accepting, where its own threshold sits relative to a trivial baseline and an achievable ceiling before treating a model’s clearing of that threshold as informative — the same question this project was willing to ask of its own gates, turned outward.

Generative Artificial Intelligence Integration: Predictions That a Hybrid Must Earn

The next integration study should test a declared division of labor rather than add an LLM and infer that the result is more cognitive. Generative artificial intelligence (AI) would remain an external predictor or tool caller; AILM would retain its explicit discrete state contract, GNN specification and pymdp inference. Tool-use work (Schick et al. 2023; Yao et al. 2023) and the hybrid reading model of Donnarumma et al. (2025) motivate this separation, but do not validate an AILM hybrid.

Our proposed tool-use prediction is that a frozen LLM given access to AILM will improve held-out correctness on bounded phoneme or role-inference tasks relative to the same LLM without the tool, under a matched inference budget. The comparison would fix the model version, prompts, decoding rules, tool schema and independently labeled evaluation targets before measurement. Matched-output sham tools and shuffled AILM messages would test whether any gain comes from informative tool content rather than extra tokens or an additional opportunity to answer. Tool refusals, invalid outputs and call costs would be scored explicitly. A demonstration of fluent explanations would not count as success, and self-reported confidence would not be substituted for measured calibration.

Our proposed receiver-side prediction is that an independently fitted, task-relevant LLM message will lower AILM’s proper predictive loss relative to the same receiver with that message disabled. The message would enter a named observation or prior interface; observation evidence and preferences would remain separate experimental arms. The fit split would determine the mapping and mixing rule. A bit-identical zero-weight anchor, shuffled messages and a same-budget non-LLM predictor would distinguish useful information from an advantage supplied by additional fitting. The primary analysis would be paired on independently held-out documents, with uncertainty reported at the document level. No gain, or gain retained under shuffled messages, would reject the claimed benefit of that interface. These predictions concern specified tasks; they do not forecast general conversational competence or preserve the current paper’s gate verdicts for a modified system.

Biometrics: Testing Linguistic Beliefs Against Human Measurements

Here biometrics means behavioral and physiological measurements during language tasks, not a claim that the current system measures a person’s cognitive state. A proposed reading study would align model predictions with fixation durations, regressions and pupil responses. Expectation-based comprehension motivates testing surprisal against processing difficulty (Hale 2001; Levy 2008), while pupillometry requires controls for illumination, gaze and arousal as well as task demand (Mathôt 2018).

Our proposed behavioral prediction is that greater pre-observation surprisal will predict longer first-pass reading times on independently held-out items. Our proposed pupil prediction is that larger model-predicted belief revisions will accompany larger task-evoked pupil responses after the nuisance controls are applied. These are hypotheses to register, not associations already observed in AILM. Surprisal, posterior uncertainty and belief revision would be specified as distinct predictors rather than selected interchangeably after seeing the data. Each predictor would identify its originating model level and conditioning history; the stimulus population, finite-score requirement and treatment of out-of-vocabulary items would be fixed in advance. Lexical frequency, word length, preceding-word effects, luminance, gaze position and baseline pupil size would enter the predefined comparison; time-shifted model traces would provide a negative control for spurious temporal alignment. Participant and item dependence would be modeled, with evaluation on held-out participants and items. The stronger cognitive claim would require predictive value beyond both simple lexical baselines and a frozen LLM predictor, not a correlation considered alone.

Electroencephalography (EEG) and event-related potentials (ERPs) offer a separate possible extension. The N400 component is sensitive to meaning-related processing (Kutas and Federmeier 2011), but the current phoneme, syntactic-role and document-position states are not validated semantic representations. A study targeting that response would therefore first need an independently justified meaning-sensitive task and an explicit extension of the state contract; it cannot obtain a semantic neural explanation by relabeling an existing state. Any such study would need its own consent, measurement and analysis protocol. Failure to generalize beyond the baseline predictors would count against the proposed model-to-measurement bridge, not invite a reinterpretation of the biometric measure as proof of active inference.

Cognitive Linguistics: Interventions on Role, Construction and Context

Case grammar and constructionist accounts offer different hypotheses about how linguistic form relates to participant roles and learned generalizations (Fillmore 1968; Goldberg 2006). AILM should test those distinctions rather than treat its present case inventory as a settled theory. A candidate extension would declare which role or construction distinctions are represented, then evaluate independently annotated minimal contrasts in argument structure, word order and contextual disambiguation. Grammatical case, semantic participant role and CEREBRUM model-functional role would remain separate annotation and state inventories.

Our proposed structural prediction is that a correctly aligned role- or construction-sensitive representation will improve held-out disambiguation over an otherwise identical receiver whose incoming observation-to-role or message-to-role correspondence is scrambled after fitting, while its learned arrays and evaluation labels remain fixed. This breaks the informative mapping; a coordinated permutation of all state axes would merely rename the states and is not a negative control. The comparator would retain the same lexical information and parameter budget, so an advantage cannot be credited simply to a larger state space. Independent annotations and human interpretation judgments would provide targets outside the features the model observes; derived-label agreement alone would not test the semantic hypothesis. Cross-linguistic work would use each language’s own state contract and overt morphology where available, with constructions held out to distinguish generalization from lexical memorization. A null effect with live controls would reject the chosen inventory or channel claim. It would not warrant replacing the target after development.

The proposed sequence is to validate the external interfaces and offline hybrid comparisons before undertaking human measurement studies. Each project would freeze its population, observation access, primary outcome, direction of the prediction, comparison family and failure criteria before its first evaluation data touch (Nosek et al. 2018). Model or protocol changes after that point would start a new exploratory record. This agenda specifies what would make the next claims worth believing; it supplies no new empirical result, human validation, paid-model acquisition or commitment to clinical deployment.