Are There Different Routes to a Delusion? A Mechanistic Framework for Convergent Psychosis

1. The Clinical Problem: One Symptom, Different Diseases

The relevant clinical observation is not that these patients are indistinguishable. Age, medication exposure, obstetric context, cognitive status, laboratory abnormalities, and neurologic findings may readily separate them. The narrower point is that the delusional belief itself may not disclose its biological origin. A fixed conviction can be comparably compelling when it arises from a developmental psychiatric disorder, an exogenous medication, a reproductive transition, a degenerative disease, or a metabolic disturbance. Phenomenology remains clinically informative, but it is not a unique marker of mechanism.

This distinction has practical consequences. Symptom form contributes to psychiatric diagnosis: thought broadcasting strongly suggests psychosis, Capgras syndrome implicates disturbances of familiarity or identification, and mood congruence can shape the differential diagnosis. Yet similar delusional phenomena may occupy very different positions in causal chains. A delusion may reflect a transient state disturbance in an otherwise intact circuit, the expression of architecture altered years earlier, progressive synaptic loss, or a biochemical process that temporarily fixes a comparator at an abnormal value. A mechanistic account must therefore explain convergence without obscuring clinically important differences in cause and course.

Five cases illustrate the problem. A 19-year-old man believes that his thoughts are being broadcast. A 55-year-old woman receiving 80 mg of prednisone believes that nursing staff are recording her. A woman 3 days after an uncomplicated delivery believes that her infant has been substituted. A 78-year-old man with Alzheimer's disease believes that his wife is an imposter. A 42-year-old woman with pyridoxine-responsive homocystinuria believes that her parents are imposters (Rahman & Cole, 2014).

Each patient presents with a fixed conviction that resists counterevidence; in the homocystinuria case, the patient maintained that her parents were imposters while they were physically present in her hospital room. Yet the expected courses differ substantially: some episodes remit completely, schizophrenia often persists, and Alzheimer disease progresses. The intensity or fixity of the belief therefore does not, by itself, specify the underlying biological process.

The question is how mechanistically distinct perturbations can converge on a shared delusional endpoint while carrying different prognoses. The proposed answer is that convergence follows from conjunctive dependence. If successful execution requires several jointly necessary components, sufficiently severe impairment of any one can produce failure of the same output. The output identifies that the system failed; it does not identify which required component was limiting.

This claim is meaningful only if the components are defined independently of the clinical examples. Section 2 therefore specifies each term by an operational test, anchors the assignments in previously described biological systems, and defines candidate molecular and circuit-level implementations before applying the framework to psychosis.

A second distinction concerns execution versus encoding. Learning and memory require both the momentary use of a neural system and the durable modification of the substrate that will be available later. A disturbance of current execution can therefore be profound yet reversible, whereas an error in durable encoding can alter future behavior after the initiating state has resolved.

Delusions frequently manifest across medical and psychiatric conditions with starkly contrasting etiologies—ranging from neurodegenerative disease and metabolic encephalopathy to medication-induced states, postpartum transitions, and schizophrenia. This clinical convergence creates a fundamental diagnostic challenge: because identical phenomenological features can stem from entirely different biological origins, the presence of a delusion alone offers limited guidance regarding underlying mechanisms or clinical prognosis. To address this gap, this article examines five distinct routes to a fixed false belief using the framework. By treating biological execution as a conjunctive system dependent on architecture, drive, context, and a permissive gating phase (Φ), this mechanistic model aims to clarify how diverse systemic failures can produce a shared clinical endpoint while carrying vastly different long-term trajectories.

2. The ARCH × Φ Framework: Four Conditions for Biological Execution

The framework is most simply understood as a model of jointly necessary conditions. Walking, for example, requires an intact musculoskeletal apparatus, sufficient motor drive, appropriate sensory context, and a physiological state that permits movement. Severe failure of any one requirement can prevent walking, although the causes differ. Observing that a patient cannot walk does not by itself distinguish paralysis, fracture, impaired consciousness, or environmental constraint. ARCH × Φ applies the same logic to biological execution.

This differs from an additive risk model. Additive models are useful for epidemiologic prediction, but they permit compensation: a low value in one variable may be offset by a high value in another. In a conjunctive system, compensation becomes limited when a required component approaches failure. The equation is therefore not intended to imply that every biological process is literally governed by four scalar quantities. It is a compact representation of the claim that several classes of condition must be simultaneously available for execution to occur.

The ARCH × Φ framework represents biological execution as the conjunction of four factors whose product must exceed a threshold (Rahman, Zorumski & Meloy, 2025; Rahman & Zorumski, 2026):

R = Φ · (A · D · C) ≥ θ

2.1. Operational Definitions

The principal discriminator is operational rather than semantic: can the missing element be supplied as a diffusible molecule? If so, the deficit is graded and, in principle, rescuable from below. If the required element must be assembled in place, increasing a diffusible input cannot substitute for it.

Animal findings are identified by species at first mention; statements without a species qualifier refer to human observations. This distinction is important because several assignments below rely on rodent or avian experiments whose relevance to human psychosis remains inferential.

A—Architecture. The assembled substrate available to be executed. Test: exogenous supply of the missing element rescues nothing at any dose.

D—Drive. The magnitude of the activating signal. Test: graded, with a floor rather than a veto; rescuable by more of the same, or by a downstream product of the same synthetic chain.

C—Context. The external condition selecting which representation receives the drive. Test: present/absent manipulation of the condition itself, with the other three terms held constant.

Φ—Phase. The permissive state determining whether execution is allowed at all. Test: shifts the effective threshold rather than scaling the gain; diffusible; measurable as availability rather than as signal.

2.2. Why the Terms Are Fixed in Advance: DNA Replication as an Anchor

In the DNA replication system, the assignments are comparatively well constrained because the relevant elements have been manipulated separately (Rahman, 2025). A is CDC6/CDT1-dependent loading of MCM double hexamers onto ORC-bound origins—the licensed but not yet fired structure. D is cyclin D-CDK4/6 catalytic activity, which attenuates with a floor rather than acting as an all-or-none veto. C is the chromatin and cell-cycle-entry state. Φ is the phosphorylation state of the RB pocket proteins, which functions as a releasable gate. D and Φ act in series; A and Φ act in parallel on the product.

Two features of this system are relevant to the neural application. First, licensing and firing are distinct operations separated in time, creating different failure modes for mis-licensing within a permitted window and re-licensing outside it. Second, cell-fusion experiments provide the reference case for the architectural test: G2 nuclei placed in S-phase cytoplasm fail to reinitiate replication despite exposure to the downstream diffusible factors required for S phase. The persistence of the deficit despite diffusible rescue defines the standard against which architectural claims are compared.

2.3. A Behavioral Anchor: Socially Triggered Sex Change

The framework has also been applied to socially triggered sex change in protandrous clownfish (Rahman, 2026b). In that formulation, A is the bipotential gonad together with the relevant dominance circuitry; D is the social-rank signal; C is removal of the dominant female; and Φ is steroid-dependent permissiveness. Neurosteroid signaling alters the effective threshold, with cortisol acting in the opposite direction.

This example contributes two constraints relevant to the psychosis cases. First, Φ can be bidirectional, allowing perturbations with opposite molecular signs to converge on the same behavioral transition. Second, the transition exhibits hysteresis, with different forward and reverse thresholds. Because hysteresis is absent in other systems to which the framework has been applied, it should be treated as an empirical property rather than a general assumption.

2.4. Candidate Implementations in the Brain

The molecular assignments in Table 1 are candidate implementations, not claims that a single molecule uniquely corresponds to each ARCH term. Architecture refers to assembled synaptic structures that make a computation possible; drive to neuromodulatory signals that increase the probability or intensity of activation; context to mechanisms that determine which incoming information controls the response; and phase to permissive variables that determine whether a computation can be executed or durably modified. A proposed mapping should therefore be coherent at both the molecular level and the circuit level relevant to clinical function.

Table 1 specifies each term at both levels. This dual specification is intended to constrain post hoc reassignment: a proposed mapping must be defensible molecularly and at the level of circuit function. A case that fits at one level but not the other remains unexplained by the framework.

2.5. Execution and Encoding Are Different Biological Problems

The distinction between execution and encoding is central to the clinical argument. A patient may behave abnormally because the current physiological state is perturbed even when the durable neural substrate remains intact, as in a transient delirious state. Conversely, an acute episode may express architecture altered by an earlier developmental process. The immediate symptom can therefore look similarly severe in both situations while the prognosis differs substantially. What produces a symptom now is not necessarily the process that determines whether the patient will return to baseline.

The variable S is intentionally absent from the execution equation. It represents the persistent substrate carried forward through time: synaptic organization, stabilized connectivity, and other durable features that constrain the architecture available for subsequent execution. A transient change in Φ_E may markedly alter present behavior without changing S. A developmental writing error may alter S and thereby constrain later execution after the initiating state has passed. Progressive neurodegeneration may continuously reduce S. Thus, similar levels of current execution failure can coexist with very different biological futures.

One extension is required. Φ is separated according to the process being gated. Φ_E governs whether a licensed structure can be executed at the present moment, whereas Φ_N governs whether experience can be durably written into the substrate. The distinction is motivated by filial imprinting experiments (Behroozi et al.), in which a 4-day-old chick can see, orient, and approach—that is, execute the behavior—while durable encoding remains absent. Formally:

R_E = Φ_E · (A_E · D_E · C_E) W_N = Φ_N · (A_N · D_N · C_N) A_E(t+1) = g[S(t)]

Writing modifies the persistent substrate S, and S in turn determines the architecture available to subsequent execution. The logarithmic form of the execution relation makes the convergence explicit: log R = log Φ + log A + log D + log C. A proportional deficit in any one term produces the same subtraction from log R. R therefore identifies the state of the product but not the identity of the limiting term. In this model, non-identifiability is a property of the architecture of the equation rather than simply a limitation of measurement. Clinically, this means that a patient may be unable to use an otherwise intact circuit correctly in the moment or may instead have undergone a durable change in the circuit that determines how it will function later.

2.6. Notation

Table 2. summarizes the notation used in the clinical sections.

Symbol	Meaning
R	Readiness for execution: the product of the four terms, which must exceed a threshold for the behaviour or computation to occur.
A	Architecture. The assembled physical substrate available to be used — synapses, receptors, circuits. Built in place; not suppliable by drug.
D	Drive. The magnitude of the activating signal, principally dopaminergic in the cases considered here.
C	Context. The external condition determining which representation receives the drive; implemented as a comparator matching expectation against input.
Φ	Phase. The permissive state determining whether execution is allowed at all. Shifts the threshold rather than scaling the signal.
subscript E	The execution layer: what the brain is doing at this moment. R_E is present readiness.
subscript N	The encoding layer: whether experience is being durably written. W_N is the rate of durable writing.
S(t)	The persistent substrate at time t — the accumulated synaptic organisation carried forward. It does not appear in the equation for present execution, which is the paper’s central point.
g[S(t)]	The function by which the substrate laid down in the past determines the architecture available now: A_E(t+1) = g[S(t)].
h variable	The Hodgkin–Huxley inactivation gate. A neuron with h near zero has full drive and cannot fire. The biophysical prototype of a term governing availability rather than signal strength.

Table 2. summarizes the notation used in the clinical sections.

Symbol	Meaning
R	Readiness for execution: the product of the four terms, which must exceed a threshold for the behaviour or computation to occur.
A	Architecture. The assembled physical substrate available to be used — synapses, receptors, circuits. Built in place; not suppliable by drug.
D	Drive. The magnitude of the activating signal, principally dopaminergic in the cases considered here.
C	Context. The external condition determining which representation receives the drive; implemented as a comparator matching expectation against input.
Φ	Phase. The permissive state determining whether execution is allowed at all. Shifts the threshold rather than scaling the signal.
subscript E	The execution layer: what the brain is doing at this moment. R_E is present readiness.
subscript N	The encoding layer: whether experience is being durably written. W_N is the rate of durable writing.
S(t)	The persistent substrate at time t — the accumulated synaptic organisation carried forward. It does not appear in the equation for present execution, which is the paper’s central point.
g[S(t)]	The function by which the substrate laid down in the past determines the architecture available now: A_E(t+1) = g[S(t)].
h variable	The Hodgkin–Huxley inactivation gate. A neuron with h near zero has full drive and cannot fire. The biophysical prototype of a term governing availability rather than signal strength.

3. Route 1: Schizophrenia—Developmental Miswriting of Neural Architecture

Schizophrenia is the most difficult of the five examples because no single lesion accounts for the disorder (Rahman and Lauriello, 2016). The proposed assignment is therefore made at the level of developmental process rather than a single molecule. Genetic risk, complement signaling, intracellular trafficking, inhibitory regulation, and activity-dependent stabilization are treated as convergent influences on the construction and maintenance of cortical architecture. The claim is not that every patient has excessive complement activity or the same epigenetic abnormality. It is that several lines of evidence are consistent with vulnerability in the selection and stabilization of synaptic architecture during a time-limited developmental period.

This formulation also provides a framework for delayed onset. A risk variant present from conception may alter developmental rules without producing childhood psychosis. Symptoms can emerge later, when the relevant circuits mature, social and cognitive demands increase, or a permissive threshold changes during a vulnerable developmental window. The model therefore separates the presence of vulnerability from the timing of its expression. It also accommodates the clinical observation that dopamine blockade may reduce positive symptoms without reconstructing the developmental substrate that confers vulnerability.

Schizophrenia is 60%-80% heritable and highly polygenic, with 287 genome-wide significant loci in the largest meta-analysis and polygenic scores accounting for approximately 7.7% of case-control variance (Trubetskoy et al., 2022; Saada & Stern, 2025). The 22q11.2 deletion is present in approximately 0.3% of cases, with an odds ratio of about 20-30, and includes TBX1, DGCR8, and COMT; rare loss-of-function variants in SETD1A, GRIN2A, and TRIO confer odds ratios above 10 at frequencies below 0.1% (Marshall et al., 2017; Singh et al., 2022). Peak onset is 20.5 years, with a median of 25 years; 12.3% of cases begin before age 18 and 3% before age 14 (Solmi et al., 2022). Approximately 13.5% of patients meet recovery criteria (Jääskeläinen et al., 2013).

The temporal problem is therefore central: genetic liability is present long before the usual emergence of psychosis. A bounded developmental process can convert early vulnerability into later architectural consequences without requiring symptoms to be continuously expressed from childhood.

3.1. Molecular Evidence

Three findings are relevant to the proposed writing failure. Structural variation associated with greater C4A expression increases schizophrenia risk, and experimental C4A overexpression promotes synaptic elimination (Sekar et al., 2016). C4 also impairs SNX27-dependent GluR1 trafficking through a complement-receptor-3-independent intracellular pathway (Phadke et al., 2025). In parallel, a putative stabilization pathway is weakened: postmortem dorsolateral prefrontal cortex shows reduced AKT, reduced phospho-AKT at Ser473, and reduced GβL (Chadha & Meador-Woodruff, 2020).

The relevance of AKT-mTORC1 is more specific than a generic association with plasticity. In filial imprinting in newborn chicks, rapamycin blocks the imprinting-induced increase in mature mushroom spines while leaving the decrease in thin spines relatively intact (Batista et al., 2018). These data dissociate an mTORC1-dependent stabilization process from a comparatively mTORC1-independent elimination process.

Φ_N should not be interpreted as fixed by chronological age. In mice, ibogaine, ketamine, LSD, MDMA, and psilocybin reopen a social-reward learning critical period; the duration of reopening parallels the duration of the acute subjective effect reported in humans, ranging from approximately 48 hours for ketamine to more than a month for ibogaine. Metaplastic restoration of oxytocin-mediated long-term depression in nucleus accumbens and extracellular-matrix remodeling were identified as common downstream features (Nardou et al., 2023). Together with the imprinting findings, these results support the more limited proposition that encoding permissiveness can be experimentally modified rather than merely inferred from age.

Epigenetic findings provide an additional candidate mechanism for Φ_N. In prefrontal cortex, the RELN promoter has been reported to be approximately 50% more methylated in schizophrenia, with a corresponding reduction in RELN mRNA and an approximately threefold increase in DNMT1 transcript and protein (Grayson et al., 2005; Veldic et al., 2005; reviewed in Costa et al., 2007). GAD1 promoter methylation has likewise been reported to be increased, with greater DNMT3A enrichment and reduced GAD67 expression (reviewed in Gavin & Sharma, 2010). Genome-wide studies have also described broader promoter hypermethylation and increased DNMT1/DNMT3A protein (reviewed in Nishioka et al., 2012). Within the present framework, these findings are interpreted as candidate mechanisms affecting the stability of cortical inhibitory architecture rather than as a unitary epigenetic lesion in schizophrenia.

3.2. Circuit-Level Evidence

Patient-derived neuronal models provide convergent evidence of altered synaptic architecture. Cortical neurons derived from patients have shown approximately 40% fewer PSD-95 puncta, 35% fewer dendritic intersections, and 50% lower spontaneous EPSC frequency (Brennand et al., 2011). In monozygotic twins discordant for schizophrenia, neurons from affected twins showed reduced dendritic complexity, immature action-potential waveforms, reduced AMPA/NMDA current ratios, and both pre- and postsynaptic deficits, with unaffected co-twins intermediate across several measures (Stern et al., 2024). Interneuron cultures have also shown reductions in VGAT-positive puncta, GAD67, gephyrin, and NLGN2 (Kathuria et al., 2019).

Human physiological data also argue against a simple model of excessive plasticity. A meta-analysis of transcranial magnetic stimulation studies found reduced LTP-like and LTD-like plasticity in schizophrenia (Mehta et al., 2019), a pattern more consistent with impaired stabilization than with indiscriminate hyperplasticity.

3.3. A Critical Challenge to the Architectural Assignment

A challenge to the architectural assignment comes from rescue experiments in patient-derived neurons. Chronic loxapine increases PSD-95 density and EPSC frequency (Brennand et al., 2011), while NLGN2 overexpression or N-acetylcysteine restores interneuron puncta and increases firing rate (Kathuria et al., 2019). Under the operational test in Section 2.1, a deficit rescued by a diffusible intervention is graded rather than strictly architectural.

One possible resolution is that these models capture architecture during construction rather than after durable developmental writing has occurred. iPSC-derived neurons at day 60 have not traversed an adolescent selection window and therefore may not contain the accumulated substrate, S, proposed to be altered in vivo. This interpretation generates a direct falsification test: if patient-derived neurons matured through an in vitro analogue of the relevant critical period remain fully rescuable, the architectural assignment for Route 1 would be weakened.

4. Route 2: Corticosteroid Psychosis—A Reversible Execution-State Disturbance

Corticosteroid psychosis provides a useful contrast because both exposure and recovery can occur over a short interval. The syndrome may include delusions, mania, depression, or mixed behavioral disturbance, yet many patients improve after the corticosteroid dose is reduced or discontinued. Severe psychosis can therefore occur in a setting in which the underlying neural substrate is presumed to remain largely intact. Symptom severity alone is consequently an unreliable index of structural injury.

The mechanistic evidence is indirect. The receptor-degradation studies cited below used repeated stress in juvenile rats rather than prednisone-induced psychosis in adult patients. The claim is therefore not that Nedd4-1 or Fbx2 has been demonstrated to cause human corticosteroid psychosis. Rather, glucocorticoid signaling provides a biologically plausible mechanism by which prefrontal glutamatergic function and dopaminergic balance can be altered through reversible regulation of receptor availability. Such a process has the expected temporal properties of a state disturbance: rapid onset, dose sensitivity, and reversibility after the perturbation is removed.

Risk is strongly dose related: severe psychiatric reactions were reported in 1.3% (6/463) of patients receiving 40 mg/day of prednisone or less, 4.6% (8/175) receiving 41-80 mg/day, and 18.4% (7/38) receiving more than 80 mg/day (Boston Collaborative Drug Surveillance Program, 1972). The highest estimate is based on only seven events and should be interpreted; accordingly, across 13 studies, the weighted estimate for severe symptoms is approximately 5.7%. Onset is usually early, often within the first week, and approximately 90% of cases resolve within 6 weeks.

There is no established genetic architecture for corticosteroid psychosis. One clinically informative observation is that a prior psychiatric reaction to corticosteroids does not reliably predict the response to a subsequent course. This weak recurrence pattern is at least consistent with a predominantly state-dependent perturbation rather than a stable inherited lesion, although it does not establish the absence of genetic susceptibility.

4.1. Molecular Evidence

In rat prefrontal cortex, glucocorticoid receptor activation promotes ubiquitin-proteasome degradation of the AMPA receptor subunit GluR1 through the E3 ligase Nedd4-1 and of the NMDA receptor subunit NR1 through Fbx2. The result is reduced AMPAR- and NMDAR-mediated transmission in prefrontal pyramidal neurons and impaired prefrontal-dependent cognition (Yuen et al., 2012). The effect is biphasic: acute stress enhances prefrontal glutamatergic transmission and working memory, whereas repeated exposure suppresses both.

The mode of injury is relevant to the proposed distinction between state and substrate. Regulated receptor proteolysis is potentially reversible because receptor populations can be replenished. By contrast, synapses removed through phagocytic elimination require structural rebuilding. Within the framework, this difference in reversibility—not the intensity of psychosis—is what distinguishes Route 2 from the proposed developmental architectural injury in Route 1.

4.2. Circuit-Level Interpretation

At the circuit level, the proposed disturbance combines reduced prefrontal comparator capacity with increased dopaminergic transmission, thereby increasing D_E. In predictive-processing terms, the balance shifts toward greater error precision relative to prior precision. Aberrant salience may then shape the content of the delusion (Kapur, 2003). This interpretation remains mechanistic and inferential; it is offered to explain how a short-lived physiological disturbance could produce marked psychosis without durable architectural injury.

5. Route 3: Postpartum Psychosis—Failure of Neurosteroid-Gate Recalibration

Postpartum psychosis is conceptually different from a simple deficiency state. Pregnancy requires adaptation to a hormonal environment that changes markedly across gestation and then abruptly at parturition. A system that functions normally before pregnancy may become unstable if ligand withdrawal and receptor reconfiguration become temporarily mismatched. Pathology can therefore arise from failed recalibration rather than from an isolated hormone concentration being simply 'too low.'

This distinction is clinically important because every mother experiences the endocrine transition of parturition, whereas postpartum psychosis occurs only in a small minority. The relevant susceptibility may therefore reside in the regulatory machinery that anticipates, accommodates, and recovers from the hormonal transition. This formulation is compatible with the strong enrichment of postpartum episodes among women with bipolar disorder and with the predominance of bipolar-spectrum, rather than schizophrenia-spectrum, recurrences outside the postpartum period.

Postpartum psychosis occurs in approximately 1-2 per 1,000 deliveries. The enrichment among women with bipolar disorder is more striking: approximately one in five experiences a postpartum psychotic or manic episode. Family-based heritability has been estimated at 55% and whole-genome-sequence-based heritability at 37%, with reported overrepresentation on the X chromosome (Jung et al., 2026). Although infanticide receives disproportionate public and forensic attention, it is a rare outcome. Resnick's classic reviews established the motive categories still used in the filicide literature and defined neonaticide as killing within the first 24 hours of life (Resnick, 1969, 1970).

This case is relatively constrained within the framework because the proposed Φ implementation preceded the present clinical application. In the lordosis model, Φ was assigned to allopregnanolone acting at tonic extrasynaptic δ-subunit GABA_A receptors (Rahman, 2026c). The important limitation is that Gabrd itself has not been tested in the lordosis paradigm; its relevant published phenotype is postpartum.

5.1. Molecular Evidence

In mice, tonic and phasic inhibition decrease across pregnancy through downregulation of GABA_A receptor δ and γ2 subunits, respectively, and rebound after delivery. Mice that fail to execute this regulation display abnormal maternal and depression-like behaviors postpartum, which are reversed by the δ-selective agonist THIP. Critically, the Gabrd deficit is behaviorally silent until pregnancy and parturition (Maguire & Mody, 2008).

The proposed disturbance is therefore a calibration mismatch rather than a simple lowering of the gate. The receptor pool is remodeled across gestation as allopregnanolone concentrations rise, followed by abrupt ligand withdrawal at parturition. If receptor reconfiguration lags behind that change, the system transiently operates with a receptor configuration adapted to the wrong hormonal environment. Such a mechanism predicts reversibility as receptor populations re-equilibrate (Guard et al., 2024).

Clinical evidence for this mechanism is indirect but temporally suggestive. In a real-world series of 17 patients treated with intravenous brexanolone, an allopregnanolone formulation, Edinburgh Postnatal Depression Scale scores improved substantially after infusion and remained lower at 1 week and 3 months; two patients who underwent precision functional neuroimaging also showed widespread connectivity changes. The principal limitations are important: the patients had postpartum depression rather than postpartum psychosis, and the series was open, uncontrolled, and conducted alongside routine clinical care.

The duration of benefit is nevertheless compatible with a recalibration model. A single 60-hour infusion was followed by improvement lasting at least 3 months. A chronic deficiency model would more naturally predict a need for continued replacement. By contrast, a transient mismatch model predicts that brief treatment could bridge the period during which receptor configuration returns toward the postpartum state.

Rare-variant findings independently nominate components of the proposed regulatory pathway. Rare coding variant analysis in postpartum psychosis identified DNMT1 and HMGCR as candidate risk genes (Jung et al., 2026). DNMT1 is also reported to be increased in schizophrenia prefrontal cortex (Veldic et al., 2005), while HMGCR is the rate-limiting enzyme of the mevalonate pathway implicated in the framework's proposed Φ implementation (Rahman & Zorumski, 2026). These convergences are hypothesis-generating rather than evidence of a shared disease mechanism.

5.2. Circuit-Level Interpretation

At the circuit level, δ-subunit-containing GABA_A receptors on parvalbumin interneurons contribute tonic rather than phasic inhibition. The proposed lesion therefore alters a standing bias on network excitability rather than the magnitude of a transient activating signal. Within the operational definitions in Table 1, that distinction is the reason for assigning the disturbance to Φ rather than D.

Routes 2 and 3 are proposed as opposite perturbations of the same general gating dimension. Glucocorticoid signaling raises the effective threshold, whereas allopregnanolone signaling lowers it. The corticosteroid and postpartum cases therefore test whether perturbations of opposite molecular sign can converge on a common clinical endpoint when they disrupt the same regulatory balance.

The clinical course is broadly consistent with a reversible disturbance occurring on an intact substrate. In prospective follow-up, approximately two-thirds of women have illness confined to the postpartum period; recurrences outside that period are predominantly bipolar-spectrum, and schizophrenia appears uncommon even when the index episode is schizophrenia-like.

6. Route 4: Alzheimer's Disease—Progressive Destruction of Architecture

Alzheimer's disease shifts the problem from abnormal calibration to progressive loss of the machinery required for cognition. A patient may still develop a delusion, but the architecture supporting perception, memory, familiarity, and belief evaluation progressively deteriorates. The framework therefore predicts not only persistence or recurrence of psychosis but also a change in its form as representational capacity declines. Relatively preserved architecture may support an elaborated persecutory account, whereas advanced architectural loss may constrain the patient to simpler misidentification or immediate false conclusions.

This proposed distinction between delusional complexity and delusional durability is clinically testable. Complexity requires representational capacity: memory for prior events, maintenance of a narrative over time, attribution of motives, and integration of new evidence. Durability instead depends on whether the underlying substrate remains altered or continues to deteriorate. The two dimensions need not covary. A transient drug-induced or metabolic episode may support a complex delusion while architecture remains intact; advanced neurodegeneration may produce a simpler but biologically less reversible disturbance.

Across 55 studies comprising 9,749 participants with Alzheimer's disease, psychosis was reported in 41%, delusions in 36%, and hallucinations in 18% (Ropacki & Jeste, 2005). Incidence rises during the first several years and then plateaus. Heritability of the psychosis phenotype has been estimated at 61%; a genome-wide meta-analysis of 12,317 individuals identified ENPP6 and SUMF1, with a gene-based association at APOE (DeMichele-Sweet et al., 2021).

Focal lesion data sharpen the anatomical argument. Darby and colleagues (2017) analyzed 17 patients in whom a single focal lesion produced delusional misidentification, including Capgras syndrome and reduplicative paramnesia. The lesions were anatomically heterogeneous, but all were functionally connected to two sites: left retrosplenial cortex, implicated in familiarity, and right ventral frontal cortex, implicated in belief evaluation. Lesions associated with other delusions did not show the same connectivity pattern.

Three aspects of this finding are relevant. First, a single focal lesion was sufficient; dementia, delirium, or a second lesion was not required. Second, the result supports a network-level two-factor account involving familiarity processing and belief evaluation. Third, it provides a useful comparison with Route 5: anatomical disconnection and reversible biochemical dysfunction could, in principle, disrupt the same computation by different physical mechanisms. The shared phenotype would then reflect convergence at the level of circuit function rather than common etiology.

Focal lesions and Alzheimer's disease can therefore be treated as two forms of architectural disturbance: one punctate and relatively static, the other diffuse and progressive. The prediction developed below is that delusional complexity should depend on the amount of surviving architecture, which may remain sufficient for elaboration after a focal lesion but decline substantially in advanced Alzheimer disease.

6.1. Molecular Evidence

In Alzheimer mouse models, synapse loss is mediated by C1q, C3, and the microglial complement receptor CR3. C1q associates with synapses before plaque deposition; inhibition of C1q, C3, or CR3 reduces phagocytic microglia and rescues early synapse loss; and C1q is required for the synaptotoxic effect of soluble amyloid-β oligomers on hippocampal long-term potentiation (Hong et al., 2016). These findings support inappropriate reactivation of a complement-dependent developmental pruning pathway in the adult brain.

This creates a mechanistic parallel with the complement findings in schizophrenia. Within the present framework, Route 1 represents abnormal selection or stabilization during a developmental window, whereas Route 4 represents reactivation of synapse-elimination machinery after that window. The parallel is proposed at the level of biological control logic; it does not imply that schizophrenia and Alzheimer's disease are manifestations of the same disorder.

The genetic data underscore that distinction. Polygenic risk for schizophrenia is inversely associated with psychosis in Alzheimer's disease (DeMichele-Sweet et al., 2018). Thus, the two conditions may engage partially overlapping effector biology despite differing, and potentially opposing, liability structures. That pattern is more consistent with shared machinery used in different pathological contexts than with a unitary disease process.

6.2. Circuit Integrity and the Form of the Delusion

The framework distinguishes two dimensions: delusional durability is proposed to track the persistent substrate S, whereas delusional complexity is proposed to track current architectural capacity A_E. Systematization requires both representational capacity and time. Schizophrenia can provide both. The corticosteroid, postpartum, and metabolic cases preserve architecture but are short-lived. Alzheimer's disease provides time but progressively diminishing architecture. It should therefore be associated with decreasing complexity as disease advances.

Available clinical data are broadly compatible with this prediction. Persecutory delusions tend to occur earlier, whereas misidentification phenomena are associated with greater cognitive impairment and more advanced disease. Reports that late-stage misidentification may be transient and less firmly fixed further suggest that fixity itself may depend partly on the representational capacity available to sustain a belief. These observations are consistent with, but do not by themselves prove, the proposed relationship between delusional form and architectural integrity.

7. Route 5: Homocystinuria—A Reversible Comparator Latch

The homocystinuria case illustrates a different principle: a clinically fixed belief need not imply that an erroneous neural representation has been durably encoded. The patient's conviction remained resistant to contradictory evidence while the metabolic disturbance was present but disappeared within days. Phenomenological fixity can therefore arise from a dynamic process that repeatedly generates the same erroneous output. The system need not have permanently stored the wrong conclusion; it may instead be temporarily unable to update while a feedback loop remains engaged.

This distinction is compatible with psychological models that emphasize abnormal inference, belief evaluation, prediction error, salience, or familiarity, but it adds a temporal mechanism. The abnormal inference could persist because the relevant comparator becomes functionally decoupled from changing input. Correction of the biochemical state would then restore responsiveness to evidence. The clinical case cannot establish this molecular mechanism, but the proposal is sufficiently specific to be tested.

Classical homocystinuria is rare, with worldwide prevalence estimates on the order of 1 in 200,000 to 1 in 344,000 and marked geographic variation. It is an autosomal recessive disorder caused by pathogenic CBS variants. Psychiatric symptoms have been reported in 64% of patients (Almuqbil et al., 2019), whereas delusional misidentification has been described only rarely.

The patient described by Rahman and Cole presented with abrupt persecutory and misidentification delusions, including the belief that her parents had been replaced by imposters. Serial Mini-Mental State Examination scores improved as homocysteine concentrations declined during treatment with pyridoxine, folic acid, and betaine. By hospital day 8, the delusions had resolved and insight had returned; she was at baseline by day 11 (Rahman & Cole, 2014).

7.1. Molecular Evidence

Homocysteine acts at two NMDA receptor sites with opposing effects: it is an agonist at the glutamate site and a partial antagonist at the glycine co-agonist site. At normal glycine concentrations, the net effect can be inhibitory; at higher glycine concentrations, agonist activity increases (Lipton et al., 1997). The direction of effect is therefore conditional on ambient glycine rather than uniformly excitatory or inhibitory.

Subsequent experimental work suggests a mechanism capable of sustaining abnormal signaling. In cultured neurons and rodent tissue, homocysteine preferentially stimulates GluN2A-containing receptors and produces sustained low-level calcium influx. Calcium entry activates Pyk2 and Src-family kinases, which phosphorylate GluN2A at Tyr1325 and sustain channel activity, while the regulatory phosphatase STEP fails to terminate the cycle. ERK phosphorylation is correspondingly prolonged rather than transient.

7.2. Why This Case Does Not Fit the Original Framework

Under the operational definitions in Section 2.1, this is not a pure C lesion. The external condition was present: the patient's parents were physically in the room. The proposed failure concerns the reading of that condition rather than its presence. Nor is the lesion architectural in the strict sense, because the syndrome resolved after diffusible metabolic treatment.

The proposed mechanism therefore exposes a limitation of the original equation. Homocysteine would not simply reduce a required factor toward zero; it could instead hold a comparator in an abnormal state through positive feedback. The Pyk2-Src-Tyr1325 cycle offers a candidate mechanism by which output becomes relatively insensitive to changing input. ARCH × Φ, as originally formulated, does not represent a component pinned at an incorrect value. Route 5 is therefore not evidence that the original equation explains every delusion; it identifies a boundary condition that a more complete model must accommodate.

7.3. Specific Delusional Content Versus Global Encephalopathy

The patient also had hyperactive delirium, fluctuating orientation, and a Mini-Mental State Examination score of 18/30, indicating a substantial component of global metabolic encephalopathy. Generalized EEG slowing is strongly associated with delirium but is nonspecific with respect to etiology (Kimchi et al., 2019).

Diffuse slowing can explain global confusion but not the specific content of a Capgras delusion. The working hypothesis is therefore that generalized metabolic dysfunction accounts for the background encephalopathy, whereas a more selective disturbance in familiarity or belief-evaluation circuitry contributes to the delusional content. These components should be separable empirically by their time courses during metabolic correction.

The comparison with Alzheimer disease is particularly informative because both conditions can produce Capgras phenomena while differing markedly in substrate integrity and prognosis. The delusional content alone does not identify whether the underlying process is progressive neurodegeneration or a reversible metabolic disturbance. The distinction emerges from the broader clinical examination, laboratory data, and longitudinal course.

8. What the Five Routes Show Together

The cross-case comparison separates three questions that are often compressed into the single label of psychosis: Which component is failing now? Has the persistent substrate been altered? Is the process reversible, stable, or progressive? These dimensions can vary independently. A medication may produce severe current dysfunction while leaving the substrate intact. A developmental process may alter the substrate long before the first psychotic episode. A degenerative disease may progressively remove architecture. A metabolic disturbance or stimulant intoxication may transiently drive a computation outside its normal operating range.

Methamphetamine provides a useful example of the latter. In a prospective cohort of 278 methamphetamine-dependent participants without lifetime schizophrenia or mania, clinically significant psychotic symptoms were approximately five times more likely during months of use than during months of abstinence, with a strong dose-response relationship and rates approaching 48% during months with 16 or more days of use (McKetin et al., 2013). Suspiciousness was the most common symptom; delusions or unusual thoughts occurred in approximately one-third of symptomatic observations, and prevalence estimates among users generally range from 13% to 24% (McKetin et al., 2006). Symptoms remit with abstinence in most patients.

Methamphetamine is important because it exposes the opposite limitation from Route 5. Rather than reducing a term toward zero, it drives dopaminergic input above its normal range. Together, excessive drive and comparator latching suggest that the original equation is incomplete if each term is treated only as a quantity that can fall below a floor. A more general formulation would need to represent an operating range, with dysfunction possible when a component is too low, too high, or abnormally decoupled from its input.

The framework therefore does not claim that all delusions share a molecular pathway, that psychotic disorders are variants of one disease, or that phenomenology is clinically uninformative. The narrower claim is a many-to-one relationship between biological perturbations and a coarse-grained clinical endpoint. Similar convergence is common in medicine: dyspnea can result from airway obstruction, pulmonary edema, anemia, metabolic acidosis, or cardiac failure. The symptom is clinically meaningful without being mechanistically unique. Delusion may sometimes occupy a comparable level of description.

Table 3 summarizes the proposed assignments.

8.1. What the Series Does—and Does Not—Demonstrate

The five cases do not provide one example of each ARCH term. Routes 1 and 4 are both assigned to architecture, differing in whether the substrate was developmentally mis-written or progressively destroyed. Routes 2 and 3 are both assigned primarily to Φ_E, differing in direction and in whether the perturbation is exogenous or endogenous. Route 5 is not a reduction of any ARCH term but a proposed comparator latch. No clean D or C lesion is represented in the five-case series.

This is a narrower claim than a four-term demonstration and is correspondingly more defensible. Methamphetamine is the closest candidate for a drive perturbation, but it increases D rather than reducing it and therefore tests a different property of the model. The series also leaves open whether relatively pure perturbations of drive or context would preferentially produce other phenomena, such as avolition or hallucinations without fixed delusional belief.

8.2. Licensing and Firing Across Biological Timescales

The sterol synthesis identifies Φ with the logic of the Hodgkin-Huxley h variable (Rahman & Zorumski, 2026). The h variable reflects channel availability rather than activating drive: a neuron may receive full depolarizing input yet fail to fire when inactivation is sufficiently strong. The same distinction between licensing and execution appears at a much longer timescale in DNA replication, where MCM loading in G1 is separated from origin firing in S phase. These analogies are used to illustrate a recurrent control principle across timescales, not to imply molecular identity across systems.

Across the five routes, the relevant processes span orders of magnitude in time: receptor or comparator dynamics over seconds to days, receptor reconfiguration across days to weeks, progressive structural loss across years, and developmental writing across adolescence. The framework treats timescale as mechanistically informative because current execution and durable substrate change need not occur together.

8.3. Heritability May Track Regulatory Architecture More Than Transient State

The heritability pattern suggests a further, tentative distinction. A largely exogenous state perturbation such as corticosteroid exposure has no established episode-specific heritability, whereas conditions involving persistent structure or endogenous regulatory machinery show substantial genetic loading. This contrast should be treated as hypothesis-generating because the disorders differ in many respects beyond their proposed ARCH assignments.

Postpartum psychosis illustrates the point most clearly. The endocrine transition of parturition occurs in every mother, so inherited liability cannot reside in the transition itself. It may instead reside in the capacity to remodel receptor populations or synthesize and regulate the relevant signaling molecules. In that sense, Φ has an architecture of its own: the δ-GABA_A receptor pool is structural, whereas allopregnanolone concentration is a state variable. This distinction predicts that exogenous manipulation of Φ should show less heritable variation than endogenous dysregulation that depends on the patient's own regulatory machinery.

9. Constraints and Limitations

The word 'same' requires qualification. The five examples converge at the level of a fixed false belief, but they are not phenomenologically identical. Thought broadcasting, persecutory surveillance, infant substitution, and Capgras misidentification differ in content, cognitive demands, affective context, and relationship to memory. A mature model must therefore account for both convergence and residual specificity: why distinct perturbations can cross a threshold for delusional belief while circuit vulnerability, prior experience, and context shape the particular content expressed.

The framework should also be distinguished from a validated quantitative biomarker. No study has simultaneously measured A, D, C, and Φ across these disorders and shown that their product predicts psychosis better than competing models. At present, the equation is a mechanistic organizing hypothesis. Its scientific value will depend on whether the proposed components can be measured independently, perturbed selectively, and shown to generate predictions that an additive or less constrained model does not.

A second limitation concerns provenance. Several foundational papers defining this framework are the author's own and are recent (Rahman, 2025; Rahman, 2026b; Rahman, 2026c; Rahman & Zorumski, 2026; Rahman, Zorumski & Meloy, 2025). The assignments in Section 2 preceded the present clinical applications, which reduces but does not eliminate the risk of circularity. Independent replication is absent, and the framework should therefore be read as a developing hypothesis rather than an established formalism.

Φ should not be treated as a scalar field with a uniform sign across the brain. Intra-VTA 3α,5α-THP can increase lordosis while decreasing social interaction in the same animals, at the same site, and in the same session. The sign of an effect therefore depends on the neural node and receptor population engaged. The present framework cannot support a general statement that lowering Φ_E causes delusions; any such claim must be node- and population-specific.

The proposed sterol implementation also does not extend straightforwardly to Route 5, in which no sterol mechanism is implicated. Either the comparator latch lies outside Φ, or Φ must be understood as substrate-plural, with sterols representing one class of membrane gate rather than the universal implementation. A related tension appears in the replication system, where statin-induced G1 arrest is rescued by geranylgeranyl pyrophosphate but not cholesterol, implicating prenylation rather than membrane sterol itself.

There is also a physiological floor beneath the equation. Generalized EEG slowing indicates failure of the machinery required to sustain computation and is nonspecific with respect to cause. ARCH describes conjunctive gating within a functioning system; it does not model the condition in which oxidative metabolism or global neural function is too impaired to support computation at all. Severe delirium provides the clearest clinical example of this boundary.

A further complication is that prolonged execution failure may itself alter the substrate. In the BRAIN-ICU cohort of 821 patients, longer delirium duration was independently associated with worse global cognition and executive function at 3 and 12 months after adjustment for major clinical covariates; at 12 months, 34% had cognitive performance comparable to moderate traumatic brain injury (Pandharipande et al., 2013). If prolonged state disturbance can produce durable neural consequences, duration becomes an additional axis alongside the identity of the perturbed term and the state of the encoding window.

Several evidentiary limitations remain. In Route 5, haloperidol was administered during metabolic correction, so resolution cannot be attributed uniquely to lowering homocysteine, even though serial cognitive scores tracked the biochemical improvement. The proposed GluN2A latch mechanism derives from cultured neurons and rodent tissue rather than patients. Yuen and colleagues studied repeated restraint stress in juvenile rats, not exogenous corticosteroid treatment in adults. Maguire and Mody studied maternal and depression-like behaviors in mice rather than psychosis. No single cohort can test the entire five-case comparison, and the framework has not yet generated a prospectively confirmed prediction. These limitations define the current evidentiary status of the model rather than exceptions to it.

10. Falsifiable Predictions

Because the framework spans molecular, circuit, and clinical levels, its predictions are necessarily heterogeneous. The most informative tests will measure the proposed ARCH component independently of the symptom and manipulate it while holding other relevant conditions as constant as possible. A successful test should do more than show that a pathway is abnormal in psychosis; it should demonstrate that changing the hypothesized limiting component changes execution in the direction specified by the model.

Gabrd encodes the δ subunit of the GABA_A receptor that carries tonic inhibition and is downregulated during pregnancy in the experiments described above. Heterozygous Gabrd mice, whose phenotype is largely silent before pregnancy, should show postpartum abnormalities in psychosis-relevant measures such as sensory gating or latent inhibition, not only affective and maternal behaviors, and these abnormalities should be reversible by THIP. This would extend an existing biological observation into a direct psychiatric test of the proposed gating mechanism.

If complement-mediated synapse elimination contributes specifically to psychosis in Alzheimer's disease, inhibition of C1q, C3, or CR3 should reduce psychotic symptoms beyond any effect on global cognitive decline. A selective effect on psychosis would provide stronger support for the proposed architectural pathway than a nonspecific neuroprotective effect.

Episodes produced by exogenous Φ manipulation should show less heritable variation than episodes arising from endogenous dysregulation of the same gating machinery. Corticosteroid psychosis and postpartum psychosis provide a clinically accessible contrast for testing this prediction.

Across conditions, delusional complexity should correlate with independently measured architectural integrity, whereas delusional durability should correlate more closely with persistent substrate change. The two dimensions should therefore dissociate rather than covary obligatorily.

In metabolic delusions accompanied by encephalopathy, EEG background slowing and specific delusional content should follow different time courses: the delusional content should track the causative analyte more closely, whereas diffuse slowing should track the severity of global encephalopathy.

The execution-encoding distinction also generates a more speculative prediction: a transient Φ_E perturbation occurring while Φ_N is experimentally open should be more likely to leave durable change than the same perturbation delivered when Φ_N is closed. Psychedelic reopening of critical-period plasticity provides one possible experimental model (Nardou et al., 2023). Any clinical extension to persistent psychosis must be stated cautiously because such outcomes are uncommon and heavily confounded by preexisting vulnerability.

If execution feeds back on gating state, duration of untreated psychosis should interact with developmental timing rather than contribute only an additive burden. The strongest durable effects would be expected when prolonged disturbance coincides with an open encoding window.

11. A Methodological Corollary

The non-identifiability result in Section 2.5 also has a methodological implication that can be tested independently of the specific clinical assignments in Routes 1-5.

If R is a sufficient statistic for the product but not for the identity of its factors, a measurement taken downstream of R inherits the same limitation. A diagnosis-anchored measure may identify the presence of dysfunction without identifying which component was perturbed. Increasing sample size improves precision around that downstream signal but cannot, by itself, recover mechanistic information that was never represented in the measured output.

This yields a specific empirical prediction. If a diagnostic category contains several mechanistically distinct perturbation classes, pooled case-control analyses will average across them and may dilute effects that are larger within mechanistic subgroups. Larger samples would estimate the pooled average more precisely without necessarily recovering the subgroup-specific signal. Brain-wide association studies demonstrate that reproducible case-control effects can be very small: across approximately 50,000 individuals from three large datasets, median reproducible effect sizes were about r=0.01, with substantial inflation and replication failure at smaller sample sizes (Marek et al., 2022).

Mechanistic heterogeneity is not the only explanation for small or unstable effects. Marek and colleagues emphasize measurement reliability and variability across population subsamples, both of which are independent considerations. The explanations are nevertheless distinguishable in principle. A reliability-limited effect should not systematically increase after stratification, because subdivision reduces power without improving measurement. A heterogeneity-limited effect should increase when stratification isolates biologically more homogeneous groups.

Existing datasets can test this possibility. A large imaging or biomarker cohort could be stratified by a mechanism-relevant variable measured independently of diagnosis, and within-stratum effect sizes compared with the pooled estimate. If mechanistically informed stratification repeatedly fails to increase effect size, the heterogeneity account would be weakened. A related pattern has been reported in treatment studies: folate supplementation in schizophrenia was null in an unstratified analysis but significant among patients homozygous for a functional FOLH1 variant (Roffman et al., 2013). Such findings do not validate ARCH × Φ, but they illustrate the broader methodological consequence of mechanistic heterogeneity.

12. Clinical and Mechanistic Conclusions

For clinical psychiatry, the principal implication is diagnostic humility about symptoms coupled with greater attention to mechanism and time course. A delusion establishes a disturbance of belief formation, evaluation, or updating, but it does not establish whether the cause is primarily psychiatric, neurologic, endocrine, pharmacologic, toxic, or metabolic. Those probabilities are supplied by the rest of the clinical encounter: age, tempo of onset, cognition, neurologic findings, medication exposure, reproductive state, laboratory data, imaging, and longitudinal course.

The framework therefore complements rather than replaces phenomenology. Careful description remains essential because delusional content and organization may localize cognitive operations and guide the differential diagnosis. The additional claim is that a similar descriptive endpoint can be generated by different biological lesions. If this framework is useful, the task for biological psychiatry is not to identify a single molecular cause of 'delusion' in the abstract, but to distinguish the mechanisms capable of producing a shared computational failure and determine which mechanism is operating in a particular patient.

The five routes illustrate three classes of perturbation represented by the present equation—developmental alteration of architecture, progressive destruction of architecture, and reversible disturbance of a permissive gating state—together with a fourth failure mode that the equation does not yet represent: a comparator held at an abnormal value by metabolic feedback. Their common feature is not a shared molecular lesion but convergence on impaired belief-related computation.

What differs clinically is the state of the persistent substrate. Because substrate integrity is not specified by the equation for momentary execution, similar delusional presentations can carry very different prognoses. The contrast between Capgras phenomena in Alzheimer's disease and in homocystinuria is therefore instructive: the delusional content may be similar, but the broader clinical examination, laboratory data, and longitudinal course distinguish progressive structural disease from a reversible metabolic disturbance. Mechanism, not phenomenology alone, determines prognosis.