Syntropic Configurations: Canonical System v1.2

Architecture Note

This document establishes the canonical system of syntropic configurations derived from H_t \in [0,1]^5, with B_t as the fifth constitutive domain.

Organizing axes. Canonical system v1.2 organizes configurations by:

• Axis 1: dominant propagation pattern in \Psi_t: the pattern by which perturbation moves between domains. Five values: psych.→B_t (propagation from psychological domains toward B_t), B_t→psych. (propagation from B_t toward psychological domains), bidirectional, global collapse, segmented. Formal definition in D4* of the Ontological Core v2.3.5. The earlier names psi_dir, psic_Bt, and Bt_out were removed from the technical vocabulary (session June 12, 2026, rules 4 and 37).

• Axis 2: basin type: the way the field has stabilized over its history. Five values: transient, reconfiguration, residency, early dispositional, failed reconfiguration. Formal definition in D4* of the Ontological Core v2.3.5.

• Axis 3: domain of origin (applied selectively): the functional domain the perturbation originates from. It operates as a configuration discriminator only when empirical comparison shows it produces distinct valleys in \mathcal{W}. Currently confirmed for dominant propagation pattern in \Psi_t with origin in B_t × basin=reconfiguration, which gives rise to C-C1 (origin R_t) and C-C2 (origin A_t). For C-A and C-F, Axis 3 remains pending pilot comparison: see the extension of G10.

\|H_t\| and \nabla H_t are derived properties of each configuration: they describe what the field produces within it, but do not define it.

Reference for intervention. Each configuration's orienting intervention profile should be read alongside C5 (Intervention Modes by Target Parameter, Ontological Core v2.3.5 and Clinical Core v0.3.0), which establishes the relationship between the model's formal parameters and types of intervention, with their timescale. C5 postdates this document: fully integrating it into the individual profiles is Pending Item 7.

Empirical basis. Each configuration's properties were derived from analysis of 105 cases in the Barnhill 2023 corpus (DSM-5-TR Clinical Cases), mapped onto the syntropic profile H_t \in [0,1]^5, and from systematic comparison against the 7 emergent organizations from k-modes clustering on that corpus. The corpus carries known selection biases: it overrepresents acute, high-complexity presentations and underrepresents subthreshold disorders, mild adaptive conditions, and cultural variants.

Note on statistical uncertainty (CC10): the percentages appearing in each individual profile (distributions of \Pi_R, modal speed, empirical domain of origin) are estimates over low, highly variable N: N per configuration ranges from 9 to 22 cases in most profiles, and is N=2 for C-L and N=1 for C-M. The variance on these estimates is high; they should be read as orienting indications of the most frequent pattern in the available corpus, not as calibrated probabilities. Their value is a starting point for the pilot's data to refine, not a statistical prediction. The absence of confidence intervals in the profile tables reflects this limitation, not a methodological omission.

Quick Reference Table

†Theoretical and clinical justification: low N in the corpus; see individual profile.

Comparison with the 7 Emergent Clustering Organizations

Systematic comparison between the 14 canonical configurations and the 7 emergent organizations from k-modes clustering (k=7, 105 cases) produced the following results:

Configurations with no clustering correspondence: C-B, C-F, C-G, C-H, C-K, C-L, C-M. The reasons differ: C-B, C-G, and C-H have low N in the corpus and likely get absorbed into adjacent clusters; C-K operates in \sigma_t, a dimension the clustering variables do not capture; C-L and C-M have N=2 and N=1 respectively: invisible to k-modes. Absence from the clustering does not invalidate their status as canonical configurations.

Open question: extension of G10. Whether domain of origin discriminates configurations within C-A (psych.→B_t × residency) and C-F (psych.→B_t × transient) remains pending empirical comparison in the pilot. The testable prediction is that \Psi_t and \varepsilon_t prior to reorganization predict whether domain of origin carries weight in the identity of the destination configuration.

Individual Profiles

C-A: Anchoring · Psychological→Bt · Chronic Residency

Definition by Axes. Dominant \Psi_t: psych.→B_t: the perturbation originates in the psychological domains (A_t, R_t) and propagates toward B_t. Basin: residency: the field is stabilized in its current configuration; the attractor is deep and long-standing.

Derived Properties.

• \|H_t\|: variable by domain: the profile is not symmetric. The psychological domains (predominantly A_t, secondarily R_t) show the primary compromise; B_t is affected as a propagated effect. The global norm can be moderate even when the domain profile is markedly asymmetric.
• \nabla H_t: sustained \approx 0: the field is not moving; the attractor is stable.
• \varepsilon_t: low, especially in the origin domains (\varepsilon_A, \varepsilon_R): accumulated history has rigidified the existential-anchoring and bonding domains.

Empirical Domain of Origin: A_t in 78% of cases, R_t in 22%.

\Pi_R: preserved (50%) / biased (33%) / encapsulated (17%). Reality testing can be biased in the direction of the basin's content (distrust, rumination, grandiosity) without being globally compromised.

Speed: decades (72%) / years (28%). This is the slowest-installing pattern in the corpus.

D_p(t): high, the history of plastic deformation is extensive. \kappa(t): reduced by accumulated history. Modal position in S_m: R2 (high D_p(t), low-to-moderate \kappa(t)).

Modal Transition-Conditions Profile: \Beta_F: low-to-moderate: the response repertoire is narrowed by the basin. \Pi_R: variable depending on the basin's content. \Tau_F: moderate: narrative continuity exists but is organized around the basin. \Upsilon_{US}: moderate: the basin itself provides a form of stability.

Representative Clinical Correlates: personality disorders (paranoid, schizoid, narcissistic, avoidant, histrionic, dependent, obsessive-compulsive), dysthymia, PTSD chronic over decades, BDD with no insight, hoarding, delusional disorder of residency, SUD with an existential basin.

Internal Logic. The field has organized its coherence around a psychological axis that chronically propagates toward B_t. The somatic disturbance is real but secondary: intervening only on B_t without changing the psychological basin produces transient relief. The residency basin means the field is not undergoing spontaneous change: it requires calibrated clinical perturbation.

Typical Clinical Error. Treating somatic symptoms without addressing the originating psychological basin. Attempting high-intensity reorganization in a field with \kappa(t) reduced by decades of accumulated D_p(t).

Orienting Intervention. P12 applies in its most demanding form: assess \kappa(t) before any work on content. Restoring \kappa(t) structurally precedes Unveiling D_p(t).

C-B: Loop · Bidirectional · Chronic Residency

Definition by Axes. Dominant \Psi_t: bidirectional: B_t and the psychological domains perturb each other in a cycle. Basin: residency: the cycle is established and self-sustaining.

Derived Properties.

• \|H_t\|: low to moderate: the cycle consumes resources from every domain. B_t and at least one psychological domain are simultaneously compromised.
• \nabla H_t: sustained \approx 0: the stability belongs to the cycle, not to a field at rest.
• \varepsilon_t: low in the cycle's domains: chronic bidirectionality rigidifies \Psi_t's channels.

Empirical Domain of Origin: B_t in 64% of cases: the cycle frequently starts from the body, even though it perpetuates itself in both directions. A_t in 29%, R_t in 7%.

\Pi_R: preserved (50%) / biased (29%) / encapsulated (14%) / globally compromised (7%). Reality testing can be biased in the cycle's direction (for instance, toward safety in mania, toward control in eating disorders).

Speed: decades (57%) / years (43%). A chronic, slow-installing pattern.

D_p(t): high, the cycle accumulates plastic deformation in both directions. \kappa(t): reduced. Modal position in S_m: R2.

Modal Transition-Conditions Profile: \Beta_F: moderate: there can be flexibility within the cycle, but not to exit it. \Pi_R: variable. \Tau_F: moderate: narrative continuity exists but is organized around the cycle. \Upsilon_{US}: moderate: the cycle itself is the form stability takes.

Representative Clinical Correlates: chronic eating disorders (bulimia nervosa, binge eating disorder), OCD with a motor component (trichotillomania, excoriation), long-standing rapid-cycling bipolar disorder, chronic somatic disorders with a pain-depression cycle, established severe alcohol use disorder, BPD with a relational-somatic cycle.

Internal Logic. The bidirectional cycle is the field's organization, not an additive dysfunction. Interrupting the cycle at only one pole (only B_t or only the psychological domain) produces transient change: the cycle reconstitutes itself from the pole that was not addressed. The relevant intervention interrupts the cycle at its most accessible point, given current \kappa(t).

Typical Clinical Error. Intervening only on the somatic pole (symptoms, medication) without addressing the psychological pole, or vice versa. Failing to recognize that the cycle is the field's organization, not an added symptom.

Orienting Intervention. Identify the cycle's most accessible entry point given current \kappa(t) and M. Simultaneous multimodal intervention on both poles is more likely to interrupt the cycle than sequential intervention.

C-C1: Bond · Psychological→Bt · Reconfiguration · Relational Origin

Definition by Axes. Dominant \Psi_t: psych.→B_t: the perturbation originates in the bonding domain (R_t) and propagates toward B_t. Basin: reconfiguration: the field is in an active process of change. Domain of origin: R_t: the perturbation that starts or sustains reconfiguration is relational: a relational rupture, sustained invalidation, loss of an attachment figure, or reframing of relational history. This is the property that distinguishes C-C1 from C-C2, and the one k-modes clustering identified as a sufficient discriminator for two distinct valleys in \mathcal{W}.

Derived Properties.

• \|H_t\|: variable across evaluations: the reconfiguration process produces variation. The R_t domain shows the most marked movement; B_t is secondarily affected through propagation.
• \nabla H_t: variable, trending positive: the field is moving toward greater coherence, though with oscillations typical of the process.
• \varepsilon_t: moderate-to-high in R_t and adjacent domains: the field is receptive in the relational dimension.

Domain of Origin: R_t: a defining property of C-C1.

\Pi_R: preserved in nearly all cases. This is the most discriminating property relative to C-C2: intact reality testing is the condition of possibility for Unveiling work from the relational domain. The field can be relationally compromised without losing the capacity to update its representations.

Speed: predominantly years. Relational reconfiguration is slower than existential reconfiguration: accumulated relational history takes longer to reorganize.

D_p(t): variable, frequently moderate-to-high in the relational domain. \kappa(t): sufficient: active reconfiguration implies the field has receptive capacity. Modal position in S_m: R3 or an R2→R3 transition.

Modal Transition-Conditions Profile: \Beta_F: moderate-to-high: there is active exploration of new ways of relating. \Pi_R: preserved: the condition of possibility for the work. \Tau_F: low-to-moderate: relational narrative continuity is still being built. \Upsilon_{US}: moderate.

Representative Clinical Correlates: social anxiety disorder in treatment, PTSD with relational reactivation being actively processed, generalized anxiety disorder with a relational component, eating disorders in recovery with active relational work, complicated grief reframing a lost bond.

Representative corpus cases: Logan (5.1, social anxiety + panic), Nadine (5.3, social anxiety + PTSD + agoraphobia), Peggy Isaac (5.5, generalized anxiety disorder).

Internal Logic. The field is undergoing reconfiguration from the relational domain: the perturbation that started the process was relational, and reconfiguration is processed mainly through the relational dimension. Preserved \Pi_R is the condition that makes the work possible: the field can be relationally compromised without losing contact with shared reality. The clinical task is to protect the pace of the relational process and build \Tau_F so relational gains integrate into narrative continuity.

Typical Clinical Error. Accelerating reconfiguration beyond the field's relational pace. Treating secondary somatic symptoms as though they were the primary object of intervention. Failing to recognize that preserved \Pi_R is the central resource, and assuming fragility the field does not have.

Orienting Intervention. The relational field is the entry point and the primary instrument. Work on relational \Tau_F to integrate gains. Intervention on B_t is complementary and secondary to the relational work.

C-C2: Existential · Psychological→Bt · Reconfiguration · Existential Origin

Definition by Axes. Dominant \Psi_t: psych.→B_t: the perturbation originates in the existential-anchoring domain (A_t) and propagates toward B_t. Basin: reconfiguration: the field is in an active process of change. Domain of origin: A_t: the perturbation that starts or sustains reconfiguration is existential: a crisis of meaning, loss of anchoring, reframing of identity, rupture of the ground the trajectory operates from. This is the property that distinguishes C-C2 from C-C1.

Derived Properties.

• \|H_t\|: variable across evaluations, and frequently low during the acute phase of existential reconfiguration. The A_t domain shows the primary compromise; B_t is secondarily affected.
• \nabla H_t: variable: it can decline during the phase of existential disorganization and rise during the phase of reorganization. Direction is more unstable than in C-C1.
• \varepsilon_t: variable by domain: A_t can be either very open (receptive to reconfiguring meaning) or severely compromised (when existential anchoring has been lost).

Domain of Origin: A_t: a defining property of C-C2.

\Pi_R: variable: preserved, encapsulated, or globally compromised depending on the nature of the existential perturbation. This variability is the most discriminating property relative to C-C1, and it determines the entry strategy. When \Pi_R is compromised (psychosis under reconfiguration, mania with an underlying existential process), intervention must restore \Pi_R before working on existential content.

Speed: predominantly months, faster than C-C1, reflecting that existential reconfigurations can resolve faster when there is enough scaffolding, but can also deteriorate quickly when there is not.

D_p(t): variable. \kappa(t): variable: depends critically on the level of \Pi_R and the depth of the existential crisis. Modal position in S_m: R3 in cases with preserved \Pi_R; R2 or R4 when \Pi_R is compromised.

Modal Transition-Conditions Profile: \Beta_F: variable: high in trajectories with preserved \Pi_R, very low when \Pi_R is compromised. \Pi_R: variable: the most critical modulator for determining intervention. \Tau_F: low: existential narrative continuity is more disrupted than in C-C1. \Upsilon_{US}: variable.

Representative Clinical Correlates: a first episode of schizophrenia in active treatment (Gregory Baker, 2.2), manic bipolar I disorder with psychosis under reconfiguration (Mark Hill, 3.1), depressive bipolar II disorder with suicidal ideation being processed (Olivia Jacobs, 3.3), peripartum major depressive disorder (Yvonne Perez, 4.2), psychotic major depressive disorder (Barbara Reiss, 4.4), melancholic major depressive disorder (Crystal Smith, 4.5), culturally rooted somatic depression (Ka Fang, 4.12), severe opioid use disorder undergoing existential reconfiguration (Raymond Xavier, 16.5).

Internal Logic. The field is undergoing reconfiguration from the existential domain: loss of anchoring in meaning is the process's engine. The variability of \Pi_R is the most clinically relevant property: it determines whether existential Unveiling work is possible directly, or whether it first requires restoring the capacity to update representations. Unlike C-C1, in C-C2 the clinician cannot assume the field has access to shared reality: it must be assessed at every encounter.

Typical Clinical Error. Assuming every existential reconfiguration has preserved \Pi_R, and starting Unveiling work on existential content when \Pi_R is compromised. This produces disorganization instead of reconfiguration. The other error: treating foreground symptoms (psychosis, mania, severe depression) without recognizing the underlying existential reconfiguration process.

Orienting Intervention. The mandatory first assessment: the state of \Pi_R. If \Pi_R is preserved: direct work on existential content with relational scaffolding. If \Pi_R is compromised: restoring \Pi_R as the first intervention, before any Unveiling work. C-C2's faster speed relative to C-C1 means the windows for intervention are narrower, for deterioration as well as for consolidation.

C-D: Chrysalis · Bidirectional · Active Reconfiguration

Definition by Axes. Dominant \Psi_t: bidirectional: an active cycle between B_t and the psychological domains. Basin: reconfiguration: the cycle is changing; there is an active process of reorganization.

Derived Properties.

• \|H_t\|: low to moderate, with variation across evaluations: the changing cycle produces fluctuation.
• \nabla H_t: variable: trending positive in most cases, but with oscillations typical of the process of exiting the cycle.
• \varepsilon_t: moderate-to-high in the cycle's domains: the reconfiguration process has opened up the field.

Empirical Domain of Origin: B_t in 80% of cases: the cycle has a predominantly somatic origin even under reconfiguration.

\Pi_R: preserved (70%) / biased (30%). A high proportion of preserved \Pi_R: a significant difference from C-B (residency).

Speed: years (70%) / months (30%). Exiting the bidirectional cycle is a slow process.

D_p(t): moderate-to-high, the cycle has left a trace. \kappa(t): sufficient for the reconfiguration process, higher than in C-B. Modal position in S_m: R3 or an R2→R3 transition.

Modal Transition-Conditions Profile: \Beta_F: moderate-to-high: there is active exploration of alternatives to the cycle. \Pi_R: predominantly preserved. \Tau_F: moderate: still being built. \Upsilon_{US}: moderate.

Representative Clinical Correlates: alcohol use disorder in active recovery, gambling disorder in treatment, cyclothymia under reorganization, panic disorder in the process of deconditioning, mild neurocognitive disorder under early intervention.

Internal Logic. The bidirectional cycle is opening up: the field has enough \kappa(t) to sustain the process. The difference from C-B (residency) is that in C-D the field is actively searching for a new organization. Preserved \Pi_R is the condition of possibility for Unveiling work.

Typical Clinical Error. Failing to recognize that the cycle's somatic origin persists even under reconfiguration: intervening only on the psychological pole without sustaining work on B_t.

Orienting Intervention. Sustain the cycle's reconfiguration process at both poles simultaneously. Build \Tau_F so that episodes of coherence without the cycle integrate into accumulable narrative.

C-E: Jolt · Bt→Out · Transient

Definition by Axes. Dominant \Psi_t: B_t→psych.: the perturbation originates in B_t and propagates toward the psychological domains. Basin: transient: the field has not established a new basin; the perturbation is acute or subacute.

Derived Properties.

• \|H_t\|: variable: depends on the somatic perturbation's magnitude and propagation speed. The psychological domains can drop quickly if the somatic perturbation is severe.
• \nabla H_t: active: declining during the perturbation, rising during recovery. Direction is the critical clinical indicator.
• \varepsilon_t: moderate-to-high in the psychological domains: the psychological field can recover once the somatic perturbation ends.

Empirical Domain of Origin: B_t in 78% of cases: a pure pattern of somatic origin.

\Pi_R: preserved (78%); the field knows what is happening to it, the difficulty is somatic, not representational. Exception: substance-induced psychosis, where \Pi_R can be compromised.

Speed: weeks (56%) / days (33%). The fastest speed in the whole system (except C-J). Timescale is part of C-E's identity.

D_p(t): low to moderate, the field has no extensive accumulated history in this basin. \kappa(t): moderate-to-high: the field has receptive capacity to recover once the perturbation ends. Modal position in S_m: R3 during recovery.

Modal Transition-Conditions Profile: \Beta_F: moderate: the repertoire is not damaged, only disturbed. \Pi_R: preserved in most cases. \Tau_F: moderate: continuity holds except in severe forms. \Upsilon_{US}: moderate: variable depending on the perturbation's magnitude.

Representative Clinical Correlates: acute cannabis/THC-induced psychosis, premenstrual dysphoric disorder, steroid-induced anxiety, (neurological) depersonalization, pharmacologic sexual dysfunction, adjustment disorder with acute somatic stress, enuresis as a Bt field symptom.

Internal Logic. The psychological field is being disturbed from B_t but has not established a new basin: it is genuinely transient. Recovery is possible once the somatic perturbation ends or is treated. The priority intervention targets B_t, not the psychological domains, which are the effect.

Typical Clinical Error. Treating psychological symptoms as though they were the origin: starting intensive psychotherapy when the perturbation is acute and somatic. Failing to identify the underlying somatic cause.

Orienting Intervention. Identify and treat the originating somatic perturbation. The psychological domains do not require direct intervention in most cases: they recover once the somatic perturbation ends.

C-F: Suspension · Psychological→Bt · Transient

Definition by Axes. Dominant \Psi_t: psych.→B_t: the perturbation originates in the psychological domains and propagates toward B_t. Basin: transient: the field has not established a new basin; there is mobility.

Derived Properties.

• \|H_t\|: moderate, with variation: the field is disturbed but has resources. The psychological domains (A_t, R_t) show the primary compromise; B_t is secondarily affected (sleep, appetite, activation).
• \nabla H_t: active: can decline during the acute phase, rise during resolution.
• \varepsilon_t: moderate-to-high: the field has receptive capacity for resolution.

Empirical Domain of Origin: A_t in 63% of cases, R_t in 37%. The existential-anchoring and relational-bonds domains are the primary foci.

\Pi_R: preserved (75%), a high proportion, which facilitates Unveiling work. Reality testing is relatively intact.

Speed: months (50%) / weeks (25%). The most common pattern is resolution within months when there is enough scaffolding.

D_p(t): low to moderate. \kappa(t): moderate-to-high. Modal position in S_m: R3.

Modal Transition-Conditions Profile: \Beta_F: moderate-to-high. \Pi_R: preserved in most cases. \Tau_F: moderate: narrative continuity can be partially disturbed by the life event. \Upsilon_{US}: moderate.

Representative Clinical Correlates: adjustment disorder, uncomplicated grief, situational subthreshold depression, a brief psychotic episode (resolving), mild situational substance use disorder, a life crisis with somatic repercussions.

Internal Logic. The field is disturbed by a life event or process affecting the psychological domains, propagating secondarily toward B_t (grief producing changes in sleep, appetite, physical activity: the example Diego described). The basin is transient because the field has the capacity to reorganize without high-intensity intervention. Relational scaffolding and time are the first instruments.

Typical Clinical Error. Medicalizing a normal response to suffering. Intervening with high intensity in a field that can reorganize with sufficient scaffolding alone. Or, the reverse: not intervening when the transient state is becoming chronic, moving toward residency.

Orienting Intervention. Relational scaffolding as the first intervention. Monitor the direction of \nabla H_t to detect chronification toward C-A (residency). Work on the primary psychological domains is appropriate; B_t recovers secondarily.

C-G: Transformation · Bt→Out · Active Reconfiguration

Definition by Axes. Dominant \Psi_t: B_t→psych.: the perturbation originates in B_t and propagates toward the psychological domains. Basin: reconfiguration: the somatic field is in an active process of change.

Derived Properties.

• \|H_t\|: variable, heterogeneous across cases: the somatic reconfiguration process produces unpredictable variation in the psychological domains.
• \nabla H_t: heterogeneous: can be rising (somatic recovery), declining (somatic illness progression), or variable. Direction depends on the somatic process's nature.
• \varepsilon_t: variable by domain: the psychological domains can have preserved \varepsilon while B_t is undergoing change.

Empirical Domain of Origin: B_t in 100% of cases: a pure pattern of somatic origin under change.

\Pi_R: preserved (50%) / globally compromised (25%) / encapsulated (25%). More heterogeneous than C-E: somatic reconfiguration can compromise \Pi_R when the somatic process affects the neurobiological substrate.

Speed: years (38%) / months (25%) / heterogeneous. The most variable speed in the system: it reflects the diversity of somatic processes under reconfiguration.

D_p(t): moderate-to-high, the somatic process leaves a trace. \kappa(t): variable depending on the process's phase. Modal position in S_m: R3 during phases of improvement; R2 during phases of progression.

Modal Transition-Conditions Profile: \Beta_F: moderate: can be limited by the somatic process. \Pi_R: variable: the most critical modulator for determining intervention. \Tau_F: moderate. \Upsilon_{US}: moderate, variable depending on the somatic phase.

Representative Clinical Correlates: HIV+ methamphetamine-induced bipolar disorder in recovery, postpartum psychosis (post-delivery reconfiguration), Parkinson's-related depression in treatment, avoidant/restrictive food intake disorder (ARFID) in recovery, Huntington's-related neurocognitive disorder (progression), post-TBI neurocognitive disorder (recovery), cocaine withdrawal-induced depression.

Internal Logic. The somatic process is active: it is a process unfolding over time, not a perturbation that ends (C-E). The somatic process's direction determines the psychological field's direction. Intervention on the psychological domains is relevant but secondary to managing the somatic process.

Typical Clinical Error. Failing to update the reading of the field when the somatic process changes phase. Intervening on the psychological domains as though they were autonomous, when they depend on the somatic process.

Orienting Intervention. Frequent monitoring: C-G's heterogeneous speed requires more frequent assessment than stable-basin configurations. Psychological intervention is calibrated to the somatic process's phase and the level of \Pi_R.

C-H: Vortex · Bidirectional · Transient

Definition by Axes. Dominant \Psi_t: bidirectional: a cycle between B_t and the psychological domains. Basin: transient: the cycle is not yet established; it can still break.

Derived Properties.

• \|H_t\|: moderate, with variation: the transient cycle has not yet produced the level of D_p(t) that C-B will produce if it becomes chronic.
• \nabla H_t: oscillating: the cycle produces variation across evaluations with no sustained direction.
• \varepsilon_t: moderate: the field has more response capacity than in C-B (residency).

Empirical Domain of Origin: heterogeneous, B_t, A_t, R_t, and multi-domain cases. Origin is less clear-cut than in other configurations, which is itself a property of C-H.

\Pi_R: variable (preserved 40%, encapsulated 20%, still developing 20%, biased 20%). The heterogeneity of \Pi_R in C-H reflects the diversity of processes producing this pattern.

Speed: weeks (40%) / months (40%). Faster than C-B: the cycle is not yet chronic.

D_p(t): low to moderate. \kappa(t): moderate-to-high: the intervention window before chronification is the main clinical resource. Modal position in S_m: R3.

Modal Transition-Conditions Profile: \Beta_F: moderate. \Pi_R: variable. \Tau_F: moderate. \Upsilon_{US}: moderate.

Representative Clinical Correlates: early-phase panic disorder, social anxiety disorder with a somatic component, acute insomnia with anxiety, disruptive mood dysregulation disorder (pediatric), a normative reaction with a somatic cycle.

Internal Logic. The bidirectional cycle is recent and not yet consolidated. This is the most valuable intervention window among the bidirectional configurations: the field can reorganize toward a cycle-free pattern before residency sets in. Early detection of C-H is the single most important preventive tool for avoiding progression to C-B.

Typical Clinical Error. Not acting on the cycle while it is still transient. Waiting for the pattern to consolidate before intervening: by then it will have become chronic, moving toward C-B.

Orienting Intervention. Act on the cycle at its most accessible point given current M. The weeks-to-months speed is the window: the field can organize itself differently if the intervention is precise during this phase.

C-I: Embodiment · Bt→Out · Chronic Residency

Definition by Axes. Dominant \Psi_t: B_t→psych.: the perturbation originates in B_t and propagates toward the psychological domains. Basin: residency: the somatic pattern is chronic, and the psychological field is organized around it.

Derived Properties.

• \|H_t\|: low to moderate: chronic somatic dysfunction has stably compromised the psychological domains. B_t is the most compromised domain; the psychological domains show established secondary compromise.
• \nabla H_t: sustained \approx 0: the field is not moving; the chronic condition is the attractor.
• \varepsilon_t: low in B_t: the chronic history of the somatic process has rigidified the somatic domain.

Empirical Domain of Origin: B_t in 100% of cases: a pure pattern of chronic somatic origin.

\Pi_R: preserved (60%) / still developing (40%). The 40% still-developing figure is the highest proportion in the corpus: it reflects that severe chronic neurocognitive and sleep disorders compromise elaborative capacity.

Speed: decades (80%) / years (20%). The slowest installation pattern among the B_t→psych. configurations.

D_p(t): high, decades of somatic process leave a deep trace. \kappa(t): reduced by chronicity. Modal position in S_m: R2.

Modal Transition-Conditions Profile: \Beta_F: low-to-moderate: the response repertoire is limited by the chronic somatic process. \Pi_R: preserved or still developing. \Tau_F: moderate: narrative continuity exists but is organized around the somatic condition. \Upsilon_{US}: low-to-moderate.

Representative Clinical Correlates: established sleep apnea-hypopnea syndrome (decades), chronic idiopathic hypersomnia, major neurocognitive disorder (Alzheimer's, Lewy body) in the residency phase, severe alcohol use disorder with established chronic withdrawal.

Internal Logic. The chronic somatic process has reorganized the psychological field around it: the psychological field is not autonomous from B_t in C-I. Intervening on the psychological domains without treating the somatic process produces minimal change. In neurocognitive disorders, the somatic process's direction (progressive vs. stable) determines the field's direction.

Typical Clinical Error. Intervening on psychological symptoms without recognizing they are a secondary effect of the chronic somatic process. In neurocognitive disorders, setting goals for psychological reorganization that are incompatible with the somatic process's progression.

Orienting Intervention. Managing the somatic process is the primary intervention. The psychological domains respond secondarily; and in progressive neurocognitive disorders, the clinical goal shifts toward preserving quality of life within the accessible field.

C-J: Collapse · Global Collapse · Transient

Definition by Axes. Dominant \Psi_t: global collapse: every \Psi_t channel is disturbed simultaneously; there is a collapse of integration, not a preferential direction. Basin: transient in most cases (though it can install as residency in chronic forms: see Lucas Sandahl, dissociative identity disorder).

Derived Properties.

• \|H_t\|: very low: global collapse compromises every domain simultaneously. H_t is a norm close to zero across every domain, not a vector with an asymmetric profile.
• \nabla H_t: < 0 during collapse, variable during recovery.
• \varepsilon_t: very low across every domain: collapse eliminates the field's receptive capacity.

Empirical Domain of Origin: B_t in 67%, R_t in 17%, A_t in 17%. Collapse frequently has an acute somatic origin, or arises through a bypass of \Pi_R.

\Pi_R: globally compromised (67%) / bypass (33%). This is the only configuration where compromised or bypassed \Pi_R is the norm, not the exception. This is C-J's most discriminating property.

Speed: hours (50%) / days (33%). The fastest configuration in the system: an hours-long timescale is definitional for C-J.

D_p(t): variable, can be low (acute collapse with no history) or high (collapse on top of a field with extensive history). \kappa(t): minimal during collapse: P12 in its most urgent form. Position in S_m: R4 (maximum urgency).

Modal Transition-Conditions Profile: \Beta_F: very low: collapse eliminates the response repertoire. \Pi_R: compromised or bypassed: the most critical variable for C-J. \Tau_F: very low: narrative continuity does not operate during collapse. \Upsilon_{US}: minimal.

Representative Clinical Correlates: postoperative delirium (hours), anticholinergic delirium (days), steroid-induced catatonia (days), acute postpartum psychosis (hours), impulsive suicidal collapse (hours: bypass), an acute panic attack (hours), dissociative identity disorder in an acute episode (residency with episodes of collapse).

Internal Logic. C-J is qualitatively distinct from every other configuration because there is no direction of propagation: there is a collapse of integration. Intervention cannot operate on the field's content because compromised or bypassed \Pi_R blocks processing. The priority intervention is restoring the field's integration before any work on content.

Note on C-J With a Residency Basin. Lucas Sandahl (dissociative identity disorder, bypass, residency, years) represents a C-J subtype where episodic collapse has become established as a residency pattern. This may justify a C-J(r) subtype in later versions.

Typical Clinical Error. Attempting psychotherapeutic or Unveiling work during collapse. Underestimating clinical urgency. Not prioritizing restoration of the field's integration.

Orienting Intervention. Priority: restore the field's integration. This structurally precedes any other work, including diagnosing the cause. In collapse through bypass, intervening on B_t^{(a)} (baseline autonomic activation) is the most urgent. In collapse through globally compromised \Pi_R, basic containment and orientation of the field precede diagnosis.

C-K: Idiosyncratic · Early Dispositional Basin

Definition by Axes. Basin: early dispositional: the field organized itself during early development, before symbolic resources existed to elaborate it. This is the deepest basin in the system: installed in \sigma_t (the pre-symbolic dispositional structure, a component of \xi_t formalized in D8 of the Ontological Core v2.3.5). \Psi_t: variable: psych.→B_t in 67% of cases, B_t→psych. in 33%.

Derived Properties.

• \|H_t\|: variable: the field can have high coherence within its own logic (as in autism without intellectual disability, or ASPD) or low coherence across multiple domains (as in autism with intellectual disability, or severe developmental relational trauma).
• \nabla H_t: sustained \approx 0: the dispositional basin's depth produces extreme stability. The field does not move toward different configurations without sustained, very-high-magnitude perturbation.
• \varepsilon_t: very low: early dispositional history has produced the deepest rigidification in the system.

Empirical Domain of Origin: R_t in 67%, B_t in 33%. Early relational bonding (attachment) is the most frequent domain of origin: consistent with the basin's dispositional nature.

\Pi_R: still developing (33%) / preserved (33%) / encapsulated (17%) / globally compromised (17%). The still-developing proportion is the highest in the corpus: it reflects that some early dispositional basins compromise the development of \Pi_R (as in autism with intellectual disability, or severe developmental relational trauma).

Speed: decades (67%) / years (33%). The slowest speed in the system: the dispositional basin is the most resistant to change.

\sigma_t: highly relevant; C-K is the configuration where \sigma_t carries the greatest weight in \xi_t. Narrative interventions have limited access; interventions centered on B_t, the early relationship, and the sensory environment have the greatest access to \sigma_t.

D_p(t): maximal, the basin is the oldest history there is. \kappa(t): structurally minimal: by the field's constitution, not from fatigue. The distinction between reduced \kappa(t) from accumulated history and constitutively low \kappa(t) is clinically critical: in C-K, low \kappa(t) is not restorable the way it is in other configurations.

Position in S_m: R2, but with the characteristic that C_{\text{umbral}}(D_p) is very low, which limits the magnitude of any intervention.

Modal Transition-Conditions Profile: \Beta_F: low-to-moderate: the repertoire is strongly conditioned by the dispositional field. \Pi_R: variable: from still developing to preserved. \Tau_F: low: conventional narrative continuity has limited access to the dispositional field. \Upsilon_{US}: low.

Representative Clinical Correlates: autism with intellectual disability and an underlying genetic syndrome, childhood-onset schizophrenia, severe developmental relational trauma, conduct disorder with callous-unemotional traits, antisocial personality disorder (installed in early development with conduct disorder as a precursor), pedophilia with antisocial personality disorder (an extreme case).

Internal Logic. C-K is the system's most radical case of isomerism: the field has a constitutive geometry installed before language. Two trajectories in C-K with a similar H_t can have radically different configurations, because the dispositional basin has specific content: autism with intellectual disability and antisocial personality disorder are polymorphs of the same dispositional basin in terms of depth and pre-symbolism, but with completely different organizations.

Genomic prediction has particular value in C-K: variants that modulate the sensitive periods of attachment and early relational development are the most direct correlates of the dispositional basin.

Typical Clinical Error. Applying interventions designed for residency or reconfiguration basins to a dispositional basin: expectations for change are incompatible with the field's nature. Confusing the dispositional basin's stability with voluntary resistance to change.

Orienting Intervention. The interventions with the greatest access to \sigma_t: centered on the body (B_t), long-standing relational work, the sensory environment. Narrative interventions have differential access: they can modify D_p(t) without direct access to \sigma_t. The clinical goal is to widen the field of possibilities \mathcal{F}_t^{(p)} within the dispositional geometry, not to reorganize the basin.

C-L: Encapsulation · Segmented · Residency/Reconfiguration

Definition by Axes. Dominant \Psi_t: segmented: some \Psi_t channels are selectively blocked. The encapsulated content exists in the field but does not propagate toward ordinary consciousness. Basin: variable (residency or reconfiguration depending on the case).

Derived Properties.

• \|H_t\|: apparently normal in the non-segmented domains: the field looks preserved on standard assessment. The observable profile does not reflect the field's real compromise.
• \nabla H_t: sustained \approx 0 in the non-segmented domains: the field looks stable from the outside. The real movement happens in the encapsulated material.
• \varepsilon_t: preserved in the accessible domains; the blocked segment has no \varepsilon assessable from outside.

Empirical Domain of Origin: A_t in 100% of the corpus cases: existential anchoring is the domain most frequently involved in segmentation. N=2: an orienting data point, not conclusive.

\Pi_R: preserved in every corpus case. This is C-L's most discriminating property: the field knows it exists, but there is content that does not propagate toward ordinary consciousness. This is not a compromise of \Pi_R: it is a segmentation of propagation.

Speed: decades in every case; the segmentation pattern is long-standing.

Note on N=2. The Barnhill corpus severely underrepresents dissociative disorders and sexual dysfunctions of psychological origin. C-L's justification as a canonical configuration is theoretical and clinical, not statistical, in this corpus.

D_p(t): high, the long-standing segmented pattern has left a deep trace. \kappa(t): low in the blocked segment: not available for direct Unveiling.

Modal Transition-Conditions Profile: \Beta_F: moderate in the accessible domains; irrelevant in the segment. \Pi_R: preserved: the condition of possibility for clinical work. \Tau_F: moderate in the accessible domains. \Upsilon_{US}: moderate.

Representative Clinical Correlates: dissociative amnesia with PTSD (Judith Vaughan), existentially rooted female sexual dysfunction (Elizabeth Olsen). On clinical and theoretical grounds: dissociative identity disorder, psychogenic amnesia, conversion disorders with a dissociative mechanism.

Internal Logic. Segmentation is the mechanism by which the field preserves coherence in the accessible domains at the cost of blocking propagation from the disturbing material. It is an organization that widened \mathcal{F}_t^{(p)} in the accessible domains and allowed functionality to be maintained, not a failure of the field. The relevant intervention is creating the conditions of \kappa(t) and relational safety under which the field can gradually integrate the blocked material, not forcing access to the segment.

Typical Clinical Error. Attempting direct access to the blocked material without establishing sufficient \kappa(t) conditions: this produces either reblocking or destabilization. Underestimating segmentation's function as an organization that widened \mathcal{F}_t^{(p)}.

Orienting Intervention. Build \kappa(t) and relational safety before any Unveiling work on the blocked material. The field, not the clinician, sets the pace of access to the segment.

C-M: Drift · Psychological→Bt · Failed Reconfiguration

Definition by Axes. Dominant \Psi_t: psych.→B_t: the perturbation originates in the psychological domains and propagates toward B_t. Basin: failed reconfiguration: the field tries to leave the basin without succeeding; there is movement with no consolidation.

Derived Properties.

• \|H_t\|: oscillating: the field produces episodes of coherence that fail to consolidate. The profile shows variability with no sustained direction.
• \nabla H_t: oscillating with no sustained direction: this is the formal property distinguishing C-M from every other configuration. \nabla H_t is oscillating without consolidation: neither sustained positive (C-C), sustained negative (historical cathexis), nor zero (residency).
• \varepsilon_t: apparently sufficient to start reorganizations, but insufficient to consolidate them: the field reaches the reorganization threshold but cannot sustain it.

N=1 in the corpus. Isaac Ulysse (major depressive disorder with prolonged grief) is the only case with this pattern in Barnhill 2023. C-M's justification as a canonical configuration is theoretical and clinical, not statistical, in this corpus.

Justification for C-M as a canonical configuration. Prolonged grief as failed reconfiguration is a clinically recognized pattern that DSM-5-TR barely formalizes as "prolonged grief disorder." In the real population, analogous reconfiguration failures are common: addictions where the recovery process repeatedly fails to establish a new, stable basin, long-standing therapeutic processes producing movement with no consolidation, life transitions that fail to reorganize the field. The Barnhill corpus is not the universe: it severely underrepresents these patterns.

\Pi_R: biased in the corpus's only case. The hypothesis is that the bias in \Pi_R is part of the failure mechanism: the field interprets reality in a way that confirms the impossibility of reconfiguration (grief that cannot complete because it would mean "betraying" the lost object, addiction that fails because recovery is "impossible").

Empirical Domain of Origin: R_t: reconfiguration failure has a relational origin in the corpus's only case.

Speed: months in the only case. The hypothesis is that C-M's speed is variable: it can be months or years depending on the magnitude of the material blocking reconfiguration.

D_p(t): moderate-to-high, failed reconfiguration attempts accumulate D_p(t). \kappa(t): variable: sufficient to start reorganizations but insufficient to consolidate them. The hypothesis is that \kappa(t) restores between attempts but gets consumed with each failed attempt.

Gap G-Duelo1. C-M is the configuration that formalizes gap G-Duelo1 from the mapping's findings log. Fully formalizing C-M requires pilot data: in particular, specifying the \xi_t conditions that produce failed reconfiguration versus successful reconfiguration.

Subform identified in the mapping (June 21, 2026): prolonged grief disorder presents a specific version of C-M with a mechanism distinguishable from the generic oscillatory cycle: there is a prior residency attractor (the relationship with the deceased person) that keeps organizing the field after its source disappeared. It is the active persistence of an attractor that cannot update itself because its external object no longer exists, not a consolidation failure from κ(t) exhaustion. In the model's terms: the field tries to reorganize toward configurations that would require an Ω_t^(p) compatible with that person's presence, which is no longer accessible. This subform may be distinguishable from the generic C-M oscillatory cycle by its Ψ_t profile (persistent propagation toward an absent relational object) and by the temporal horizon of reorganization attempts (correlated with significant dates in the lost relationship). Pending full formalization in Pending Item 3 of this same section.

Modal Transition-Conditions Profile (hypothetical: N=1): \Beta_F: moderate: the field can attempt reorganizations but not consolidate them. \Pi_R: biased: in the direction that confirms change is impossible. \Tau_F: low: gains do not integrate into continuous narrative. \Upsilon_{US}: moderate.

Hypothetical Clinical Correlates: prolonged grief disorder, addictions with repeated failed recovery attempts, long-standing therapeutic processes with no consolidation, blocked life transitions (forced emigration with unprocessed cultural grief, post-traumatic cases with failed elaboration).

Internal Logic. The field is not in residency: there is movement. It is not in successful reconfiguration: gains do not consolidate. The failure is in the new basin's consolidation mechanism: the field reaches the reorganization threshold, but something pulls the mass back to the previous basin before the new organization can establish itself. Identifying that mechanism is the central clinical object in C-M.

Typical Clinical Error. Treating C-M as C-C1 or C-C2 (successful reconfiguration) and increasing intervention intensity when gains fail to consolidate: this can produce plasticity that restricts \mathcal{F}_t^{(p)}. Or treating it as voluntary resistance to change.

Orienting Intervention. Identify the specific consolidation-failure mechanism for this trajectory. The biased \Pi_R that confirms change is impossible is the first entry point. Building \Tau_F so episodes of coherence become recognizable and accumulable is the central work.

Relational Vocabulary (Retired: Historical Status)

The relational vocabulary (7 technical terms of Greek root: Eutropy, Dysintropy, Neotropy, Cathexy, Apexy, Anastropy, Heterotropy, formalized on June 10, 2026, alongside the names of the 14 canonical configurations) was retired from the corpus by Diego F. Pereira-Perdomo's explicit instruction. It served its heuristic function during the model's construction and merges, in status, with the 7 already-historical Greek terms (Eudaimonia, Euexia, Allotropy, Anexia, Epitropy, Entelopy, Proexia: see the Formal Dictionary). No Greek term, from either generation, is active. The only nomenclature system currently in force is canonical system v1.2's 14 names and their canonical phrases, below.

Canonical Phrases by Configuration

Canonical phrases are approved clinical formulations for communicating each configuration's internal logic to the patient. They are the bridge between technical formalization and the language of the clinical encounter.

Cross-Cutting System Properties

Relationships Between Configurations

The individuation field \Omega_t^{(p)} distributes mass across multiple configurations simultaneously: configurations are not mutually exclusive states. The configurations that most frequently coexist:

Structural Transition Hypothesis (HST). The Ontological Core's research agenda v2.3.5 (extension of G10, horizon H1) proposes the falsifiable hypothesis that transitions between configurations satisfy three qualitative properties: hysteresis (the threshold for entering \mathfrak{C}_j from \mathfrak{C}_i differs from the threshold for leaving it); neighborhood (short-range transitions in canonical space are more probable than long-range ones); and S_m condition (when \kappa(t) < \kappa_{\text{umbral}}, transitions that restrict \mathcal{F}_t^{(p)} are more probable). The HST is what the pilot can refute, not what it confirms. Its quantitative formalization as a transition function is the object of H2. The transition-routes table (Pending Item 2) should be derived once pilot data allow testing the three properties.

• C-A and C-B: chronic psychological entrenchment and the chronic cycle share the residency basin; movement between them is frequent when the cyclical somatic component is added or lost.
• C-C1, C-C2, and C-D: psychological reconfiguration (relational and existential) and bidirectional-cycle reconfiguration share the active process of change; they can coexist in trajectories with mixed components.
• C-E and C-F: acute somatic perturbation and situational psychological perturbation share the transient basin; grief with somatic repercussions is the paradigmatic example of both active simultaneously.
• C-J and any other: global collapse can overlay any base configuration when the perturbation exceeds every threshold.

\|H_t\| and \nabla H_t as Derived Properties

Each configuration has modal ranges of \|H_t\| and \nabla H_t:

Pendientes formales

1. \Omega_t^{(p)} profiles by configuration: require pilot data to specify the distribution of mass across adjacent configurations.

2. Transition-routes table: the historical system had a table of frequent routes (Chapter 6, §6.4.2) derived from the 14 configurations. This table needs to be re-derived from canonical system v1.2. Closed at the level of per-pair determination (June 21, 2026): Mathematical Core v0.4.21, §III.12bis, gives explicit status to all 182 possible directed pairs among the 14 configurations, through an auditable rule system (not 182 loose judgment calls): 64 declared verbatim in "Global Topology," 41 extended by analogy (32 textual, 9 structural), 77 with no reasonable textual or analogical basis, explicitly declared as such. What remains open, and does require the pilot: no \mu_{\text{alto}} has a fixed numerical magnitude; the 77 baseless pairs stay at \mu=1 by default, for lack of grounding, not by decision: most involve C-M (whose own profile states "full formalization requires pilot data"), entry into C-K, or C-L (N=2 in its own profile). Full table with per-cell provenance: tabla_mu_ij_completa.csv.

3. Formalizing C-M: G-Duelo1. Requires a dedicated session with the Mathematical Core §II.7bis (D_p(t) as a function over \mathcal{W}: differential erosion) and pilot data on the \xi_t conditions that produce consolidation failure versus successful reconfiguration. (ApB absorbed into Mathematical Core v0.4.0.)

4. C-J(r) subtype: C-J with a residency basin (Lucas Sandahl, dissociative identity disorder). Closed (June 21, 2026): not introduced as a separate configuration. Applying the same policy already established for C-A/C-F ("while the pilot has not produced that evidence, they remain unified: introducing the split before having empirical evidence that distinguishes them would produce unsupported configurations, which the model avoids," Ontological Core, "Global Topology"): a single case (N=1) is the exact same situation already decided against resolving by subdivision. C-J(r) stays documented as a note within C-J's profile (already there, see line 956), not as a separate candidate configuration. This reopens if the pilot produces more cases of the same pattern.

5. Integration with the 7 emergent organizations: completed in v1.1. The systematic comparison produced 5 direct correspondences and motivated splitting C-C into C-C1 and C-C2. The residual open questions are declared as an extension of G10.

6. Mathematical closure: assess whether there are combinations of dominant propagation organization × basin with theoretical justification but N=0 in the corpus that should be declared speculative candidate configurations. Assessed (June 21, 2026): systematically reviewed the 9 crossings of the regular grid (all populated) and the crossings of each special value of Axis 1 (segmented, global collapse) and Axis 2 (early dispositional, failed reconfiguration) against the rest of the space. One real, non-forced candidate: segmented × transient: C-L (N=2 in the corpus) is documented as a "decades" pattern exclusively; an acute/transient segmentation (e.g. transient dissociative amnesia after acute trauma, distinct from C-L's chronic pattern) is theoretically plausible and consistent with the segmentation logic already described, and C-L's own profile states that "the Barnhill corpus severely underrepresents dissociative disorders": N=0 is more likely a sampling artifact than a real absence. Not introduced as a new configuration (that would be exactly the error the C-A/C-F policy already avoids); it is recorded here as a named speculative candidate, pending confirmation or rejection by the pilot (or a future clinical case). No other reviewed crossing had sufficient theoretical justification to be named.

Relationship to the Historical System

The 14 configurations of the historical system (v0.3.0) remain as a record of the model's conceptual development. Some names and internal logics carry over into system v1.1: the correspondence is not exact, but there is partial alignment:

The configurations with no direct equivalent (C-E, C-G, C-I, C-K, C-L, C-M) are the specific contribution of incorporating B_t as the fifth constitutive domain and of the 105-case mapping analysis. C-C1 and C-C2 are the contribution of systematic comparison with the 7 emergent organizations from k-modes clustering.

Version 1.3.15 — June 22, 2026. Author: Diego F. Pereira-Perdomo MD, MSci. Approved by Diego F. Pereira-Perdomo. Empirical basis: profile matrix, 105 Barnhill 2023 cases (matriz_perfiles_sintr_v0_1_0.tsv). Comparison: 7 emergent organizations from k-modes clustering. Cross-check against: Ontological Core v2.3.16, Formal Dictionary v0.4.18. Any modification requires a new semantic version and explicit approval.