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1. Purpose

The Basin Geometry Mapper maps the attractors, basins, boundaries, exit costs, snap-back forces, transition paths, and stabilizing conditions that shape system behavior over time.

It exists because many systems do not move according to stated intention alone.

They move according to the field geometry created by:

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incentives
memory
resource flows
trust gradients
dependencies
exit costs
hidden debt
power asymmetry
role boundaries
classification habits
technical architecture
institutional routines
external pressure

A system may claim one goal while repeatedly returning to another pattern.

BGM asks:

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What basin is the system actually in, and what attractors are shaping its motion?

The Constructs & Operating Systems Registry identifies Basin Geometry Mapper as the construct used to map basins, attractors, snap-back forces, exit costs, transition pathways, and recurrence fields before restoration or redesign proceeds.

2. Core Question

What attractor basin is active, what forces stabilize it, and what transition pathways exist toward a more coherent basin?

Secondary questions:

What basin is the system currently in?
What attractor dominates behavior?
What secondary attractors compete with it?
What boundaries define the basin?
What keeps the system inside the basin?
What exit costs prevent transition?
What snap-back forces return the system after repair?
What support structures stabilize the current basin?
What support structures would stabilize a target basin?
What hidden debt reinforces the basin?
What affected nodes are trapped, burdened, or stabilized?
What transition energy is required?
Is recurrence evidence of an unmapped basin?
Is ∅ required because the basin cannot yet be mapped coherently?

3. Construct Class

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Field	Value
Construct Class	Basin Geometry / Attractor Mapping Construct
Secondary Class	Field Geometry / Recurrence / Transition Mapping Construct
Operating System	No
Primary Module	Basin Geometry / Coherence / Restoration
Related Modules	Scaling, Cybernetics, Institutions, Security, AI Governance, JGL

BGM is a mapping construct.

It does not primarily repair the basin. That is the role of Basin-Aware Restoration.

Its core role is:

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make the basin visible before restoration, redesign, reintegration, or transition is attempted

4. Core Basin Model

BGM distinguishes between:

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current basin
target basin
failure basin
restoration basin
transition basin
collapsed basin
pseudo-coherent basin

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Basin Type	Meaning
Current Basin	The field the system is presently organized within.
Target Basin	The desired coherent field.
Failure Basin	A basin that reproduces a known failure mode.
Restoration Basin	A basin where repair becomes self-supporting.
Transition Basin	A temporary field between basins.
Collapsed Basin	A basin where boundaries, trust, and function have degraded.
Pseudo-Coherent Basin	A basin that appears stable while hiding debt or burden.

BGM’s core mapping pattern:

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behavior recurrence
→ attractor identification
→ basin boundary mapping
→ exit-cost mapping
→ snap-back mapping
→ transition-pathway mapping
→ time validation

Compressed:

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BGM = Μ(attractors + basins + boundaries + transitions)

Its core distinction:

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stated goal is not dominant attractor

5. When to Use

Use the Basin Geometry Mapper when recurring behavior, institutional drift, AI behavior, social dynamics, security regimes, economic structures, or restoration failures suggest a hidden basin is shaping outcomes.

Use BGM when:

a failure repeats after repair
the system keeps returning to an old pattern
incentives contradict stated values
an institution says one thing but does another
AI behavior drifts back after prompt, policy, or model adjustment
a security regime escalates after every incident
a contract creates dependency or lock-in
a platform captures users through exit costs
trust does not return after formal repair
reintegration risks restoring old coupling
economic extraction persists despite reform
legitimacy loss becomes self-reinforcing
hidden debt explains recurrence better than visible events
restoration requires basin change rather than isolated repair

Do not use BGM as the primary construct when the central question is:

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If the question is...	Prefer...
How should restoration be designed around basin pull?	Basin-Aware Restoration
What executive interface controls attractor transition?	AGEI
Which restoration arc applies?	RAM
What operator sequence should run?	OSB
Is coupling becoming capture?	DCRL
Can trust/access return?	Reintegration Membrane
Did the system settle?	RDE
What failure mode is active?	FMM
Is institutional trajectory improving?	ICTE

BGM maps basin geometry; BAR uses that map to design restoration.

6. Derivation

BGM is derived from a recurring UTS pattern:

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system declares target state
+ behavior repeatedly returns to old pattern
+ visible explanations change
+ recurrence remains
= dominant attractor is not stated goal

A second pattern:

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repair action succeeds briefly
+ basin forces remain unchanged
+ system snaps back
= unmapped basin geometry

A third pattern:

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nodes want exit
+ dependency, cost, identity, access, or risk blocks exit
+ basin persists through lock-in
= exit-cost basin stabilization

BGM exists because repeated behavior reveals field geometry.

Its core distinction is:

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recurrence reveals basin structure

7. UTS Basis

BGM assembles the following UTS mechanics.

7.1 State Variables

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Variable	Role in BGM
O	Measures coherence of current basin and target basin.
H	Tracks hidden debt that stabilizes old or pseudo-coherent basins.
ε	Tracks uncertainty in basin identification and transition pathway.
ι	Detects inversion where a stated restoration basin is actually failure-basin restoration.
Au	Measures traceability of attractor forces, recurrence, and basin boundaries.
µᵢ	Preserves meaning, identity, and affected-node standing during basin mapping.
BΣ	Tracks basin boundaries, exit boundaries, and coupling boundaries.
K	Tracks compatibility between system state, basin conditions, and possible transitions.
R	Measures restoration capacity required to shift or stabilize a basin.
Φ	Tracks attractor force, pressure, control, urgency, scarcity, and environmental forcing.

7.2 Primary U-Layer Pattern

BGM most commonly localizes through:

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U6 → U7 → U2 → U5 → U8

Meaning:

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coherence field / attractor
→ recurrence memory
→ basin boundaries and exit costs
→ transition timing
→ external forcing

Basin geometry appears first as field behavior, repeats through memory, is stabilized by boundaries and exit costs, changes through time, and is pressured by the environment.

8. Inputs

8.1 Core Observational Inputs

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Input	Description
System under mapping	The system, institution, AI workflow, platform, security regime, economy, relationship, or field being analyzed.
Dominant behavior pattern	The pattern that repeatedly appears regardless of stated goals.
Current basin	The basin the system appears to occupy now.
Candidate basins	Possible basin classes that may explain recurrence.
Dominant attractor	The strongest pull shaping system behavior.
Secondary attractors	Other attractors competing with or reinforcing the dominant one.
Basin boundaries	Conditions that separate this basin from other basins.
Entry conditions	What causes nodes or systems to enter the basin.
Exit costs	What makes leaving difficult.
Snap-back forces	Forces that return the system to the basin after intervention.
Transition pathways	Routes from current basin to target basin.
Support structures	Conditions that stabilize the basin or target basin.
Recurrence history	Repeated behavior, relapse, drift, or snap-back evidence.
Affected nodes	Nodes shaped, trapped, stabilized, burdened, or protected by the basin.
External forcing	Environment, adversary, market, crisis, scarcity, policy, or cultural pressure.

8.2 Diagnostic Inputs

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Diagnostic	What It Measures	Why It Matters
Attractor Pull	Strength of dominant and secondary attractors	Determines likely motion.
Basin Stability	How stable or fragile the current basin is	Guides transition difficulty.
Basin Boundary Integrity	Whether basin boundaries are clear or leaking	Needed for map accuracy.
Exit Cost	Cost of leaving basin	High cost stabilizes basin.
Snap-Back Risk	Likelihood of return after intervention	Core BGM diagnostic.
Transition Energy	Energy required to move basin	Determines feasibility.
Hidden Debt	Deferred burden stabilizing basin	Reveals pseudo-coherence.
Feedback Integrity	Whether basin behavior can learn from signals	Determines adaptability.
Damping	Whether basin transition settles or oscillates	Needed for transition planning.
Recurrence Risk	Likelihood old behavior repeats	Confirms basin pull.
Legitimacy Baseline	Trust supporting or undermining basin	Critical for institutional basins.
Dependency Load	How much nodes depend on basin structure	Raises lock-in.
Coupling Depth	How deeply nodes are bound to the basin	Determines release difficulty.
Restoration Capacity	Capacity available to shift or stabilize basin	Required for basin change.
Time Validation	Whether basin map holds across time	Prevents premature classification.

9. Outputs

BGM produces basin maps, attractor maps, transition maps, and recurrence interpretations.

9.1 Basin Classification Assessment

Possible outputs:

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Current basin identified
Current basin provisional
Failure basin active
Pseudo-coherent basin active
Transition basin active
Collapsed basin active
Restoration basin possible
Target basin under-supported
Basin unclear

9.2 Attractor Assessment

Possible outputs:

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Dominant attractor identified
Dominant attractor provisional
Secondary attractors identified
Attractor conflict active
Attractor concealed
Attractor misidentified
Attractor pull high
Attractor pull low

9.3 Transition Assessment

Possible outputs:

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Transition pathway visible
Transition pathway partial
Transition pathway blocked
Transition energy high
Transition energy underfunded
Exit cost blocking transition
Support structure missing
Snap-back risk high
No coherent transition path

9.4 Decision Outputs

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Output	Meaning
Basin mapped	Basin geometry is sufficiently mapped for next construct.
Identify dominant attractor	Dominant behavior-shaping force must be named.
Map secondary attractors	Competing or reinforcing attractors require mapping.
Repair basin boundary	Boundary between basins is unclear, collapsed, or leaking.
Reduce exit cost	Nodes or system cannot leave old basin coherently.
Reduce snap-back risk	Old attractor forces must be weakened.
Increase support	Target basin lacks stabilizing structures.
Map transition pathway	Need route from current to target basin.
Rerun basin mapping	Basin evidence is insufficient or contradictory.
Return ∅	No coherent basin map exists under current observability.

10. Operating Logic

10.1 Basic Flow

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1. Identify system under mapping.
2. Identify dominant recurring behavior.
3. Identify current basin candidates.
4. Identify dominant attractor.
5. Identify secondary attractors.
6. Map basin boundaries.
7. Map entry conditions.
8. Map exit costs.
9. Map snap-back forces.
10. Map support structures.
11. Map transition pathways.
12. Assess recurrence and hidden debt.
13. Assess external forcing.
14. Classify basin geometry.
15. Output basin map, transition needs, rerun mapping, or ∅.
16. Validate over time.

10.2 Basin Identification Rule

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IF behavior repeatedly returns despite changed surface conditions,
THEN map the basin before adding another repair.

IF stated goal and repeated behavior conflict,
THEN repeated behavior reveals the stronger attractor.

IF exit cost is high,
THEN basin stability may be produced by lock-in rather than coherence.

IF a system appears stable while hidden debt rises,
THEN pseudo-coherent basin risk is active.

10.3 Transition Rule

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A basin transition requires:

- a visible target basin
- reduced exit cost from old basin
- weakened old attractor
- support structures for new basin
- sufficient transition energy
- feedback during transition
- damping after shift
- recurrence validation

If these are absent,
the system will likely snap back.

11. Operators Used

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Operator	Role in BGM
Ξ — Classification	Classifies basin type, attractor type, transition status, and snap-back risk.
Δ — Differentiation	Separates stated goal from dominant attractor, basin from behavior, stability from lock-in.
Μ — Mapping	Maps basin boundaries, attractors, exit costs, transition paths, and support structures.
Π — Constraint / Scoping	Defines basin map scope and limits premature transition claims.
Λ — Compatibility	Tests fit between target basin, system capacity, and transition pathway.
⊗ — Coupling	Evaluates dependency, capture, lock-in, basin attachment, and recoupling.
ℛ — Restoration	Identifies what must be repaired to enable basin transition.
Σ — Integration / Coherence Binding	Integrates basin map into coherent restoration or governance model.
Τ — Time Validation	Confirms basin classification and transition stability over recurrence.

12. Gates Required

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Gate	Required Condition	Failure Result
Basin Identification Gate	Current basin and candidate basins are sufficiently mapped.	Rerun basin mapping.
Attractor Classification Gate	Dominant and secondary attractors are identified or marked provisional.	Increase observation or mapping.
Basin Boundary Gate	Basin boundaries are clear enough to distinguish fields.	Boundary repair or deeper mapping.
Exit Validity Gate	Exit pathways can be evaluated coherently.	Map exit costs and dependencies.
Au-Traceability	Attractor evidence, recurrence, and basin forces are traceable.	Auditability restoration required.
BΣ validity	Basin boundaries, exit boundaries, and coupling boundaries hold.	Boundary reconstitution required.
FI-Gate	Feedback can update basin map.	Feedback restoration required.
R sufficiency	Restoration capacity can support transition mapping or basin shift.	Increase support or defer transition.
Transition Validity Gate	Transition pathway is coherent enough to attempt.	Use BAR before transition.
Τ validation	Basin map holds across time and recurrence.	Keep basin classification provisional.

13. Failure Modes Detected

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Failure Mode	Detection Signal
Basin Misidentification	Wrong basin is named, leading to wrong repair.
Attractor Obscuration	Dominant attractor is hidden by stated goals or surface narratives.
Dominant Attractor Blindness	Repeated behavior is ignored as evidence of attractor pull.
Basin Boundary Collapse	Current and target basins cannot be distinguished.
Exit Cost Lock-In	High cost prevents leaving old basin.
Snap-Back Underestimation	Transition plan ignores old attractor pull.
Transition Pathway Illusion	A claimed transition path does not actually leave the old basin.
Support Structure Blindness	Target basin lacks stabilizing supports.
Old Basin Restoration	Intervention strengthens the old basin.
Pseudo-Basin Shift	Language changes while field geometry remains.
Hidden Debt Recurrence	Unrepaired debt reproduces old basin.
Recurrence Without Basin Mapping	Repeated failure continues without attractor analysis.
Legitimacy Basin Collapse	Trust field collapses and destabilizes basin.
Field Geometry Compression	Complex basin structure is collapsed into one cause.

14. Restoration Links

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Restoration Arc	When Activated
Basin Reorientation	Current basin does not support coherent target state.
Attractor Supersession	Failure attractor must be replaced by stronger restoration attractor.
Boundary Reconstitution	Basin boundaries, role boundaries, or exit boundaries fail.
Exit Cost Reduction	Nodes cannot leave old basin.
Support Structure Restoration	Target basin lacks resources, roles, slack, or stabilizing practices.
Feedback Restoration	Basin map cannot update from real signals.
Damping Restoration	Basin transition oscillates or fails to settle.
Slack Regeneration	Transition requires headroom.
Legitimacy Re-Anchoring	Trust field must support target basin.
Recurrence Reduction	Old pattern repeats after intervention.
Origin-Layer Repair	Attractor pull originates below visible behavior.

15. U-Layer Localization

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U-Layer	Relevance
U0 — Substrate	Material, technical, biological, legal, or infrastructural base supporting the basin.
U1 — Power / Budgets	Resources, authority, staffing, funding, energy, and capacity stabilizing or shifting basins.
U2 — Configuration / Boundaries	Basin boundaries, exit paths, role boundaries, access boundaries, and recoupling boundaries.
U3 — Execution / Runtime	Repeated behaviors, workflows, enforcement patterns, repair attempts, and operational routines.
U4 — Classification / Metrics	Basin classes, attractor labels, recurrence markers, and transition metrics.
U5 — Coordination / Time	Transition timing, recurrence windows, snap-back periods, damping, and validation intervals.
U6 — Coherence Field	Attractor field, legitimacy, trust, meaning, and system coherence basin.
U7 — Memory / Recurrence	Institutional memory, habit, repeated patterns, prior attempts, and old-basin memory.
U8 — Environment / Forcing	Market pressure, adversarial pressure, crisis, scarcity, regulation, social pressure, or ecological force.

BGM most commonly localizes through:

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U6 → U7 → U2 → U5 → U8

This means basin mapping begins with the field, verifies recurrence memory, maps boundaries and exits, sequences transition through time, and accounts for external forcing.

16. Example Use Case

Scenario

A company repeatedly claims it wants ethical AI deployment.

Each incident results in:

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new policy language
new review committee
public reassurance
minor dashboard updates
temporary caution

But behavior keeps returning to:

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ship quickly
minimize disclosure
treat user feedback as support burden
centralize control
avoid deep auditability
frame concerns as edge cases

BGM Evaluation

The construct checks:

stated goal
repeated behavior
dominant attractor
basin boundaries
exit costs
snap-back forces
support structures
recurrence history

Likely Findings

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Current basin: velocity / control basin
Stated target basin: ethical AI governance
Dominant attractor: deployment speed + legitimacy preservation
Secondary attractor: public safety narrative
Exit cost: high for teams slowing deployment
Snap-back risk: high
Support structures for target basin: insufficient
Pseudo-basin shift risk: active

Recommended Output

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Do not treat policy language as basin shift.
Map velocity and control as dominant attractors.
Identify incentives preserving the current basin.
Reduce penalties for slowing deployment.
Fund auditability and repair infrastructure.
Create feedback pathways with authority.
Use BAR before claiming restoration.
Validate over repeated deployment cycles.

Interpretation

The company’s stated basin and actual basin differ.

BGM maps the actual field geometry before restoration design begins.

17. Anti-Patterns

Do not use BGM to:

treat stated goals as attractors
ignore repeated behavior
explain recurrence as isolated failure
map only incentives while ignoring memory and legitimacy
ignore exit costs
ignore snap-back forces
confuse policy change with basin shift
ignore affected nodes trapped in the basin
map target basin without support structures
claim basin transition without time validation
reduce basin geometry to one cause
ignore external forcing
treat a temporary transition state as a stabilized basin
skip BAR after mapping restoration-relevant basin pull

18. Completion Criteria

A BGM assessment is complete when:

system under mapping is identified
dominant recurring behavior is identified
current basin candidates are listed
dominant attractor is identified or marked provisional
secondary attractors are mapped
basin boundaries are mapped
entry conditions are mapped
exit costs are assessed
snap-back forces are mapped
support structures are identified
transition pathways are mapped or marked blocked
hidden debt and recurrence are assessed
affected nodes are identified
external forcing is assessed
basin geometry is classified
basin map, transition needs, rerun mapping, or ∅ is returned
time validation is defined

19. Machine-Readable Summary

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construct_id: "CONSTRUCT-043"
title: "Basin Geometry Mapper"
abbreviation: "BGM"
type: "construct"
status: "draft-integrated"
construct_class: "Basin Geometry / Attractor Mapping Construct"
operating_system: false
primary_module: "Basin Geometry / Coherence / Restoration"
related_modules:
  - "Scaling"
  - "Cybernetics"
  - "Institutions"
  - "Security"
  - "AI Governance"
  - "Justice · Governance · Legitimacy"

core_question: "What attractor basin is active, what forces stabilize it, and what transition pathways exist toward a more coherent basin?"

definition: "The Basin Geometry Mapper maps the attractors, basins, boundaries, exit costs, snap-back forces, transition paths, and stabilizing conditions that shape system behavior over time."

core_distinctions:
  - "stated goal is not dominant attractor"
  - "recurrence reveals basin structure"

core_pattern: "behavior recurrence → attractor identification → basin boundary mapping → exit-cost mapping → snap-back mapping → transition-pathway mapping → time validation"

compressed_form: "BGM = Μ(attractors + basins + boundaries + transitions)"

inputs:
  state_variables:
    - "O"
    - "H"
    - "ε"
    - "ι"
    - "Au"
    - "µᵢ"
    - "BΣ"
    - "K"
    - "R"
    - "Φ"
  diagnostics:
    - "Attractor Pull"
    - "Basin Stability"
    - "Basin Boundary Integrity"
    - "Exit Cost"
    - "Snap-Back Risk"
    - "Transition Energy"
    - "Hidden Debt"
    - "Feedback Integrity"
    - "Damping"
    - "Recurrence Risk"
    - "Legitimacy Baseline"
    - "Dependency Load"
    - "Coupling Depth"
    - "Restoration Capacity"
    - "Time Validation"
  gates:
    - "Basin Identification Gate"
    - "Attractor Classification Gate"
    - "Basin Boundary Gate"
    - "Exit Validity Gate"
    - "Au-Traceability"
    - "BΣ validity"
    - "FI-Gate"
    - "R sufficiency"
    - "Transition Validity Gate"
    - "Τ validation"
  observations:
    - "system under mapping"
    - "dominant behavior pattern"
    - "current basin"
    - "candidate basins"
    - "dominant attractor"
    - "secondary attractors"
    - "basin boundaries"
    - "entry conditions"
    - "exit costs"
    - "snap-back forces"
    - "transition pathways"
    - "support structures"
    - "recurrence history"
    - "affected nodes"
    - "external forcing"

outputs:
  assessments:
    - "basin classification"
    - "dominant attractor status"
    - "secondary attractor status"
    - "basin boundary status"
    - "exit cost status"
    - "snap-back risk"
    - "transition pathway status"
    - "support structure status"
    - "recurrence risk"
    - "time-validation requirement"
  decisions:
    - "basin mapped"
    - "identify dominant attractor"
    - "map secondary attractors"
    - "repair basin boundary"
    - "reduce exit cost"
    - "reduce snap-back risk"
    - "increase support"
    - "map transition pathway"
    - "rerun basin mapping"
    - "return ∅"
  maps:
    - "basin geometry map"
    - "attractor map"
    - "basin boundary map"
    - "exit-cost map"
    - "snap-back map"
    - "transition pathway map"
    - "support structure map"
    - "recurrence map"
    - "time-validation map"

dependencies:
  operators:
    - "Ξ"
    - "Δ"
    - "Μ"
    - "Π"
    - "Λ"
    - "⊗"
    - "ℛ"
    - "Σ"
    - "Τ"
  failure_modes:
    - "Basin Misidentification"
    - "Attractor Obscuration"
    - "Dominant Attractor Blindness"
    - "Basin Boundary Collapse"
    - "Exit Cost Lock-In"
    - "Snap-Back Underestimation"
    - "Transition Pathway Illusion"
    - "Support Structure Blindness"
    - "Old Basin Restoration"
    - "Pseudo-Basin Shift"
    - "Hidden Debt Recurrence"
    - "Recurrence Without Basin Mapping"
    - "Legitimacy Basin Collapse"
    - "Field Geometry Compression"
  restoration_arcs:
    - "Basin Reorientation"
    - "Attractor Supersession"
    - "Boundary Reconstitution"
    - "Exit Cost Reduction"
    - "Support Structure Restoration"
    - "Feedback Restoration"
    - "Damping Restoration"
    - "Slack Regeneration"
    - "Legitimacy Re-Anchoring"
    - "Recurrence Reduction"
    - "Origin-Layer Repair"

u_layers:
  primary:
    - "U2"
    - "U5"
    - "U6"
    - "U7"
    - "U8"
  secondary:
    - "U0"
    - "U1"
    - "U3"
    - "U4"

null_outcome_allowed: true
stated_goal_is_not_dominant_attractor: true
recurrence_reveals_basin_structure: true

20. Citation

Citation ID: construct-basin-geometry-mapper-v1-0

Recommended citation:

Universal Theory Stack. “CONSTRUCT-043 — Basin Geometry Mapper.” UTS Constructs Registry, Version 1.0.0, 2026.

21. Summary

The Basin Geometry Mapper maps the attractor field shaping system behavior.

Its core distinctions are:

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stated goal is not dominant attractor
recurrence reveals basin structure

BGM maps current basin, target basin, dominant attractor, secondary attractors, basin boundaries, entry conditions, exit costs, snap-back forces, support structures, transition pathways, recurrence, affected nodes, and external forcing.

Its core logic is:

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A system’s repeated behavior reveals the basin it is actually in.

When the basin cannot be identified, attractors are obscured, transition pathways are illusory, or recurrence evidence is insufficient, BGM recommends deeper basin mapping, boundary repair, exit-cost analysis, transition-pathway mapping, or:

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∅

BGM gives UTS a field-geometry map for understanding why systems return to the patterns they claim to leave.

CONSTRUCT-042 — Coherence-Valid Contract Test

Registry Tool Spec

CONSTRUCT-044 — Economic Circulation Mapper