D9 Tables I: Fundamentals

Geometry of Normativity / Ethical Alignment

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Table 1. D9 at a Glance

Category	D9 Formulation
Dimension	D9
Name	Geometry of Normativity
Short Definition	The geometry of normativity, ethics, value, and alignment
Core Question	Is this aligned?
Receives From	D6 meaning, D7 salience, D8 selected trajectory
Evaluates	Actions, intentions, choices, relations, promises, laws, rituals, institutions, identities, cultures
Central Function	Normative adjudication
Core Output	Alignment, force, responsibility, repair, residue, virtue, norm
Main Symbol	$K_9(x)$
Central Orientation	The Good
Relation to D12	The Good is D12 coherence disclosed under D9 evaluation
Relation to D5	D9 value must become manifest through D5 recoverable form
Key Warning	D9 must not be reduced to feeling, choice, consensus, law, identity, or manifestation

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Table 2. Short D9 Glossary

Term	Definition
Normativity	The field of value, obligation, permission, justice, worth, sacredness, and meaning
Alignment	Local participation in the Good
The Good	D12 coherence disclosed under D9 evaluation
Value	Coherence-relevance under D9 evaluation
Norm	D9-structured constraint or guide on possible trajectories
Obligation	Binding normative force
Permission	Normative admissibility
Prohibition	Binding negative normative force
Justice	Coherence in relation
Worth	Dignity, honor, esteem, fitting recognition
Sacredness	Inviolability, ultimacy, reverence
Significance	Existential weight
Conscience	D9 pressure registered inside D10 selfhood
Responsibility	Answerability for a coherence-relevant trajectory
Repair	Restoration of normative coherence
Residue	Unresolved normative charge
Attractor	Stable normative basin
Virtue	Stable D9/D10 capacity for alignment
Vice	Stabilized D9 distortion inside selfhood
Moral Conflict	Multiple genuine goods making non-identical demands
Dilemma	A situation where every option leaves residue
D12 Collapse	Ultimate coherence used to bypass local responsibility
Recoverability	Whether D9 value remains legible in manifest form

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Table 3. D9 Registers / Operators

Register	Polarity	Operator
1.Value	Good / Bad	$Val_9$
2.Rightness	Right / Wrong	$Right_9$
3. Ordering	Better / Worse	$Ord_9$
4. Obligation	Ought / Ought Not	$Obl_9$
5. Permission	Permissible / Impermissible	$Perm_9$
6. Justice	Just / Unjust	$Just_9$
7. Worth	Worthy / Unworthy	$Worth_9$
8. Sacredness	Sacred / Profane	$Sac_9$
9. Significance	Meaningful / Trivial	$Sig_9$

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Table 4. D9 Canonical Package

Component	Symbol	Role
Dimension	$D_9$	Normative dimension
State-Space	$\Omega_9$	Set of normatively evaluable structures
Register Grammar	$G_9$	Nine D9 operators
Input Bundle	$I_9$	Meaning, salience, choice, context, relation, history, embeddability
Value Vector	$\mathcal V_9$	Nine-register normative profile
Alignment	$K_9$	Alignment with the Good
Force	$F_9$	Normative pressure
Responsibility	$Resp_9$	Answerability
Repair	$R_9$	Restoration vector
Repair Coherence	$C_9^{repair}$	Successful repair condition
Residue	$Res_9$	Unresolved normative charge
Coherence	$Coh_9$	Integrated alignment
Decoherence	$Decoh_9$	Normative distortion
Distance	$d_9$	Distance from D9 coherence
Gradient	$\nabla_9 K$	Direction of increased alignment
Attractors	$\mathfrak A_9$	Stable normative basins
Conflict Logic	$Conf_9$	Moral conflict and dilemma structure
Virtue	$Virtue_{9/10}$	Stable D9/D10 mature capacity
Transduction	$\mathcal T_{9\to m}$	D9 encoded into action, identity, culture, or manifestation

Table 5. D9 Evaluative Vector

Component	Register	What It Measures
$Val_9(x)$	Value	Basic good/bad polarity
$Right_9(x)$	Rightness	Correctness of action or response
$Ord_9(x)$	Ordering	Comparative better/worse ranking
$Obl_9(x)$	Obligation	Binding ought / ought-not demand
$Perm_9(x)$	Permission	Whether the option is normatively allowed
$Just_9(x)$	Justice	Fairness, proportion, harm, responsibility, repair
$Worth_9(x)$	Worth	Dignity, honor, esteem, recognition
$Sac_9(x)$	Sacredness	Inviolability, reverence, consecration
$Sig_9(x)$	Significance	Existential or moral weight

Formula:

$\mathcal V_9(x)= ( Val_9(x), Right_9(x), Ord_9(x), Obl_9(x), Perm_9(x), Just_9(x), Worth_9(x), Sac_9(x), Sig_9(x) )$

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Table 6. D9 State-Space

Category	D9-Relevant Examples
Actions	Speech, restraint, harm, help, betrayal, repair
Intentions	Motives, aims, purposes, hidden desires
Choices	Commitments, refusals, sacrifices, priorities
Relationships	Family, friendship, marriage, community, authority
Promises	Vows, contracts, pledges, covenants
Laws	Rights, duties, codes, prohibitions, permissions
Institutions	Courts, schools, churches, governments, professions
Rituals	Apologies, oaths, ceremonies, consecrations, memorials
Memories	Moral memory, trauma memory, public memory
Life Paths	Vocation, duty, calling, repentance, reform
Collective Norms	Customs, taboos, expectations, moral languages
Traumas	Moral injury, desecration, betrayal, unresolved wrong
Duties	Role duties, personal duties, sacred duties
Repairs	Restitution, apology, reform, boundary, reintegration
Identities	Moral identity, dignity, conscience, shame, integrity
Civilizational Patterns	Justice systems, honor cultures, punishment cultures, sacred orders

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Table 7. D9 Input Bundle

Input	Symbol	Source	D9 Role
Semantic Structure	$\sigma_6(x)$	D6	What the situation means
Affective Salience	$A_7(x)$	D7	Why it matters emotionally
Selected Trajectory	$a_8(x)$	D8	What is being chosen
Context	$C$	Situation	What changes the meaning of the evaluation
Relational Field	$R$	Interpersonal / collective	Who is involved and how
History	$H$	Prior residue	What has already happened
World-Embeddability	$W$	D5 / D12 interface	Whether the judgment can responsibly become real

Formula:

$I_9(x)= ( \sigma_6(x), A_7(x), a_8(x), C, R, H, W )$

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Table 8. D9 Evaluative Pipeline

Stage	Name	Description
1	Presentation	Something becomes normatively live
2	Semantic Intake	D6 meaning is received
3	Salience Intake	D7 affective charge is received
4	Volitional Intake	D8 selected trajectory is received
5	Register Evaluation	The nine-register profile is generated
6	Contextual Integration	The value profile is interpreted in context
7	Force Assignment	Normative pressure is calibrated
8	Alignment Judgment	$K_9(x)$ is evaluated
9	Responsibility / Repair	Answerability and repair vectors are generated
10	Residue or Integration	The event integrates or leaves unresolved normative charge

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Table 9. D9 Normative Primitives

Primitive	Symbol	Definition	Common Confusion
Value	$Val_9$	Coherence-relevance under D9 evaluation	Preference
Norm	$N_9$	D9-structured guide or constraint on possible trajectories	Social habit
The Good	$Good_9$	Coherence disclosed as value	What is liked
Goodness	$Goodness_9$	Positive participation in coherence	Pleasantness
Duty	$Duty_9$	Personally or role-specifically binding obligation	Any possible good
Obligation	$Obl_9$	Binding normative force	Pressure or anxiety
Permission	$Perm_9$	Normative admissibility	Goodness
Prohibition	$Proh_9$	Binding negative normative force	Disgust
Justice	$Just_9$	Coherence in relation	Revenge or punishment
Conscience	$Conscience_{10/9}$	D9 alignment-pressure registered inside D10 selfhood	Infallible moral truth
Responsibility	$Resp_9$	Answerability for a coherence-relevant trajectory	Guilt
Repair	$Repair_9$	Restoration of coherence after rupture	Apology or punishment alone

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Table 10. Normative Force Ladder

Force Level	Meaning	Example
Forbidden	Must not be done	Deliberate cruelty
Impermissible	Not allowed under the conditions	Betrayal of trust
Permitted	Allowed, but not necessarily good	A neutral personal choice
Optional-Good	Good, but not required	Extra generosity
Recommended	Strongly fitting, though not strictly required	Offering support where appropriate
Obligatory	Required by the moral situation	Telling truth where concealment would harm
Duty-Bound	Required by role, vow, relation, or office	Parent protecting a child
Reparative	Required because rupture has occurred	Restitution after harm
Sacredly Binding	Required by sacredness, vow, dignity, or consecrated relation	Refusing desecration of what must be honored

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Table 11. D9 Coherence Conditions

Condition	Symbol	Meaning
Register Integration	$Int_9(\mathcal V_9^C(x))$	The nine registers form an integrated contextual profile
Positive Alignment	$K_9(x)>0$	The state participates positively in the Good
Proportionate Force	$Prop_9(F_9(x))$	Moral pressure is calibrated correctly
Just Responsibility	$JustResp_9(x)$	Answerability is fairly assigned
Embeddability	$Emb_9(x)$	The judgment can responsibly become manifest
Repair-Capability	$RepairCap_9(x)$	The state can move toward repair if rupture appears
D12 Humility	$Humility_{9/12}(x)$	Local judgment remains answerable to a Good beyond itself

Formula:

$Coh_9(x) \iff Int_9(\mathcal V_9^C(x)) \wedge K_9(x)>0 \wedge Prop_9(F_9(x)) \wedge JustResp_9(x) \wedge Emb_9(x) \wedge RepairCap_9(x) \wedge Humility_{9/12}(x)$

Table 12. D9 Attractors

Attractor	Coherent Form	Distorted Form
Justice	Relational repair	Revenge
Resentment	Signal of unrepaired wrong	Grievance identity
Mercy	Release without denial	Bypass
Purity	Reverent protection of sacredness	Contamination-control
Punishment	Proportionate consequence	Suffering-as-repair
Responsibility	Answerability	False guilt or saviorhood
Sacrifice	Costly higher good	Martyrdom or self-erasure
Loyalty	Fidelity under the Good	Tribal cover-up
Compassion	Care with truth and boundary	Enabling
Righteousness	Uprightness before the Good	Self-righteousness
Guilt	Signal of responsibility	Shame spiral or manipulation
Shame	Signal of violated worth	Identity collapse
Honor	Fitting recognition	Status obsession
Duty	Binding answerability	Duty inflation
Meaning	Existential weight	Dramatization or nihilistic flattening

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Table 13. D9 Distance Metric Components

Component	Symbol	Measures
Register Distance	$D_{reg}$	Fragmentation, absolutization, or inversion of registers
Force Distance	$D_{force}$	Overforce, underforce, misforce, displacement
Responsibility Distance	$D_{resp}$	Difference between assigned and proper responsibility
Repair Distance	$D_{repair}$	Difference between actual and needed repair
Residue Distance	$D_{res}$	Amount of unresolved normative charge
D12 Alignment Distance	$D_{12}$	Misalignment from global coherence

Formula:

$d_9(x,Coh_9) = \alpha D_{reg} + \beta D_{force} + \gamma D_{resp} + \delta D_{repair} + \epsilon D_{res} + \zeta D_{12}$

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Table 14. D9 Alignment Gradients

Gradient Direction	Repair Movement
More Truth	Name what is real
Clearer Responsibility	Assign answerability properly
Proportionate Justice	Restore fairness without revenge
Better Boundary	Protect what remains vulnerable
Deeper Mercy	Release without denial
Real Restitution	Restore what can be restored
Structural Reform	Change the pattern that produced rupture
Dignity Restoration	Restore worth where shame or contempt entered
Sacred Reconsecration	Restore reverence after desecration
Existential Integration	Integrate meaning after rupture

Table 15. Core D9 Formulas

Formula Name	Compact Form	Meaning

D9 Grammar

$D_9 = Grammar(K_9)$

D9 is the grammar of normative alignment

D9 State-Space

$x \in \Omega_9$

$x$ is normatively evaluable

Value Vector

$\mathcal V_9(x)$

The nine-register D9 value profile

Alignment Function

$K_9(x)=Align_9(…)$

Full D9 alignment judgment

Normative Force

$F_9(x)$

Degree and kind of moral pressure

Repair Vector

$R_9(x)$

The vector of normative repair

Residue

$Res_9=Decoh_9-C_9^{repair}$

Unresolved normative charge

Distance Metric

$d_9(x,Coh_9)$

Distance from normative coherence

Alignment Gradient

$x_{t+1}=x_t+\eta\nabla_9K(x_t)$

Repair as movement toward alignment

The Good

$Good=D12\vert_{D9}$​

D12 coherence disclosed under D9 evaluation

Responsibility Chain

$D12\rightarrow D9\rightarrow R_9$​

Ultimate coherence grounds finite responsibility

Full Forms:

$\mathcal V_9(x)= ( Val_9, Right_9, Ord_9, Obl_9, Perm_9, Just_9, Worth_9, Sac_9, Sig_9 )$

$K_9(x)= Align_9 ( \mathcal V_9, F_9, Resp_9, R_9, \Phi, \Phi_{12}, C )$

$F_9(x) \in { forbidden, impermissible, permitted, optional\text{-}good, recommended, obligatory, duty\text{-}bound, reparative, sacredly\text{-}binding }$

$R_9= ( Truth, Ack, Conf, Apology, Restitution, Boundary, Mercy, Reform, Reintegration )$

$Res_9= ( \rho_T, \rho_R, \rho_J, \rho_D, \rho_P, \rho_W, \rho_S, \rho_M, \rho_I )$

$Coh_9(x) \iff Int_9(\mathcal V_9^C(x)) \wedge K_9(x)>0 \wedge Prop_9(F_9(x)) \wedge JustResp_9(x) \wedge Emb_9(x) \wedge RepairCap_9(x) \wedge Humility_{9/12}(x)$

$Decoh_9(x) \iff RegDist_9(x) \vee ForceDist_9(x) \vee RespDist_9(x) \vee RepairDist_9(x) \vee Capture_9(x) \vee Inv_9(x)$

$d_9= \alpha D_{reg} + \beta D_{force} + \gamma D_{resp} + \delta D_{repair} + \epsilon D_{res} + \zeta D_{12}$

$\mathcal T_{9\to5}(x)= ( \mathcal E_{9\to5}(x), \mathcal K_{9\to5}(x), \mathcal R_{5\to9}(x), \mathcal A_5(x), W_{12}(x) )$

$Conf_9(x,C) \iff \exists r_i,r_j \in G_9 [ F_{9,i}(x,C)>0 \wedge F_{9,j}(x,C)>0 \wedge \neg CoEmb_5(r_i,r_j,x,C) ]$

Table 16. D9 Closure Axioms

Axiom	Statement
1	D9 is normative alignment
2	D9 receives D6 meaning, D7 salience, and D8 selection
3	D9 is not reducible to its inputs
4	The Good is D12 disclosed under D9
5	D9 coherence is not moral purity
6	D9 repair is not punishment
7	D9 residue is not merely emotion
8	D9 distance is not personal worth
9	Consensus is not moral truth
10	Ultimate coherence does not erase finite responsibility
11	Law is not the source of normativity
12	D9 judgment must remain humble