KFD-4 formal reference

KFD-4 Formal Reference

Authoritative decision · Formal model · Usage · Documentation map

• Status: experimental
• Normative: no
• Formal model version: 2
• Authority: decisions/KFD-4.md
• Decision status: active

Imported vocabulary

Perspective, Observer, FactCut, CausalRecord, EvidenceCut, SituatedView, ReferenceFrame, ProjectionPolicy, PerspectiveTransformation, FrameInvariant, Replay, ContrastiveReplay, DeclaredLoss.

Domain objects

Define a perspective:

P = (observer, position, acceptedFactCut, naturalObjects,
     consequences, knownGaps)

A view is a declared projection:

V = Project(F, P, policy)

A replay is:

R = Replay(sourceViews, replayObserver, sharedContext,
           reconstructionPolicy, preservedElements, declaredLoss)

Project and Replay do not create an observer-independent view. They create new declared views whose relation to source facts and perspectives remains inspectable.

Let F be a state space of admitted fact cuts. A perspective defines an observation map into the objects visible from that frame:

pi_P: F -> O_P
V_P(f) = pi_P(f)

For a causal record or path gamma, the frame observes pi_P(gamma). A perspective transformation is:

T_PQ: (P, V_P, gamma_P) -> (Q, V_Q, gamma_Q)
J(T_PQ) = declared invariants preserved across the transformation

J(T_PQ) may include source and object identity, content roots, evidence cuts, known causal relations, receipts, and applicable authority boundaries. The projection may change while these declared invariants remain stable.

Relations and predicates

Bound(V, P)           view V retains its perspective declaration
Preserves(R, x)       replay R declares element x as preserved
Loses(R, x)           replay R declares element x as lost or degraded
Invents(R, e)         replay R presents generated material as source evidence
Contrasts(R)          R retains at least two source views and one shared context
Material(P1, P2)      perspective change can alter relevance, ordering, object
                      boundary, consequence, or action
InvariantUnder(x, T)  transformation T preserves the declared identity or
                      relation x
Covariant(V1, V2, T)  V2 declares how V1 changes under T without pretending
                      either view is observer-independent
CausalBefore(x, y)    preserved evidence establishes that x causally precedes y

Invariants

I1  PerspectiveBearing(V) -> exists P: Bound(V, P)
I2  ReplayOf(R, V) -> SourceIdentified(V) and ReconstructionDeclared(R)
I3  Loses(R, x) -> VisibleLoss(R, x)
I4  Invents(R, e) -> Invalid(R)
I5  Contrasts(R) -> SourcePerspectivesRemainDistinct(R)
I6  Material(P1, P2) and GuidesAction(V) -> TransformationDeclared(P1, P2)
I7  FirstPersonReport(p) may be preserved as fact while Interpretation(p)
    remains a claim
I8  PerspectiveBearing(V) -> not AbsoluteContext(V)
I9  PerspectiveTransformation(T) -> Declared(J(T))
I10 x in J(T) -> InvariantUnder(x, T)
I11 CausalBefore(x, y) -> no transformed view may present y as a possible
    cause of x without declaring a contradiction or revised evidence
I12 Covariant(V1, V2, T) permits changed coordinates, relevance, ordering, and
    object boundaries, but not silent mutation of J(T)

I8-I12 are an engineering reference-frame model. They are analogous to coordinate changes with preserved invariants, but they do not claim physical relativity, a differentiable manifold, or one complete transformation group for reality.

Transformation transition

declare source perspective and evidence cut
  -> preserve a perspective-bound view
  -> select replay or transformation policy
  -> reconstruct with declared preservation and loss
  -> compare in a declared shared context when contrastive
  -> expose newly visible objects, burdens, gaps, or consequences
  -> hand any Primitive candidate to KFD-5

For a causal path, replay preserves a view-specific projection rather than collapsing the path into endpoint state:

gamma: f_c0 -> ... -> f_cn
Replay_P(gamma) = pi_P(gamma) + declared loss

Two frames may expose different natural objects over the same causal path. Their comparison is valid only when source identity, boundaries, causal constraints, and transformation loss remain inspectable.

Proof obligations

• Identify observer, position, accepted fact cut, and known gaps.
• State the projection or reconstruction policy.
• Preserve source identity and causal constraints.
• Declare the frame invariants that a transformation promises to preserve.
• Show how perspective-dependent projections changed without silently changing the fact cuts or causal record beneath them.
• Expose degradation, redaction, generated interpolation, and loss.
• Keep source perspectives distinct in contrastive replay.
• Represent consequence-bearing participants when effects are asymmetric.
• Separate a preserved report from a wider interpretation.

Invalid states

• A consensus, aggregate, default, developer, or model view is presented as a view from nowhere.
• A transformed view silently changes source identity, evidence cut, causal relation, receipt, or applicable authority boundary.
• A replay substitutes endpoint state for the causal path it claims to expose.
• Replay fills missing evidence with generated certainty.
• Contrastive replay erases source observers into one synthetic history.
• A transformation guides action without declaring what changed.
• A perspective claim is used to deny causal facts or responsibility.

Machine mappings

Non-normative marginal-cost hypothesis

Let B123 denote an installed KFD-1 through KFD-3 foundation and let Cq(m | B123, E) be the total cost of producing a KFD-5-qualified Primitive from evidence E with genesis method m:

Cq = Cgenesis + Cqualification + Cfalse-candidates + Creality-validation

For perspective transformation, the marginal genesis cost after B123 is installed is approximately:

Delta Cperspective =
    Cmissing-capture + Creplay + Ccontrast

H4 is the bounded hypothesis that, where trusted multi-perspective evidence already exists and object boundaries materially depend on position, perspective transformation is the smallest new general operator and therefore the lowest-marginal-cost default probe for moving the observation horizon. H4 does not claim the lowest total Cq in every domain or superiority over specialized methods.

Evidence against H4 includes:

• capture, privacy, reconstruction, or replay loss dominating the search cost;
• anomaly, causal, compression, reconstruction, or hybrid methods producing equally qualified candidates at lower total cost under comparable evidence and budgets;
• perspective transformation producing enough false candidates that qualification cost dominates; or
• the same candidate becoming visible without a material change in observation horizon.

This hypothesis is not enforced by the current schemas. KFD-5 and KFD-6 provide the qualification and comparative-learning boundaries needed to test it.

Non-claims and extension points

KFD-4 does not claim that all interpretations are equally supported, that causal facts are relative, or that perspective transformation dominates other genesis methods. The current schemas are timeline and replay profiles, not a universal perspective ontology. Other profiles may be added if they preserve observer, evidence, transformation, loss, causality, and responsibility.

Active KFD-7 uses this frame model to distinguish perspective, direction, authority, and realized causal experience. KFD-4 does not by itself prove KFD-7’s proposed names, minimality, activation, or universal transfer.