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CERBERUS_FIELD_EFFECT-64_Candidate_Semantic_Kernel_Specification_v0.1.docx

Text edition. See the original for figures and page layout.
CERBERUS

FIELD_EFFECT-64

Candidate Semantic Kernel Specification

Procedural Pattern Generation Over Declared Effect Domains

	CORE SPECIFICATION STATEMENT

FIELD_EFFECT-64 defines a bounded procedural Generator Semantic Kernel that evaluates a registered Formula Profile over a supplied Effect Domain to produce a typed procedural Field Signal. It declares the pattern family, exact Formula Profile selection, domain basis, spatial scale, temporal rate, phase, waveform or shape semantics, propagation direction and speed, falloff/envelope, controlled variation, seed/stability behavior, output shaping, and interpretation version.

Field

	Specification

	Document

	CERBERUS FIELD_EFFECT-64 Candidate Semantic Kernel Specification

	Version

	0.1

	Date

	August 2026

	Series

	FIELD_EFFECT-64

	Member

	FIELD_EFFECT-64¹

	Effects Studio Role

	FIELD_EFFECT / Generator

	Bounded Question

	What mathematical pattern is generated over the supplied domain?

	Hard Effect-SK Dependencies

	None; requires a supplied Effect Domain / adapter and registered Formula Profile semantics

	Output

	Typed Effect Field Signal

	Authoring Basis

	CERBERUS Semantic Kernel Specification Authoring Standard v1.0; Effects Studio SK Interoperability Reference v0.1; MASK-32-64 visual precedent; AUDIO_EFFECT-64 v0.2 visual-first precedent

	Spec Role

	Human-facing instruction manual, planning artifact, and compressed map of the live record architecture

	Spec Class

	Candidate Spec: Reader topology, physical allocation, candidate D requirements, and semantic contracts are planned; exact registered D#.# / BOSS / COLOR / Formula records remain an implementation promotion gate.

Section Index

Ref.

	Section

	Part 1

	Purpose, scope, ownership, interoperability, and normative laws

	Part 2

	Member architecture, mathematical inventory, and Reader topology

	Part 3

	FIELD_EFFECT-64¹ Reader-role interface specifications

	Part 4

	Interface-0, D requirements, and complete DARTBOARD

	Part 5

	Binary encoding, Reader algorithm, output, and interoperability

	Part 6

	Worked examples, invalid states, and conformance

	Part 7

	Planning handoff and promotion gate

	Appendix A

	Complete Reader state enumerations

	Appendix B

	Complete B000:B063 physical Bit map

	Appendix C

	Candidate D requirement index

	Appendix D

	Conformance / build checklist

	SPEC ROLE

The records are the working machine. This document is the compressed human map: an illustrated instruction manual for learning, refreshing, reviewing, planning, and teaching how FIELD_EFFECT-64¹ is built and used. Runtime operation should resolve the live records directly rather than parse this document.

	INTERPRETATION RULE

Reusable SCALAR BitGroups remain mathematical. Pattern Family, Phase, Propagation Speed, Variation, and every other Field-specific meaning arise only through FIELD Reader placement. Figures are explanatory projections for humans and do not become canonical semantic identity.

Part 1 — Purpose, Scope, Ownership, Interoperability, and Normative Laws

1. Purpose and Bounded Question

FIELD_EFFECT-64¹ is the bounded Effects Studio Generator for procedural patterns over supplied mathematical domains. It answers one question: what mathematical pattern is generated over this domain? The same generated Field may drive movement, light, color, geometry, particles, audio, haptics, camera behavior, masking, or another compatible consumer without becoming any of those downstream application semantics.

Figure 1. FIELD_EFFECT-64¹ Kernel Card.

2. Ownership and Non-Ownership

FIELD owns

	FIELD does not own

	Pattern family and selected registered Formula Profile

	Canonical target identity, target ontology, or source geometry

	Domain-basis interpretation required by the Formula

	Canonical world coordinates or Frame identity

	Spatial scale, temporal rate, phase, waveform, propagation, envelope, and controlled variation

	Global start, duration, repetition, synchronization, or scene placement

	Seed/stability and output-shaping semantics

	Movement, Light, Color, Geometry, Material, Particle, Audio, Haptic, Camera, or other application meaning

	Typed Field Signal emission and validity

	Renderer implementation, world consequence, or downstream action

	Explicit domain requirements and unresolved behavior

	Silent fabrication of missing normals, tangents, paths, distances, Frames, or other domain data

Figure 2. Domain Preservation: values are generated over the domain without rewriting it.

3. Shared-Cause Interoperability

FIELD is intentionally useful because its output is a typed procedural cause rather than an application effect. A single Shimmer Field may feed several Application SKs. Each consumer preserves its own ownership boundary, while provenance remains traceable to one upstream field generator.

Figure 3. One Field Signal can drive multiple independent application semantics.

4. Effect Domain Adapter

FIELD consumes a declared mathematical view of the target domain. Different target kinds may expose points, axes, paths, surfaces, regions, volumes, or other normalized domain structures through an adapter. The Formula Profile declares which fields are required. FIELD does not need target-specific ontology merely to evaluate the pattern.

Figure 4. Domain Adapter: diverse target kinds expose a normalized mathematical view to FIELD.

5. Normative FIELD Laws

Law

	Normative statement

	FIELD-R01 Bounded Generation

	FIELD SHALL generate procedural Field semantics only; downstream application meaning remains externally owned.

	FIELD-R02 Domain Preservation

	FIELD SHALL sample the supplied domain without silently mutating its canonical geometry, identity, or retained source.

	FIELD-R03 Typed Output

	Every resolved output SHALL expose its declared Effect Signal Class and semantic basis.

	FIELD-R04 Pattern/Profile Separation

	Pattern Family SHALL identify the conceptual procedural family; Formula Profile SHALL own the exact registered equation and interpretation contract.

	FIELD-R05 Basis Declaration

	Any Formula Profile requiring domain coordinates or relations SHALL validate that the declared Domain Basis is available.

	FIELD-R06 Local Timing

	Temporal Rate and Phase are intrinsic FIELD semantics; global start, duration, repetition, and synchronization remain externally owned.

	FIELD-R07 Rate/Speed Separation

	Temporal Rate and Propagation Speed SHALL remain distinct when the active Formula Profile uses both.

	FIELD-R08 Formula Locality

	Primitive Bits and generic SCALAR BitGroups SHALL NOT embed Field-specific equations or domain meaning.

	FIELD-R09 Explicit Output Shaping

	Raw, normalized, bipolar, rectified, remapped, or profile-shaped output behavior SHALL remain inspectable.

	FIELD-R10 Stochastic Declaration

	Controlled irregularity SHALL expose Variation and Seed/Stability behavior sufficient to determine replay posture.

	FIELD-R11 Safe Zero

	A1=0 SHALL resolve to NO FIELD / OFF and SHALL NOT fabricate a procedural pattern.

	FIELD-R12 No Silent Coercion

	Unavailable domain fields or incompatible Formula requirements SHALL remain unresolved unless a declared transform/profile explicitly handles them.

	FIELD-R13 Application Non-Ownership

	FIELD SHALL NOT become Movement, Light, Color, Geometry, Material, Particle, Audio, Haptic, Camera, or other application semantics.

	FIELD-R14 Human Reconstructibility

	The instruction manual SHALL preserve enough structure for a knowledgeable human to understand how the BitWord was built without treating the document as runtime truth.

Part 2 — Member Architecture, Mathematical Inventory, and Reader Topology

6. Minimum Sufficient Resolution

FIELD begins at 64¹. A 32-bit member would be misleading because four continuous controls—Spatial Scale, Temporal Rate, Phase, and Propagation Speed—already consume 32 Bits at eight-bit resolution before the Generator can declare Pattern Family, Formula Profile, basis, waveform, direction, falloff, variation, seed policy, output shaping, or version.

Figure 5. Why there is no FIELD_EFFECT-32¹ member.

7. Mathematical BitGroup Inventory

Figure 6. Reusable SCALAR inventory used by FIELD_EFFECT-64¹.

BitGroup

	Width

	Formula

	Range

	FIELD uses

	SCALAR-2

	2

	Σ bᵢ·2ⁱ

	0–3

	Seed / Stability

	SCALAR-3

	3

	Σ bᵢ·2ⁱ

	0–7

	Waveform, Direction, Falloff, Variation, Output Shaping, Version

	SCALAR-4

	4

	Σ bᵢ·2ⁱ

	0–15

	Pattern Family, Formula Profile / Variant, Domain Basis

	SCALAR-8

	8

	Σ bᵢ·2ⁱ

	0–255

	Spatial Scale, Temporal Rate, Phase, Propagation Speed

No FIELD Reader lane in v0.1 uses additive numeric continuation across multiple placements. Every SCALAR placement is a distinct semantic role. A future higher-resolution member must preserve B000:B063 literally and earn any added Reader lanes or numeric depth through a new bounded capability.

8. Physical Allocation

Reader

	Bits

	BitGroup

	FIELD Reader meaning

	A1

	B000:B003

	SCALAR-4

	Pattern Family

	B1

	B004:B007

	SCALAR-4

	Pattern Variant / Formula Profile

	C1

	B008:B011

	SCALAR-4

	Domain Basis

	D1

	B012:B019

	SCALAR-8

	Spatial Scale / Frequency

	E1

	B020:B027

	SCALAR-8

	Temporal Rate / Frequency

	F1

	B028:B035

	SCALAR-8

	Phase

	G1

	B036:B038

	SCALAR-3

	Waveform / Shape

	H1

	B039:B041

	SCALAR-3

	Propagation Direction

	I1

	B042:B049

	SCALAR-8

	Propagation Speed

	J1

	B050:B052

	SCALAR-3

	Falloff / Envelope

	K1

	B053:B055

	SCALAR-3

	Noise / Variation

	L1

	B056:B057

	SCALAR-2

	Random Seed / Stability

	M1

	B058:B060

	SCALAR-3

	Output Shaping

	N1

	B061:B063

	SCALAR-3

	Version / Reserved

Figure 7. Physical order and semantic Reader topology.

9. Scale, Rate, and Propagation Are Different Questions

Spatial Scale, Temporal Rate, and Propagation Speed can all make a pattern appear “faster” or “denser” in casual language, but they are not interchangeable. Spatial Scale changes pattern density over the domain. Temporal Rate changes local evolution through time. Propagation Speed changes how quickly the pattern travels through the domain.

Figure 8. Spatial Scale, Temporal Rate, and Propagation Speed remain semantically distinct.

10. Pattern Family and Formula Profile

A1 describes the conceptual procedural family. B1 selects the registered mathematical interpretation within that family. The same Pattern Family can therefore remain stable while its precise equation, required domain data, invalid conditions, or output class change through a versioned Formula Profile.

Figure 9. Pattern Family is conceptual; Formula Profile owns the exact equation.

Part 3 — FIELD_EFFECT-64¹ Reader-Role Interface Specifications

	FIGURE CONTRACT

Each semantic Reader role below uses the same document grammar: declaration strip, real interface control, role-specific consequence viewport, Candidate D Class/requirement, mathematical carrier, zero/unset behavior, validation boundary, and non-ownership. The shell repeats; the semantic diagram does not.

11. Pattern Family — A1

Figure 10. Pattern Family — A1.

	DECLARATION

Pattern Family | A1 | SCALAR-4 | DREQ-CAT.FIELD_PATTERN

	Property

	Contract

	D Class

	Categorical Pattern Selection

	D Requirement Key

	DREQ-CAT.FIELD_PATTERN

	Purpose

	Defines the conceptual procedural pattern family. A1=0 is OFF / NO FIELD and suppresses generated Field output.

	Representative states

	0 OFF; 1 WAVE; 2 SHIMMER; 3 PULSE; 4 RIPPLE; 5 SWEEP; 6 CHASE; 7 SPIRAL; 8 VORTEX; 9 NOISE; 10 DRIFT; 11 FLICKER; 12 FALLOFF; 13 PROPAGATION; 14–15 RESERVED

	Validation / boundary

	A1=0 is safe zero. Family selection does not contain the exact formula; B1 resolves the registered Formula Profile / variant.

12. Pattern Variant / Formula Profile — B1

Figure 11. Pattern Variant / Formula Profile — B1.

	DECLARATION

Pattern Variant / Formula Profile | B1 | SCALAR-4 | DREQ-PROFILE.FIELD_FORMULA

	Property

	Contract

	D Class

	Profile Selection

	D Requirement Key

	DREQ-PROFILE.FIELD_FORMULA

	Purpose

	Selects the registered Formula Profile or bounded variant used within the active Pattern Family.

	Representative states

	0 FAMILY_DEFAULT; 1–14 REGISTERED_PROFILE / VARIANT slots governed by the active family; 15 EXTERNAL / RESERVED

	Validation / boundary

	The selected profile MUST declare accepted domain/context, required fields, exact equation, output Signal Class, undefined conditions, determinism posture, and human explanation.

13. Domain Basis — C1

Figure 12. Domain Basis — C1.

	DECLARATION

Domain Basis | C1 | SCALAR-4 | DREQ-SPATIAL.DOMAIN_BASIS

	Property

	Contract

	D Class

	Spatial Basis Selection

	D Requirement Key

	DREQ-SPATIAL.DOMAIN_BASIS

	Purpose

	Declares the coordinate, relation, or supplied basis through which the active Formula Profile evaluates the domain.

	Representative states

	0 PROFILE_DEFAULT; 1 X; 2 Y; 3 Z; 4 XY; 5 XZ; 6 YZ; 7 XYZ; 8 RADIAL; 9 DISTANCE; 10 PATH_DISTANCE; 11 NORMAL; 12 TANGENT; 13 SUPPLIED_VECTOR; 14–15 RESERVED

	Validation / boundary

	The Domain Adapter MUST expose the required basis. Missing normals, tangents, paths, distances, or vectors remain unresolved unless the Formula Profile declares a valid fallback.

14. Spatial Scale / Frequency — D1

Figure 13. Spatial Scale / Frequency — D1.

	DECLARATION

Spatial Scale / Frequency | D1 | SCALAR-8 | DREQ-SCALAR.SPATIAL_SCALE

	Property

	Contract

	D Class

	Scalar

	D Requirement Key

	DREQ-SCALAR.SPATIAL_SCALE

	Purpose

	Carries a normalized spatial-scale coordinate σ = D1 / 255 for the active Formula Profile.

	Representative states

	0 → 0.000; 64 → 0.251; 97 → 0.380; 128 → 0.502; 255 → 1.000

	Validation / boundary

	Normalization is FIELD Reader semantics, not SCALAR-8 identity. Physical wavelength or domain-unit scale belongs to the Formula Profile / domain mapping.

15. Temporal Rate / Frequency — E1

Figure 14. Temporal Rate / Frequency — E1.

	DECLARATION

Temporal Rate / Frequency | E1 | SCALAR-8 | DREQ-SCALAR.TEMPORAL_RATE

	Property

	Contract

	D Class

	Scalar

	D Requirement Key

	DREQ-SCALAR.TEMPORAL_RATE

	Purpose

	Carries a normalized intrinsic temporal-rate coordinate r = E1 / 255.

	Representative states

	0 frozen / minimum profile rate; 61 → 0.239; 128 → 0.502; 255 → 1.000 profile maximum

	Validation / boundary

	E1 governs local pattern evolution. Global start, duration, repeat, synchronization, and scene timing remain externally owned.

16. Phase — F1

Figure 15. Phase — F1.

	DECLARATION

Phase | F1 | SCALAR-8 | DREQ-CYCLE.PHASE

	Property

	Contract

	D Class

	Cyclic Scalar

	D Requirement Key

	DREQ-CYCLE.PHASE

	Purpose

	Carries the pattern phase as φ = F1 / 256 cycles, equivalent to θ = 2πF1/256.

	Representative states

	0 → 0°; 64 → 90°; 128 → 180°; 192 → 270°; 255 → 358.59375°

	Validation / boundary

	The /256 mapping provides 256 unique phase states on [0,1) without duplicating the zero position at both ends. Phase does not change frequency.

17. Waveform / Shape — G1

Figure 16. Waveform / Shape — G1.

	DECLARATION

Waveform / Shape | G1 | SCALAR-3 | DREQ-PROFILE.WAVEFORM

	Property

	Contract

	D Class

	Profile Selection

	D Requirement Key

	DREQ-PROFILE.WAVEFORM

	Purpose

	Selects the semantic shape of the active cycle or family-specific local profile.

	Representative states

	0 SMOOTH; 1 TRIANGULAR; 2 STEPPED; 3 PULSE_WIDTH; 4 CUSTOM_PROFILE; 5 FAMILY_SPECIFIC; 6 EXTERNAL; 7 RESERVED

	Validation / boundary

	Exact curve equations remain Formula/Profile-owned. Changing G1 does not silently change Spatial Scale, Temporal Rate, or Phase.

18. Propagation Direction — H1

Figure 17. Propagation Direction — H1.

	DECLARATION

Propagation Direction | H1 | SCALAR-3 | DREQ-DIR.PROPAGATION

	Property

	Contract

	D Class

	Direction Selection

	D Requirement Key

	DREQ-DIR.PROPAGATION

	Purpose

	Declares the semantic direction through which a propagating pattern travels.

	Representative states

	0 FORWARD/POSITIVE; 1 REVERSE/NEGATIVE; 2 RADIAL_OUT; 3 RADIAL_IN; 4 TANGENT_FORWARD; 5 TANGENT_REVERSE; 6 SUPPLIED_ORIENTATION; 7 PROFILE/EXTERNAL

	Validation / boundary

	Direction states requiring radial/tangent/supplied orientation are valid only when compatible domain basis/context exists. Invalid combinations are not silently remapped.

19. Propagation Speed — I1

Figure 18. Propagation Speed — I1.

	DECLARATION

Propagation Speed | I1 | SCALAR-8 | DREQ-SCALAR.PROPAGATION_SPEED

	Property

	Contract

	D Class

	Scalar

	D Requirement Key

	DREQ-SCALAR.PROPAGATION_SPEED

	Purpose

	Carries normalized travel speed v = I1 / 255 for propagating Formula Profiles.

	Representative states

	0 stationary; 107 → 0.420; 128 → 0.502; 255 → 1.000 profile maximum

	Validation / boundary

	Propagation Speed describes travel through the domain. It is distinct from Temporal Rate, which describes local pattern evolution.

20. Falloff / Envelope — J1

Figure 19. Falloff / Envelope — J1.

	DECLARATION

Falloff / Envelope | J1 | SCALAR-3 | DREQ-PROFILE.FIELD_FALLOFF

	Property

	Contract

	D Class

	Profile Selection

	D Requirement Key

	DREQ-PROFILE.FIELD_FALLOFF

	Purpose

	Selects how generated magnitude is shaped across the active domain or boundary context.

	Representative states

	0 NONE/UNIFORM; 1 LINEAR; 2 SMOOTH; 3 CENTER_EMPHASIS; 4 BOUNDARY_FADE; 5 PROFILE/MODEL; 6 EXTERNAL; 7 RESERVED

	Validation / boundary

	The exact profile equation remains externally registered. Envelope changes spatial magnitude shaping without redefining Pattern Family.

21. Noise / Variation — K1

Figure 20. Noise / Variation — K1.

	DECLARATION

Noise / Variation | K1 | SCALAR-3 | DREQ-PROFILE.FIELD_VARIATION

	Property

	Contract

	D Class

	Profile / Magnitude Selection

	D Requirement Key

	DREQ-PROFILE.FIELD_VARIATION

	Purpose

	Declares the requested degree/source class of controlled irregularity added to the base pattern.

	Representative states

	0 NONE; 1 LOW; 2 MEDIUM; 3 HIGH; 4 PROFILE/MODEL; 5 SOURCE_DERIVED; 6 FAMILY_SPECIFIC; 7 RESERVED

	Validation / boundary

	K1 describes irregularity magnitude/type. Replay and seed stability are separately governed by L1.

22. Random Seed / Stability — L1

Figure 21. Random Seed / Stability — L1.

	DECLARATION

Random Seed / Stability | L1 | SCALAR-2 | DREQ-POLICY.SEED

	Property

	Contract

	D Class

	Seed Policy

	D Requirement Key

	DREQ-POLICY.SEED

	Purpose

	Declares how stochastic or varied FIELD behavior obtains and retains its seed.

	Representative states

	0 STABLE_SEED; 1 PER_EVENT_SEED; 2 RUNTIME_SEED; 3 EXTERNAL_SEED

	Validation / boundary

	Stable seed supports repeatable output for the same inputs. Per-event seed remains stable within an event but may change across events. Runtime seed does not promise replay. External seed requires supplied context.

23. Output Shaping — M1

Figure 22. Output Shaping — M1.

	DECLARATION

Output Shaping | M1 | SCALAR-3 | DREQ-POLICY.OUTPUT_SHAPING

	Property

	Contract

	D Class

	Output Policy

	D Requirement Key

	DREQ-POLICY.OUTPUT_SHAPING

	Purpose

	Declares a post-generation numerical-basis transform applied before the typed Field Signal is emitted.

	Representative states

	0 RAW; 1 NORMALIZED; 2 BIPOLAR; 3 RECTIFIED; 4 REMAPPED; 5 PROFILE_SHAPED; 6–7 RESERVED

	Validation / boundary

	Output shaping does not change the semantic Signal Class declared by the Formula Profile. Any remap/profile requirements must remain explicit and inspectable.

24. Interpretation Version — N1

Figure 23. Interpretation Version — N1.

	DECLARATION

Interpretation Version | N1 | SCALAR-3 | DREQ-META.VERSION_INSPECT

	Property

	Contract

	D Class

	Metadata Inspection

	D Requirement Key

	DREQ-META.VERSION_INSPECT

	Purpose

	Pins the bounded Reader interpretation for replay, inspection, and historical resolution.

	Representative states

	0 current base interpretation; 1–6 registered future interpretations; 7 RESERVED

	Validation / boundary

	Ordinary DARTBOARD treatment is read-only. Migration is a separate governed operation rather than an incidental interface edit.

Part 4 — Interface-0, D Requirements, and Complete DARTBOARD

25. Interface-0 Composition

Interface-0 composes the declared symbol, Reader/interface name, color treatment, and D contract into a human-facing control. The BitGroup never infers the interaction geometry. F1 Phase is the clearest example: it uses SCALAR-8 mathematics but requires a cyclic dial rather than a generic linear slider.

Figure 24. Interface-0 assembly for the Phase Reader role.

26. Candidate D Requirement Plan

Reader

	Candidate D Class

	Requirement

	A1

	Categorical Pattern Selection

	DREQ-CAT.FIELD_PATTERN

	B1

	Profile Selection

	DREQ-PROFILE.FIELD_FORMULA

	C1

	Spatial Basis Selection

	DREQ-SPATIAL.DOMAIN_BASIS

	D1

	Scalar

	DREQ-SCALAR.SPATIAL_SCALE

	E1

	Scalar

	DREQ-SCALAR.TEMPORAL_RATE

	F1

	Cyclic Scalar

	DREQ-CYCLE.PHASE

	G1

	Profile Selection

	DREQ-PROFILE.WAVEFORM

	H1

	Direction Selection

	DREQ-DIR.PROPAGATION

	I1

	Scalar

	DREQ-SCALAR.PROPAGATION_SPEED

	J1

	Profile Selection

	DREQ-PROFILE.FIELD_FALLOFF

	K1

	Profile / Magnitude Selection

	DREQ-PROFILE.FIELD_VARIATION

	L1

	Seed Policy

	DREQ-POLICY.SEED

	M1

	Output Policy

	DREQ-POLICY.OUTPUT_SHAPING

	N1

	Metadata Inspection

	DREQ-META.VERSION_INSPECT

	CANDIDATE STATUS

These DREQ keys are planning requirements, not exact registered D#.# contracts. Promotion requires resolving exact registered contracts and the associated BOSS/COLOR/interface metadata.

27. Complete FIELD_EFFECT-64¹ Interface

The complete generated surface is a human-learning projection of the live Reader architecture. It assembles the same controls established in the individual Reader figures, presents synchronized inspection views, and exposes deterministic Reader output. The preview is disposable; the records are canonical.

Figure 25. Generated DARTBOARD surface for FIELD_EFFECT-64¹.

28. One Control to Exact Bits

The Phase control demonstrates reversibility from interface back to the physical word. A human can understand the cycle through the dial, while the system resolves the exact Reader placement and constituent Bits directly from records.

Figure 26. Phase control → F1 → SCALAR-8 → B028:B035 → 90° Reader meaning.

Part 5 — Binary Encoding, Reader Algorithm, Output, and Interoperability

29. Complete Physical Word

Figure 27. Complete 64-Bit visual map.

FIELD_EFFECT-64¹ uses all 64 physical Bits. There is no reserved padding. Reserved code combinations live inside selected Reader vocabularies rather than in unowned physical gaps.

30. Reader Algorithm

Figure 28. FIELD Reader pipeline from supplied domain to typed Field Signal.

Conceptually, the Reader resolves the domain and required basis, selects the registered Formula Profile, evaluates the procedural field using the configured scale/rate/phase/waveform/propagation/envelope/variation/seed semantics, applies explicit output shaping, validates the resulting Signal Class and domain requirements, and emits the typed Field Signal with validity and provenance. A1 routes or validates the conceptual family; N1 pins interpretation.

31. Output Signal Typing

Figure 29. Formula Profile declares Signal Class; M1 shapes numerical basis without collapsing semantic type.

Output class

	Meaning / example posture

	Scalar Field

	One scalar value per evaluated domain element / coordinate

	Signed Scalar Field

	Bipolar scalar value per domain location

	Vector Field

	Vector-valued procedural output where the Formula Profile declares vector semantics

	Angular Field

	Angular procedural output under a declared angular basis

	Probability Field

	Probability semantics remain typed as Probability rather than generic scalar

	Mask Field

	Participation semantics remain typed as Mask / Mask Field

	Event Field

	Event-like activation semantics over the domain

	Declared extension

	Additional types require an explicit registered Formula Profile and consumer compatibility

32. Interoperability Card

Figure 30. FIELD interoperability card.

33. Continuation, Compound, and Runtime Graph

Figure 31. Semantic continuation, Compound membership, and runtime graph flow are distinct grammars.

`<R>` means the local FIELD meaning continues into explicitly external semantic context, such as a registered Formula or domain interpretation. Compound membership means FIELD_EFFECT-64¹ is one complete constituent of a saved assembly. Runtime graph edges connect producer and consumer nodes during execution. None of these relationships should be inferred from the others.

Part 6 — Worked Examples, Invalid States, and Conformance

34. Worked Example Set

Figure 32. Minimal, rich, and cross-SK FIELD examples.

35. Minimal Valid Example — Static Wave Field

Reader

	State

	A1 Pattern Family

	WAVE

	B1 Formula Profile

	Family/default registered Wave profile

	C1 Domain Basis

	X

	D1 Spatial Scale

	0.25 normalized

	E1 Temporal Rate

	0 / frozen

	F1 Phase

	0

	G1 Waveform

	SMOOTH

	H1 Direction

	FORWARD

	I1 Propagation Speed

	0 / stationary

	J1 Falloff

	NONE / UNIFORM

	K1 Variation

	NONE

	L1 Seed / Stability

	STABLE_SEED

	M1 Output Shaping

	BIPOLAR

	N1 Version

	0

Expected result: a deterministic, static signed scalar Wave Field over the supplied X basis. The domain remains unchanged. No downstream application is implied.

36. Rich Example — Shimmer Field

A richer Shimmer configuration can combine a surface-appropriate basis, moderate spatial scale, live temporal rate, moving phase, smooth waveform, forward/radial propagation where valid, smooth falloff, low variation, stable seed, and normalized or bipolar output. The Formula Profile determines the exact shimmer equation and typed output.

37. Cross-SK Example — Dragon Scale Shimmer

A normalized dragon-scale domain may feed FIELD_EFFECT to generate one Shimmer Field. That output can then feed MASK to scope a subset, MOVEMENT for small rotation, COLOR for palette position, LIGHT for brightness, and GATE/PARTICLE behavior for event-triggered sparks. Each consumer remains a separate complete semantic responsibility.

38. Invalid / Unresolved Domain Basis

Figure 33. Missing required domain data resolves visibly as unresolved rather than fabricating a basis.

39. Intrinsic Pattern Timing and Global Timing

Figure 34. Temporal Rate / Phase / Propagation belong to FIELD; start/duration/repeat/synchronization remain external.

40. Conformance Tests

Test

	Requirement

	Expected

	C-FIELD-01

	A1=0 emits no Field regardless of other stored roles

	PASS required

	C-FIELD-02

	SCALAR BitGroups remain generic and do not acquire Field-specific identity

	PASS required

	C-FIELD-03

	Missing required basis/domain field remains unresolved; no fabricated data

	PASS required

	C-FIELD-04

	Temporal Rate and Propagation Speed remain independently inspectable

	PASS required

	C-FIELD-05

	Phase uses cyclic F1/256 semantics and does not duplicate 0 at the upper endpoint

	PASS required

	C-FIELD-06

	Formula Profile owns exact equation, accepted inputs, required domain fields, undefined conditions, output class, and determinism posture

	PASS required

	C-FIELD-07

	K1 Variation and L1 Seed/Stability remain distinct

	PASS required

	C-FIELD-08

	M1 output shaping cannot silently change the Formula Profile Signal Class

	PASS required

	C-FIELD-09

	Domain and world geometry remain unchanged by Field generation unless another authorized operation mutates them

	PASS required

	C-FIELD-10

	Global timing is not inferred from E1/F1/I1

	PASS required

	C-FIELD-11

	DARTBOARD is reconstructible from Reader/D contract/metadata and is not treated as canonical state

	PASS required

	C-FIELD-12

	Cross-SK consumers preserve independent application semantics and provenance

	PASS required

41. Minimum Sufficient Resolution Gate

Figure 35. A future 128² member must add a genuinely new FIELD capability and preserve B000:B063 literally.

Part 7 — Planning Handoff and Promotion Gate

42. Deterministic Planning Manifest

Figure 36. Human-facing planning manifest from reusable mathematics to a typed Field Signal.

43. Record Construction Plan

Record family

	Planning requirement

	Primitive Bits

	Reuse/register scalar contribution Bits needed by SCALAR-2 / SCALAR-3 / SCALAR-4 / SCALAR-8.

	BitGroups

	Reuse exact generic SCALAR-2, SCALAR-3, SCALAR-4, and SCALAR-8 mathematics.

	BitWord

	Create FIELD_EFFECT-64¹ with exact B000:B063 physical allocation.

	Reader Placements

	Create A1–N1 placements with the exact semantic roles defined by this Candidate Spec.

	Reader Enumerations

	Register the approved Pattern, Basis, Waveform, Direction, Falloff, Variation, Seed, Output, and Version vocabularies.

	Formula Profiles

	Register exact pattern-family equations, required domain fields, accepted context, output Signal Classes, undefined conditions, determinism, and human explanation.

	D Contracts

	Resolve Candidate DREQs to exact registered D#.# contracts during promotion.

	BOSS / COLOR

	Bind human-facing symbols, labels, and interface treatment without making projection metadata semantic identity.

	Validation

	Implement domain-requirement checks, safe zero, invalid combination handling, Signal typing, and explicit unresolved states.

	Tests

	Run the conformance matrix plus deterministic replay/seed tests and DARTBOARD reconstruction checks.

44. Candidate → Formal Promotion Gate

	PROMOTION GATE

Formal promotion requires exact registered D#.# bindings; exact BOSS/COLOR interface records; approved Formula Profile identities and versions; finalized Reader enumeration registrations; domain-adapter validation; output Signal typing; conformance tests; and verification that a human-facing DARTBOARD can be regenerated from the live records without treating this document as canonical runtime state.

45. Human-Learning Completion Test

A knowledgeable human should be able to return to this manual months later, skim the figures, and recover the correct mental model: FIELD evaluates registered mathematics over a supplied domain; its four SCALAR families remain generic; A1–N1 provide bounded Field meaning; Formula Profiles own exact equations; the Generator emits typed procedural causes; and downstream Application SKs decide what those causes do.

If the BitWord has not yet been built, this Spec should provide enough precision to guide record construction and identify unresolved registrations. Once built, the live CERBERUS records are the machine; this document remains the compressed human map.

Appendix A — Complete Reader State Enumerations

Reader role

	Enumeration / formula

	A1 Pattern Family

	0 OFF; 1 WAVE; 2 SHIMMER; 3 PULSE; 4 RIPPLE; 5 SWEEP; 6 CHASE; 7 SPIRAL; 8 VORTEX; 9 NOISE; 10 DRIFT; 11 FLICKER; 12 FALLOFF; 13 PROPAGATION; 14–15 RESERVED

	B1 Formula Profile

	0 FAMILY_DEFAULT; 1–14 registered profile/variant slots governed by Pattern Family; 15 EXTERNAL/RESERVED

	C1 Domain Basis

	0 PROFILE_DEFAULT; 1 X; 2 Y; 3 Z; 4 XY; 5 XZ; 6 YZ; 7 XYZ; 8 RADIAL; 9 DISTANCE; 10 PATH_DISTANCE; 11 NORMAL; 12 TANGENT; 13 SUPPLIED_VECTOR; 14–15 RESERVED

	D1 Spatial Scale

	0–255; Reader coordinate σ=D1/255

	E1 Temporal Rate

	0–255; Reader coordinate r=E1/255

	F1 Phase

	0–255; Reader phase φ=F1/256 cycles

	G1 Waveform

	0 SMOOTH; 1 TRIANGULAR; 2 STEPPED; 3 PULSE_WIDTH; 4 CUSTOM_PROFILE; 5 FAMILY_SPECIFIC; 6 EXTERNAL; 7 RESERVED

	H1 Direction

	0 FORWARD; 1 REVERSE; 2 RADIAL_OUT; 3 RADIAL_IN; 4 TANGENT_FORWARD; 5 TANGENT_REVERSE; 6 SUPPLIED_ORIENTATION; 7 PROFILE/EXTERNAL

	I1 Propagation Speed

	0–255; Reader coordinate v=I1/255

	J1 Falloff

	0 NONE/UNIFORM; 1 LINEAR; 2 SMOOTH; 3 CENTER_EMPHASIS; 4 BOUNDARY_FADE; 5 PROFILE/MODEL; 6 EXTERNAL; 7 RESERVED

	K1 Variation

	0 NONE; 1 LOW; 2 MEDIUM; 3 HIGH; 4 PROFILE/MODEL; 5 SOURCE_DERIVED; 6 FAMILY_SPECIFIC; 7 RESERVED

	L1 Seed / Stability

	0 STABLE_SEED; 1 PER_EVENT_SEED; 2 RUNTIME_SEED; 3 EXTERNAL_SEED

	M1 Output Shaping

	0 RAW; 1 NORMALIZED; 2 BIPOLAR; 3 RECTIFIED; 4 REMAPPED; 5 PROFILE_SHAPED; 6–7 RESERVED

	N1 Version

	0 base interpretation; 1–6 registered future interpretations; 7 RESERVED

Appendix B — Complete B000:B063 Physical Bit Map

Global Bit

	Reader

	BitGroup

	Local Bit

	Contribution

	Reader interpretation

	B000

	A1

	SCALAR-4

	0

	1

	Pattern Family

	B001

	A1

	SCALAR-4

	1

	2

	Pattern Family

	B002

	A1

	SCALAR-4

	2

	4

	Pattern Family

	B003

	A1

	SCALAR-4

	3

	8

	Pattern Family

	B004

	B1

	SCALAR-4

	0

	1

	Formula Profile

	B005

	B1

	SCALAR-4

	1

	2

	Formula Profile

	B006

	B1

	SCALAR-4

	2

	4

	Formula Profile

	B007

	B1

	SCALAR-4

	3

	8

	Formula Profile

	B008

	C1

	SCALAR-4

	0

	1

	Domain Basis

	B009

	C1

	SCALAR-4

	1

	2

	Domain Basis

	B010

	C1

	SCALAR-4

	2

	4

	Domain Basis

	B011

	C1

	SCALAR-4

	3

	8

	Domain Basis

	B012

	D1

	SCALAR-8

	0

	1

	Spatial Scale

	B013

	D1

	SCALAR-8

	1

	2

	Spatial Scale

	B014

	D1

	SCALAR-8

	2

	4

	Spatial Scale

	B015

	D1

	SCALAR-8

	3

	8

	Spatial Scale

	B016

	D1

	SCALAR-8

	4

	16

	Spatial Scale

	B017

	D1

	SCALAR-8

	5

	32

	Spatial Scale

	B018

	D1

	SCALAR-8

	6

	64

	Spatial Scale

	B019

	D1

	SCALAR-8

	7

	128

	Spatial Scale

	B020

	E1

	SCALAR-8

	0

	1

	Temporal Rate

	B021

	E1

	SCALAR-8

	1

	2

	Temporal Rate

Appendix B — Complete B000:B063 Physical Bit Map (continued)

Global Bit

	Reader

	BitGroup

	Local Bit

	Contribution

	Reader interpretation

	B022

	E1

	SCALAR-8

	2

	4

	Temporal Rate

	B023

	E1

	SCALAR-8

	3

	8

	Temporal Rate

	B024

	E1

	SCALAR-8

	4

	16

	Temporal Rate

	B025

	E1

	SCALAR-8

	5

	32

	Temporal Rate

	B026

	E1

	SCALAR-8

	6

	64

	Temporal Rate

	B027

	E1

	SCALAR-8

	7

	128

	Temporal Rate

	B028

	F1

	SCALAR-8

	0

	1

	Phase

	B029

	F1

	SCALAR-8

	1

	2

	Phase

	B030

	F1

	SCALAR-8

	2

	4

	Phase

	B031

	F1

	SCALAR-8

	3

	8

	Phase

	B032

	F1

	SCALAR-8

	4

	16

	Phase

	B033

	F1

	SCALAR-8

	5

	32

	Phase

	B034

	F1

	SCALAR-8

	6

	64

	Phase

	B035

	F1

	SCALAR-8

	7

	128

	Phase

	B036

	G1

	SCALAR-3

	0

	1

	Waveform

	B037

	G1

	SCALAR-3

	1

	2

	Waveform

	B038

	G1

	SCALAR-3

	2

	4

	Waveform

	B039

	H1

	SCALAR-3

	0

	1

	Direction

	B040

	H1

	SCALAR-3

	1

	2

	Direction

	B041

	H1

	SCALAR-3

	2

	4

	Direction

	B042

	I1

	SCALAR-8

	0

	1

	Propagation Speed

	B043

	I1

	SCALAR-8

	1

	2

	Propagation Speed

Appendix B — Complete B000:B063 Physical Bit Map (continued)

Global Bit

	Reader

	BitGroup

	Local Bit

	Contribution

	Reader interpretation

	B044

	I1

	SCALAR-8

	2

	4

	Propagation Speed

	B045

	I1

	SCALAR-8

	3

	8

	Propagation Speed

	B046

	I1

	SCALAR-8

	4

	16

	Propagation Speed

	B047

	I1

	SCALAR-8

	5

	32

	Propagation Speed

	B048

	I1

	SCALAR-8

	6

	64

	Propagation Speed

	B049

	I1

	SCALAR-8

	7

	128

	Propagation Speed

	B050

	J1

	SCALAR-3

	0

	1

	Falloff

	B051

	J1

	SCALAR-3

	1

	2

	Falloff

	B052

	J1

	SCALAR-3

	2

	4

	Falloff

	B053

	K1

	SCALAR-3

	0

	1

	Variation

	B054

	K1

	SCALAR-3

	1

	2

	Variation

	B055

	K1

	SCALAR-3

	2

	4

	Variation

	B056

	L1

	SCALAR-2

	0

	1

	Seed / Stability

	B057

	L1

	SCALAR-2

	1

	2

	Seed / Stability

	B058

	M1

	SCALAR-3

	0

	1

	Output Shaping

	B059

	M1

	SCALAR-3

	1

	2

	Output Shaping

	B060

	M1

	SCALAR-3

	2

	4

	Output Shaping

	B061

	N1

	SCALAR-3

	0

	1

	Version

	B062

	N1

	SCALAR-3

	1

	2

	Version

	B063

	N1

	SCALAR-3

	2

	4

	Version

Appendix C — Candidate D Requirement Index

Reader

	Semantic role

	D Class

	Candidate requirement

	A1

	Pattern Family

	Categorical Pattern Selection

	DREQ-CAT.FIELD_PATTERN

	B1

	Pattern Variant / Formula Profile

	Profile Selection

	DREQ-PROFILE.FIELD_FORMULA

	C1

	Domain Basis

	Spatial Basis Selection

	DREQ-SPATIAL.DOMAIN_BASIS

	D1

	Spatial Scale / Frequency

	Scalar

	DREQ-SCALAR.SPATIAL_SCALE

	E1

	Temporal Rate / Frequency

	Scalar

	DREQ-SCALAR.TEMPORAL_RATE

	F1

	Phase

	Cyclic Scalar

	DREQ-CYCLE.PHASE

	G1

	Waveform / Shape

	Profile Selection

	DREQ-PROFILE.WAVEFORM

	H1

	Propagation Direction

	Direction Selection

	DREQ-DIR.PROPAGATION

	I1

	Propagation Speed

	Scalar

	DREQ-SCALAR.PROPAGATION_SPEED

	J1

	Falloff / Envelope

	Profile Selection

	DREQ-PROFILE.FIELD_FALLOFF

	K1

	Noise / Variation

	Profile / Magnitude Selection

	DREQ-PROFILE.FIELD_VARIATION

	L1

	Random Seed / Stability

	Seed Policy

	DREQ-POLICY.SEED

	M1

	Output Shaping

	Output Policy

	DREQ-POLICY.OUTPUT_SHAPING

	N1

	Version / Reserved

	Metadata Inspection

	DREQ-META.VERSION_INSPECT

	PROMOTION NOTE

Candidate requirement keys are human-facing planning handles. Exact registered D#.# records remain authoritative once implementation is complete.

Appendix D — Conformance / Build Checklist

□ B000:B063 allocation matches the approved FIELD_EFFECT-64¹ map.

□ SCALAR-2 / SCALAR-3 / SCALAR-4 / SCALAR-8 are reused as generic mathematics rather than Field-specific duplicates.

□ A1=0 yields safe OFF / no Field output.

□ Every Reader role has a registered definition, state enumeration or formula, validation rule, and explicit ownership boundary.

□ B1 Formula Profiles declare accepted context/domain, required fields, exact equation, output Signal Class, undefined conditions, determinism, version, and human explanation.

□ C1 basis requirements are validated against the Domain Adapter; missing requirements remain unresolved.

□ D1/E1/I1 are normalized Reader coordinates rather than silently assumed physical units.

□ F1 phase uses 256 unique cyclic states and does not duplicate zero at the upper endpoint.

□ K1 Variation and L1 Seed/Stability remain distinct and replay behavior is testable.

□ M1 output shaping cannot silently alter the semantic Signal Class.

□ Global timing remains external to FIELD intrinsic rate/phase/propagation.

□ Cross-SK consumers preserve independent semantics and provenance.

□ Candidate DREQs are resolved to exact D#.# before Formal promotion.

□ BOSS symbols and COLOR/interface profiles are bound without becoming semantic identity.

□ DARTBOARD can be regenerated from records and is treated as a disposable human-facing projection.

□ Rendered instruction manual has been visually inspected for figure legibility, clipping, and semantic clarity.

	PRODUCTION PRINCIPLE

The records are the machine. The Spec is the human compression artifact. The figures should let a knowledgeable person reconstruct the mental model quickly; the live system should resolve the records directly.