7 - CERBERUS_Semantic_Bitword_Notation_Formal_System_Specification_v2.0.docx

DRAGON LEARNING NETWORK CERBERUS SEMANTIC BITWORD NOTATION & BIGFOOT SEMANTIC IDENTITY REGISTRY Formal System Specification CORE DEFINITION A Semantic Bitword is a bounded binary semantic structure whose constituent Bits, Bit Groups, composition, extension routes, and cross-domain relationships are identified through stable registry identities. Pure Bitwords grow through prefix extension; Compound Bitwords grow through ordered composition; semantic depth may continue through canonical or namespaced Bitlink Extensions without rewriting the source Bitword. PURE BITWORD PREFIX-### COMPOUND BITWORD [PREFIX]-### CANONICAL EXTENSION A ↳ B CUSTOM EXTENSION A ↳{NAMESPACE} B Version 2.0 | 13 August 2026 System Notation • Registry Identity • Bitlink Extension • Compound Composition FRONT MATTER Specification Status This specification defines the formal notation, registry identities, composition rules, Bitlink behavior, extension grammar, runtime state-binding distinctions, and BIGFOOT registry architecture used to construct and interpret CERBERUS Semantic Bitwords. It supersedes the earlier Bitword Notation v1.0 by adding canonical Bitlink Extensions, Custom Bitlink Extensions, Route Bits, Extension Routing States, namespaced extension bindings, and an explicit four-table BIGFOOT identity spine for Bits, Bit Groups, Pure Bitwords, and Compound Bitwords. NORMATIVE LANGUAGE MUST / SHALL identify conformance requirements. SHOULD identifies a strong default that may be departed from only for a documented reason. MAY identifies permitted but non-required behavior. Executive Summary The Bitword system separates semantic meaning from display, implementation, and application. A canonical Bit is identified once, assigned a stable Bit ID, and then reused wherever the same semantic primitive appears. Bit Groups collect reusable semantic primitives under stable BitGroup IDs. Pure Bitwords assemble ordered groups and Bits under stable BitWord IDs. Compound Bitwords compose complete Bitwords in a declared order without rewriting their constituent semantics. The new extension grammar removes the need for any Bitword to predict all future semantic depth. A Route Bit or Extension Routing State may direct the interpreter into another registered Bitword through a canonical Bitlink Extension (↳). A Custom Extension Route may direct into a private, organizational, community, FRINGE, FASK, or other namespaced structure using ↳{NAMESPACE}. The source Bitword remains byte-for-byte stable; the additional semantic depth lives in the graph. BIGFOOT therefore becomes the explicit semantic identity backbone for the binary layer. Its canonical Bitword spine consists of four linked registries: Bits, Bit Groups, Pure Bitwords, and Compound Bitwords. Stable IDs make semantic reuse deliberate. When two structures reuse the same registered Bit, the system knows that the semantic primitive is identical. When the same instantiated Bit state is bound into both structures, one State transition can update every projection that depends on that shared Bit identity. FOUR SHORT RULES || means “made from.” ⇄ means “related to.” ↳ means “resolve deeper through.” ↳{NS} means “resolve deeper through a namespaced extension.” FRONT MATTER Notation Quick Reference Notation Name Meaning Example PREFIX-### Pure Bitword One canonical semantic prefix lineage. HEALTH_DATA-64 [PREFIX]-### Compound Bitword Ordered composition of complete registered Bitwords. [CARDIAC]-512 :B### Bit address Exact local Bit address inside a Bitword. HEALTH_DATA-128:B096 :B###-B### Bit range / local group Contiguous local Bit range. HEALTH_DATA-128:B064-B095 :: Semantic descent Descend through a Compound or named structure. [CARDIAC]-512::HEART-256:B042 || Composition Assemble complete Bitwords without rewriting them. BODY-256 || HEART-256 ≡BIT Same Bit identity Two occurrences resolve to the same canonical Bit ID. A:B003 ≡BIT B:B007 ⇄ Registered Bitlink Different semantic objects have an explicit registered relation. A:B003 ⇄ B:B007 ⇄{ΔS} Statebound Bitlink Different Bits participate in the same declared State change. A:B003 ⇄{ΔS(X)} B:B007 ↳ Canonical Bitlink Extension Resolve additional semantic depth through a governed registered route. CardiacDetail ↳ [CARDIAC]-512 ↳{NS} Custom Bitlink Extension Resolve additional semantic depth through a namespaced binding. B124 ↳{CIRCUIT} MY_RECOVERY-128 ↳* Extension Branch One source has multiple extension destinations. MetabolicConcern ↳* {A,B,C} π(TYPE) Projection Extract a declared constituent from a Compound. π(HEART-256)([CARDIAC]-512) ΔS(a→b) State transition Declared change of a bounded state. ΔS(BodyMass:80→81) DOCUMENT MAP Contents Ref. Section Ref. Section 1 Purpose and Scope 16 Route Bits and Extension Routing States 2 Constitutional Design Principles 17 Compound Composition and Recursive Trees 3 Semantic Identity and Stable IDs 18 Ordering and Composition Manifests 4 BIGFOOT Four-Table Identity Spine 19 Runtime State Bindings and Scope 5 Bits Registry 20 HEALTH_DATA Resolution Pattern 6 Bit Groups Registry 21 Cross-Domain Reuse and Model Inputs 7 Pure Bitwords Registry 22 Privacy, Permission, and Epistemic Status 8 Compound Bitwords Registry 23 Models, Operators, and Goal-Seek Behavior 9 Pure and Compound Notation 24 Formal Laws and Invariants 10 Bit Addresses, Paths, and Projection 25 Worked Examples 11 Semantic Identity and Automatic Bitlinking A Reference Grammar 12 Explicit and Statebound Bitlinks B Reference Registry Fields 13 Prefix Extension C Conformance Tests 14 Canonical Bitlink Extension G Glossary 15 Custom Bitlink Extension and Namespaces I Subject Index by Section The Subject Index uses stable section references instead of page numbers so that it remains valid as the specification evolves. SECTION 1 Purpose and Scope A compact formal language for bounded semantic state, reusable identity, recursive composition, and open-ended extension. This specification defines how semantic primitives are identified, assembled into binary words, reused across domains, composed into larger words, related through Bitlinks, and extended into greater semantic depth without rewriting established encodings. Its purpose is not to prescribe one storage engine or runtime. Its purpose is to define stable meaning and deterministic relationships that multiple runtimes, interfaces, databases, applications, and institutions can interpret consistently. 1.1 In scope Stable identifiers for Bits, Bit Groups, Pure Bitwords, and Compound Bitwords. Notation for Pure and Compound Bitwords, local bit addresses, semantic paths, composition, identity, Bitlinks, Statebound Bitlinks, and extension routes. BIGFOOT registry relationships required to deliberately reuse canonical semantic primitives. Rules for automatic identity linkage when the same Bit ID appears in multiple semantic structures. Canonical and custom/namespaced extension mechanisms. Runtime distinction between canonical Bit meaning and record-specific Bit state. Recursive composition and recursive extension under bounded traversal. Privacy and permission behavior for extension routes and detailed semantic branches. 1.2 Out of scope A universal transport encoding or programming language. A requirement that every semantic structure be binary at runtime. A universal medical, fitness, food, or other domain ontology. Permission to infer unregistered relationships merely because two concepts appear similar. A requirement that every application traverse every available extension route. SECTION 2 Constitutional Design Principles Principle Requirement Canonical Identity A semantic primitive SHOULD be registered once and reused by stable ID when the intended meaning is the same. Local Position, Global Meaning Bit addresses are local to a layout; Bit IDs define semantic identity across layouts. Prefix Invariance Higher-resolution Pure Bitwords preserve established lower-resolution prefix bits, order, and meaning. Composition Invariance Compound composition MUST NOT rewrite constituent Bitwords. Extension Without Migration Additional semantic depth SHOULD be reached through prefix extension, composition, or explicit Bitlink Extension rather than reinterpretation of established bits. Explicit Relation Canonical Bitlinks and extension routes are registry relationships, not similarity guesses. Bounded Word, Open Graph Bitword width bounds encoded payload; reachable semantic depth may continue through explicit finite extension paths. Namespace Isolation Custom extensions MAY vary by namespace without changing canonical source semantics. State Scope Canonical Bit identity does not imply one global mutable value; state is bound within an authorized record/context. Permission Before Traversal A registered extension route does not itself confer authority to inspect or execute against its destination. MASTER DESIGN RULE Standardize the common core. Reuse registered semantic identity. Compose complete words. Bitlink the specialized edge. Let unanticipated meaning extend through explicit routes instead of forcing schema migration. SECTION 3 Semantic Identity and Stable IDs Every canonical semantic layer receives its own stable identity. The ID is not the current binary value and is not the local position of the object inside a particular word. It is the persistent reference through which BIGFOOT, Models, Operators, documentation, Instances, and runtimes agree that they are talking about the same semantic object. Object Required ID Example Identity means Bit Bit ID BIT-000184 One exact semantic primitive. Bit Group BitGroup ID BG-000041 One governed conceptual grouping of Bits. Bitword BitWord ID BW-000092 One governed binary semantic word definition, Pure or Compound. Compound composition BitWord ID + composition manifest BW-000155 One ordered composition definition whose constituents retain their own identities. 3.1 IDs versus addresses BIT IDENTITY BIT-000184 = Body Mass semantic primitive LOCAL OCCURRENCE HEALTH_DATA-64:B016-B026 ANOTHER OCCURRENCE PERSONAL_BODY_INPUT-128:B004-B014 If both occurrences reference BIT-000184, they are semantically identical even though their local positions differ. CRITICAL DISTINCTION Bit ID is semantic identity. B### is layout position. A runtime MUST NOT infer same meaning from matching bit position alone. SECTION 4 BIGFOOT Four-Table Identity Spine The binary semantic layer becomes deliberately addressable instead of being buried inside individual SK specifications. BIGFOOT remains the human-readable semantic viewing and indexing graph over explicit registered relations. For Bitword semantics, its canonical identity spine consists of four linked tables. These tables make every primitive, group, word, and compound composition independently addressable and reusable. Level Registry table Primary identity Core responsibility 1 Bits Bit ID Define canonical primitive meaning, state domain, encoding, provenance, and relationships. 2 Bit Groups BitGroup ID Define reusable conceptual groupings of linked Bit IDs and their group-level meaning. 3 Pure Bitwords BitWord ID Define prefix, width, ordered groups/bits, prefix lineage, route bits, and Pure semantics. 4 Compound Bitwords BitWord ID Define ordered composition of complete Pure and/or Compound Bitwords and total width. BIGFOOT SEMANTIC IDENTITY SPINE BITS ↓ linked by Bit ID BIT GROUPS ↓ linked by BitGroup ID + ordered manifests PURE BITWORDS ↓ linked by BitWord ID COMPOUND BITWORDS Cross-cutting relations: Bitlinks • Extension routes • Models • Operators • Normatives • Documentation • SKs • Instances 4.1 Why four tables matter New SKs can reuse existing Bits instead of inventing near-duplicates. A reused Bit ID creates a deterministic semantic identity relation across every word that references it. Bit Groups become reusable semantic modules instead of repeated prose descriptions. Compound Bitwords can be recursively decomposed because every constituent has its own BitWord ID. Documentation and BIGFOOT views can navigate from a user-facing term all the way to exact binary primitives and back. Automatic impact analysis becomes possible: changing a governed Bit definition reveals every Group, Bitword, Compound, Model, and application that depends on it. SECTION 5 Bits Registry The Bits Registry is the lowest canonical semantic identity layer. A Bit record defines what the primitive means; it does not store every user’s or record’s current value of that primitive. Field Purpose Bit ID Stable canonical identity. Canonical Bit Name Human-readable governed name. Formal Definition Exact semantic meaning. State Domain Boolean, bounded enum, signed quantity, mask member, route state, etc. Encoding Rule How encoded values map to semantic state. Unit / Scale Where numeric interpretation requires a unit or fixed-point scale. Known/Unknown Semantics How absence, unknown, explicit zero, and not-applicable are distinguished. Epistemic / Publication Scope CIRCLE, FRINGE, private, organizational, FASK, etc. where applicable. Provenance / Version Origin, authority, revision lineage. Linked Groups BitGroup IDs that reuse this Bit. Linked Bitwords Derived/linked words in which the Bit occurs. Bitlinks Explicit relations to different Bit IDs. Extension Targets Canonical or custom extension routes if the Bit functions as a route. 5.1 Reuse rule BIT REUSE PRINCIPLE When a new SK requires a primitive whose intended semantics are exactly equivalent to an existing registered Bit, the new SK SHOULD reuse the existing Bit ID rather than minting a new Bit. A new Bit ID is appropriate only when the semantic meaning materially differs. Approximate similarity is insufficient. If a new field is “body mass at measurement time” while an existing Bit means “current canonical body mass,” the two may require different Bits with an explicit mapping or Bitlink rather than identity reuse. SECTION 6 Bit Groups Registry A Bit Group is a governed conceptual grouping of Bits. Groups provide an intermediate semantic module between individual primitives and complete Bitwords. A Group may be reused across multiple Pure Bitwords when its meaning and constituent identities are the same. Field Purpose BitGroup ID Stable group identity. Group Name Human-readable semantic label. Formal Definition Meaning of the grouping as a unit. Linked Bit IDs Explicit member Bits. Bit Order Manifest Canonical ordered list where order is material to encoding. Width Derived or declared width of the group. Encoding / Decode Rule How the member bits jointly represent state. Parent / Related Groups Broader, narrower, alternative, or related group relationships. Reuse Status Whether the group is canonical reusable infrastructure or locally scoped. Provenance / Version Governance history. ORDERING RULE A BitGroup ID identifies meaning; an ordered manifest identifies layout. If the same semantic group is encoded in a materially different order, the implementation MUST preserve the difference explicitly rather than assuming identity from name alone. SECTION 7 Pure Bitwords Registry The Pure Bitwords Registry defines every PREFIX-### word whose complete payload belongs to one canonical prefix lineage. A Pure Bitword links to registered Bit Groups and Bits rather than treating bit meanings as anonymous fields embedded in a document. Field Purpose BitWord ID Stable word identity. Prefix Canonical prefix token, e.g. HEALTH_DATA. Width Total payload width in bits. Notation PREFIX-###. Prefix Parent Lower-resolution Pure Bitword preserved as prefix, if any. Prefix Children Known higher-resolution words in the same lineage. Linked BitGroups Governed groups used by the word. Bit Layout Manifest Ordered mapping of local bit ranges to Bit IDs / BitGroup IDs. Route Bits Canonical Extension Route Bits. Custom Route Slots Namespaced Custom Extension Route Bits. Version / Reserved Semantics Version control and explicitly defined reserved behavior. Documentation / Models / Operators Linked semantic infrastructure using the word. HEALTH_DATA-64 BitWord ID: BW-000092 Kind: Pure Width: 64 HEALTH_DATA-128 BitWord ID: BW-000093 Kind: Pure Prefix Parent: BW-000092 Rule: B000-B063 preserved byte-for-byte and semantically unchanged SECTION 8 Compound Bitwords Registry The Compound Bitwords Registry defines [PREFIX]-### objects assembled from complete registered Bitwords. A Compound does not acquire ownership of the semantics inside its constituents. It declares ordered composition. Field Purpose BitWord ID Stable identity in the same overall BitWord ID namespace. Compound Prefix Name inside brackets. Notation [PREFIX]-###. Total Width Sum of constituent widths. Ordered Constituent Manifest Sequence of child BitWord IDs and occurrence indexes. Pure Constituent Links Linked Pure Bitword records used directly. Compound Constituent Links Linked nested Compound records used directly. Flattened Layout Derived full bit layout for execution/serialization. Composition Model Declared grammar describing why the components form this Compound. Version / Provenance Governance and lineage. [CARDIAC]-512 BitWord ID: BW-000155 Composition Manifest 01 BODY-256 → BW-000121 02 HEART-256 → BW-000154 Total width 256 + 256 = 512 COMPOUND IDENTITY A Compound Bitword receives its own BitWord ID while every constituent retains its original BitWord ID. The parent identity represents composition; the children retain semantic ownership. SECTION 9 Pure and Compound Notation 9.1 Pure Bitword — PREFIX-### A Pure Bitword belongs to one canonical semantic prefix lineage. Increasing width within the same lineage is a resolution extension, not a composition. COLOR_EFFECT-8 COLOR_EFFECT-16 COLOR_EFFECT-32 HEALTH_DATA-64 HEALTH_DATA-128 9.2 Compound Bitword — [PREFIX]-### A Compound Bitword is composed from two or more independently meaningful registered Bitwords under a declared ordered composition. [FITNESS_RECORD]-160 = TIME-32 || FIT-128 [MEAL_PREP]-256 = FOOD-128 || COOKING-128 [CARDIAC]-512 = BODY-256 || HEART-256 VISUAL RULE Brackets mean “decompose before interpreting.” An unbracketed PREFIX-### is read as one Pure grammar. A bracketed [PREFIX]-### is resolved through its composition manifest. SECTION 10 Bit Addresses, Paths, and Projection Local addresses locate bits in a specific layout; semantic paths preserve ownership through nested compositions. Notation Meaning HEALTH_DATA-128:B096 Local Bit B096 in HEALTH_DATA-128. HEALTH_DATA-128:B064-B095 Local contiguous range. [CARDIAC]-512::HEART-256:B042 B042 of HEART-256 inside the CARDIAC Compound. [SYNESTHETIC]-128::[VISUAL]-64::COLOR-16:B003 Nested semantic path through multiple Compounds. π(HEART-256)([CARDIAC]-512) Project/extract the HEART-256 constituent. PATH RULE Semantic paths SHOULD reference constituent identities, not only flattened parent offsets, when the operation depends on semantic ownership. Flattened offsets are execution coordinates; constituent paths are semantic coordinates. SECTION 11 Semantic Identity and Automatic Bitlinking Reuse of a Bit ID creates automatic semantic identity across every structure that references it. If two Bitword layouts both reference the same registered Bit ID, BIGFOOT does not need a manually authored relationship to discover that they encode the same primitive. The relationship is derived from identity reuse. This is different from an explicit Bitlink between different Bits. BIT-000184 = BODY_MASS HEALTH_DATA-64:B016-B026 ↘ ≡BIT BIT-000184 BODY_MODEL_INPUT-128:B004-B014 ↗ 11.1 Automatic identity relation The system MAY surface all occurrences of the same Bit ID as automatically Bitlinked for navigation, impact analysis, Model discovery, and state dependency resolution. The underlying reason is identity, not inferred similarity. 11.2 State coupling requires shared binding NO GLOBAL MUTABLE BIT Reusing a Bit ID does not mean every person or every record shares one global value. Canonical Bit identity defines meaning. A runtime-specific Bit State Binding defines the value for a particular record, person, event, or authorized context. Canonical meaning BIT-000184 = Body Mass User A state binding BIT-000184 @ CIRCUIT:A = 82.5 kg User B state binding BIT-000184 @ CIRCUIT:B = 71.0 kg Identity is shared. State is scoped. When HEALTH_DATA and a Fitness Model in User A’s CIRCUIT both bind to BIT-000184 @ CIRCUIT:A, a change to that bound state can update both projections automatically. User B is unaffected. SECTION 12 Explicit and Statebound Bitlinks Relation Notation Meaning Same canonical Bit ≡BIT Two occurrences resolve to the same Bit ID. Explicit Bitlink ⇄ Different semantic objects have a registered relationship. Statebound Bitlink ⇄{ΔS} Different Bits participate in the same declared state transition. Canonical extension ↳ Target provides additional governed semantic resolution. Custom extension ↳{NS} Target provides additional namespaced semantic resolution. COLOR_EFFECT-8:B002 ⇄{ΔS(Note.Attack:0→1)} HAPTIC_EFFECT-8:B005 Statebound Bitlinks are especially useful for multimodal behavior: one State event may change several different Bits across otherwise independent Bitwords. The Bitwords remain separate; coordinated behavior lives in the declared state relation. SECTION 13 Prefix Extension Prefix Extension increases the resolution of one Pure Bitword lineage while preserving the established prefix byte-for-byte, order-for-order, and meaning-for-meaning. HEALTH_DATA-64 1010 ... [64 bits] HEALTH_DATA-128 1010 ... [same first 64 bits] || [64 new extension bits] SEMANTIC PREFIX INVARIANCE For a Pure Bitword family K, if K-m extends K-n and m > n, then the first n bits of K-m SHALL be identical to K-n in both encoding and interpretation. Prefix Extension is appropriate when the higher-resolution structure remains the same semantic family. It is not the correct mechanism for adding an unrelated domain such as HEART-256 to BODY-256; that is composition or Bitlink Extension. SECTION 14 Canonical Bitlink Extension ↳ means: the semantic path continues through another governed registered structure. A Canonical Bitlink Extension provides greater semantic depth without increasing the payload width of the source word. The source Bit or state establishes that a governed extension route exists; the target owns the detailed semantics. HEALTH_DATA-128::CardiacDetailAvailable<R> ↳ [CARDIAC]-512 [CARDIAC]-512 = BODY-256 || HEART-256 WIDTH RULE Bitword width bounds encoded state, not reachable semantic depth. HEALTH_DATA-128 remains exactly 128 bits even if one Route Bit can resolve through a 512-bit cardiac word and then through further specialist structures. 14.1 Canonical extension requirements The source and target identities MUST be registered. The relation MUST declare that the target is an extension/deeper-resolution route rather than merely a related object. The target MAY be Pure or Compound. The route MAY continue recursively, subject to finite acyclic traversal for any actual evaluation. Following the route MUST NOT imply write permission or disclosure authority. SECTION 15 Custom Bitlink Extension and Namespaces ↳{NAMESPACE} lets people, organizations, communities, FRINGE branches, and FASKs extend a canonical word without redefining it. A Custom Bitlink Extension uses a canonical Custom Extension Route Bit or other explicitly namespaced extension point whose destination is not globally fixed by the source Bitword specification. The binding is defined by a namespace. HEALTH_DATA-128:B124<R:X> ↳{CIRCUIT} MY_RECOVERY-128 HEALTH_DATA-128:B125<R:X> ↳{FRINGE} EXPERIMENTAL_METABOLIC_MODEL-256 HEALTH_DATA-128:B126<R:X> ↳{FASK} [DRAGON_PHYSIOLOGY]-1024 Namespace form Use {CIRCUIT} Private user-owned binding. {ORG:name} Organization-scoped extension. {COMMUNITY:name} Community-governed extension. {FRINGE} Shared experimental or provisional extension. {FASK} Explicit fantasy / alternate-rule extension. {CIRCLE} Explicit governed Commons destination where useful. {CUSTOM:name} Other declared namespace under applicable governance. CUSTOM EXTENSION ISOLATION PRINCIPLE A Custom Bitlink Extension MAY bind a declared extension slot to arbitrary registered semantic structures without altering the canonical meaning, width, order, or interoperability of the source Bitword. SECTION 16 Route Bits and Extension Routing States A Route Bit is a Bit whose canonical function is to signal or participate in semantic routing. Route Bits make availability and extension intent machine-readable without placing the target’s detailed content in the source word. Notation Class Meaning <R> Route Bit Bit participates in semantic extension routing. <R:C> Canonical Route Bit Destination or destination class is governed canonically. <R:X> Custom Route Bit Destination is bound by a namespace rather than globally fixed. 16.1 Extension Routing State A bounded enum may reserve one state to mean that the local vocabulary is intentionally insufficient and the interpreter should follow a registered extension route. “Other” therefore becomes a routing instruction rather than a miscellaneous bucket. HEALTH_DATA-64::PhysiologicalModelClass 00 Unknown 01 Class A 10 Class B 11 EXT — resolve registered extension ↳ HEALTH_DATA_OTHER-64 EXT INTERPRETATION EXT means “continue resolution through an explicit registered route.” It MUST NOT be interpreted as a vague catch-all whose downstream meaning is unknown or untracked. SECTION 17 Compound Composition and Recursive Trees Compound Bitwords encode assembly. They allow complex objects to be built from stable reusable words without minting a new monolithic Pure schema for every combination. [SYNESTHETIC_EFFECT]-128 │ ├── [VISUAL_EFFECT]-64 │ ├── COLOR_EFFECT-16 │ ├── SHAPE_EFFECT-16 │ └── MOTION_EFFECT-32 │ ├── [TACTILE_EFFECT]-32 │ ├── HAPTIC_EFFECT-16 │ ├── PRESSURE_EFFECT-8 │ └── TEXTURE_EFFECT-8 │ └── SPATIAL_EFFECT-32 17.1 Width conservation For an ordered composition A || B || C, the Compound width equals the sum of constituent widths. Nesting does not change the flattened total. W([ABC]) = W(A) + W(B) + W(C) 17.2 Constituent identity invariance Embedding COLOR_EFFECT-16 in a Compound does not create a new color grammar. The constituent continues to resolve through the original BitWord ID and the original Bit IDs. SECTION 18 Ordering and Composition Manifests Order is part of a Compound’s canonical identity. A composition manifest provides a deterministic, inspectable declaration of constituent sequence and occurrence. It also allows recursive flattening into execution offsets. Manifest field Meaning Order 1-based or otherwise declared stable sequence position. Constituent BitWord ID Stable identity of Pure or Compound child. Occurrence Index Disambiguates repeated use of the same child type. Local Offset Derived starting bit offset in flattened payload. Width Child width. Role / Alias Optional semantic role within the parent composition. Version Composition manifest version. [EFFECT_MATRIX]-128 01 EFFECT-16[0] offset 000 02 EFFECT-16[1] offset 016 03 EFFECT-16[2] offset 032 04 EFFECT-16[3] offset 048 05 EFFECT-16[4] offset 064 06 EFFECT-16[5] offset 080 07 EFFECT-16[6] offset 096 08 EFFECT-16[7] offset 112 SECTION 19 Runtime State Bindings and Scope BIGFOOT defines semantic identity. Runtime state belongs to records, Instances, CIRCUIT contexts, events, or other authorized operational scopes. This prevents the identity graph from accidentally becoming a global mutable state store. Layer Owns BIGFOOT Bit record Canonical meaning and relationships. Bitword definition Layout, composition, prefix, and extension grammar. Record / Instance state Current value of the Bit for this object/context. State transition Change from one bounded state to another. Projection / screen Rendered interpretation of current authorized state. BIT-000184 = Body Mass Record R-001 binding BIT-000184 = 82.50 kg Record R-002 binding BIT-000184 = 71.00 kg Same meaning. Different state. AUTOMATIC UPDATE RULE When two projections or Bitwords within the same operational scope reference the same Bit ID and the same state binding, a State change to that binding SHOULD invalidate or update every dependent projection. This is identity-based dependency propagation, not a global mutation of the canonical Bit record. SECTION 20 HEALTH_DATA Resolution Pattern A compact private router demonstrates how common state, clinical concern flags, canonical detail branches, and custom extensions fit together. HEALTH_DATA is not intended to contain a complete medical record. HEALTH_DATA-64 holds frequently reused physiological/model-input state. HEALTH_DATA-128 preserves the 64-bit prefix and adds broad concern/routing information. Detailed specialist semantics remain in separately governed Bitwords reached through explicit extension routes. HEALTH_DATA-128 │ ├── B000-B063 HEALTH_DATA-64 common inputs │ ├── B064-B095 broad concern states │ ├── B096-B111 canonical detail availability / Route Bits │ ├── B112-B119 detailed measurement availability │ └── B120-B127 extension / custom route space 20.1 Cardiac example HEALTH_DATA-128::CardiacConcern = PRESENT HEALTH_DATA-128::CardiacDetailAvailable<R:C> = 1 │ ↳ ▼ [CARDIAC]-512 │ ├── BODY-256 └── HEART-256 │ ↳ deeper specialist structures as required The compact word reveals that a cardiac concern and a detailed branch exist; it does not disclose the detailed cardiac state. A Model may stop at HEALTH_DATA-64, inspect HEALTH_DATA-128, locally evaluate [CARDIAC]-512, or continue deeper depending on declared need and authorization. 20.2 Custom health extension HEALTH_DATA-128:B124<R:X> ↳{CIRCUIT} MY_RECOVERY-128 HEALTH_DATA-128:B126<R:X> ↳{FASK} [DRAGON_BODY]-1024 HEALTH ROUTING PRINCIPLE HEALTH_DATA identifies what common state is available and where deeper health semantics may exist. Bitlinks resolve as deeply as a Model needs and permissions allow. SECTION 21 Cross-Domain Reuse and Model Inputs Stable Bit IDs make common personal and domain variables reusable across Models without duplicating their semantics into each application schema. BIT-000184 = Body Mass │ ├── HEALTH_DATA-64 ├── Personal Body Matrix ├── Fitness Workload Model ├── Nutrition Model └── authorized NETWORK application A new application that needs body mass links to the existing Bit ID rather than inventing AppWeight, MealWeight, FitnessWeight, and HealthWeight as unrelated concepts. The application may still maintain its own internal schema; an Adapter or DataSpec maps that schema to the canonical Bit identity. 21.1 Derived metrics are Models, not necessarily Bits Values such as BMI, total work, average power, caloric targets, or recovery scores SHOULD generally remain Model outputs when they are deterministically derivable from more fundamental registered state. If a derived metric becomes a reusable semantic object in its own right, it may receive its own Bit or Model Key identity under appropriate governance. SECTION 22 Privacy, Permission, and Epistemic Status Semantic addressability is not disclosure authority. A private CIRCUIT may know that HEALTH_DATA-128 has a canonical cardiac extension, a custom recovery branch, and a FRINGE experiment while revealing none of those payloads to an external application. External application asks: "Is this fitness configuration valid under the authorized health constraints?" CIRCUIT locally resolves: HEALTH_DATA-128 ↳ [CARDIAC]-512 ↳{CIRCUIT} MY_RECOVERY-128 + applicable Models / Normatives External application receives: VALID / INVALID / bounded constraint result Not the underlying health graph. BITLINKABILITY ≠ DISCLOSURE A registered Bitlink or extension route proves semantic relationship and navigability under governance. It does not grant read, write, mutation, publication, or traversal authority. 22.1 Epistemic status preservation Custom routes may point into CIRCLE, FRINGE, FASK, private, or proprietary structures. Traversal MUST preserve the destination’s declared epistemic and ownership status. A FASK route does not become clinical truth because it originated from a real HEALTH_DATA word. SECTION 23 Models, Operators, and Goal-Seek Behavior Bitwords supply bounded semantic state. Models interpret or derive values from that state. Operators transform permitted state. Goal-Seek behavior searches allowable candidate states under a declared objective rather than attaching universal “better” recommendations to individual records. [FITNESS_RECORD]-160 = TIME-32 || FIT-128 │ ├── shared Bits / Models ▼ HEALTH_DATA-64/128 │ ▼ FITNESS + ENERGY MODEL │ ▼ Target metrics │ ⇄{GOAL-SEEK} ▼ [MEAL_PREP]-256 candidates = FOOD-128 || COOKING-128 Because Bits and Groups have stable IDs, the Model can declare exact semantic inputs. If several structures reuse the same Bit ID, the Model resolves one semantic primitive rather than relying on label matching. If more detail is required, a declared extension route can be followed to the minimum necessary depth. SECTION 24 Formal Laws and Invariants Law Invariant L1 — Stable Bit Identity A Bit ID SHALL retain one governed semantic meaning across all canonical reuse. L2 — Local Address Independence Matching B### positions SHALL NOT imply semantic identity. L3 — Exact Reuse Exactly equivalent semantics SHOULD reuse an existing Bit ID. L4 — Prefix Invariance A Pure extension SHALL preserve its lower-resolution prefix byte-for-byte and semantically. L5 — Composition Invariance A Compound SHALL preserve constituent identity, width, ordering, and interpretation. L6 — Width Conservation Compound width SHALL equal the sum of constituent widths. L7 — Explicit Extension ↳ and ↳{NS} SHALL resolve only through registered extension relations. L8 — Extension Non-Containment An extension target SHALL NOT be treated as physically contained in the source payload unless separately composed. L9 — Namespace Isolation Custom extension bindings SHALL NOT redefine canonical source semantics. L10 — State Scope Canonical identity SHALL NOT imply one global runtime value. L11 — Permission Separation Relation existence SHALL NOT imply authorization to traverse, disclose, or mutate. L12 — Epistemic Preservation Extension traversal SHALL preserve CIRCLE/FRINGE/FASK/private/proprietary status. L13 — Finite Traversal Every actual extension/composition traversal SHALL be finite and acyclic even though the registry may support open-ended future depth. L14 — Registry Traceability Every canonical Bitword SHALL be decomposable to registered Bit IDs through explicit BIGFOOT relations/manifests. SECTION 25 Worked Examples 25.1 Fitness record [FITNESS_RECORD]-160 = TIME-32 || FIT-128 TIME-32 → calendar placement FIT-128 → fitness semantic state The Calendar is a projection; the Compound is the canonical assembled payload. 25.2 Meal preparation [MEAL_PREP]-256 = FOOD-128 || COOKING-128 FOOD-128 → what food / ingredient state COOKING-128 → how it is prepared 25.3 Shared primitive across domains BIT-000184 = Body Mass HEALTH_DATA-64:B016-B026 ≡BIT BIT-000184 BODY_MATRIX-256:B040-B050 ≡BIT BIT-000184 One state binding changes: ΔS(BIT-000184 @ CIRCUIT:A : 82.5 → 82.0 kg) Dependent projections invalidate / update automatically. 25.4 Canonical specialist route HEALTH_DATA-128::CardiacDetailAvailable<R:C> ↳ [CARDIAC]-512 ├── BODY-256 └── HEART-256 25.5 Custom extension route HEALTH_DATA-128:B124<R:X> ↳{CIRCUIT} [PERSONAL_RECOVERY]-512 [PERSONAL_RECOVERY]-512 ├── SLEEP-128 ├── FITNESS_RECOVERY-128 ├── NUTRITION_RECOVERY-128 └── STRESS-128 25.6 FRINGE / FASK extension HEALTH_DATA-128:B126<R:X> ↳{FASK} [ELVEN_PHYSIOLOGY]-1024 Canonical health meaning remains real/private. The FASK destination remains explicitly fantasy/alternate. SECTION A Reference Grammar PURE := PREFIX "-" WIDTH COMPOUND := "[" PREFIX "]-" WIDTH BIT := WORD ":B" INDEX BIT_RANGE := WORD ":B" INDEX "-B" INDEX PATH := WORD ("::" CONSTITUENT)* (":" BIT)? COMPOSITION := WORD "||" WORD ("||" WORD)* BIT_IDENTITY := BIT "≡BIT" BIT BITLINK := OBJECT "⇄" OBJECT STATE_LINK := OBJECT "⇄{ΔS(" STATE ")}" OBJECT EXTENSION := OBJECT "↳" OBJECT CUSTOM_EXT := OBJECT "↳{" NAMESPACE "}" OBJECT BRANCH_EXT := OBJECT "↳*" "{" OBJECT_LIST "}" PROJECTION := "π(" TYPE ")(" COMPOUND ")" STATE_CHANGE := "ΔS(" STATE ":" OLD "→" NEW ")" A.1 Interpretive rules || SHALL mean ordered composition, not semantic equality. ⇄ SHALL mean a registered relationship whose exact relation type is resolved from the registry. ↳ SHALL mean that the target provides additional semantic resolution of the source context. ↳{NS} SHALL mean that the extension binding is controlled by the named namespace. ≡BIT SHALL be reserved for canonical Bit identity, not loose equivalence. :: SHALL preserve semantic ownership through nested structures. SECTION B Reference Registry Fields Registry Minimum fields Bits Bit ID; Name; Definition; State Domain; Encoding; Unit/Scale; Unknown semantics; Version; Provenance; linked Groups; Bitlinks; extension routes. Bit Groups BitGroup ID; Name; Definition; linked Bit IDs; Bit Order Manifest; Width; Decode rule; Version; Provenance. Pure Bitwords BitWord ID; Prefix; Width; Notation; Prefix Parent; linked BitGroups; Bit Layout Manifest; Route Bits; Custom Route Slots; Version. Compound Bitwords BitWord ID; Compound Prefix; Total Width; Ordered Constituent Manifest; linked Pure children; linked Compound children; flattened layout; Composition Model; Version. B.1 Suggested identifier examples BIT-000001 BG-000001 BW-000001 One BitWord ID namespace MAY contain both Pure and Compound words. Kind is determined by the registry/table and definition, not by changing the semantic identity model. SECTION C Conformance Tests ID Test Pass condition BW-001 Bit identity reuse Create two Pure Bitwords using the same canonical primitive and verify both reference the same Bit ID. BW-002 Local address independence Place the same Bit ID at different local positions and verify semantic identity remains intact. BW-003 No false identity Place unrelated Bits at the same local B003 position in different words and verify no identity is inferred. BW-004 Prefix invariance Extend a Pure word and verify all lower-prefix bits and meanings are unchanged. BW-005 Compound invariance Compose two words and verify each child remains byte-for-byte identical to standalone form. BW-006 Width conservation Verify Compound width equals constituent width sum. BW-007 Recursive decomposition Resolve a nested Compound to its leaf Pure BitWord IDs and Bit IDs. BW-008 Canonical extension Follow ↳ from a Route Bit and verify the registered target resolves without being treated as source payload. BW-009 Custom isolation Bind the same custom slot to different namespace targets in two CIRCUITs and verify canonical source semantics remain identical. BW-010 State scope Change one user’s bound Bit state and verify another user sharing the same Bit ID is unaffected. BW-011 Automatic dependency update Bind two projections to the same Bit ID/state binding and verify one state change updates or invalidates both. BW-012 Permission separation Register an extension route without read authority and verify traversal is denied while relation existence remains known as permitted. BW-013 Epistemic preservation Follow a FASK extension and verify the destination remains fantasy/alternate. BW-014 Finite traversal Introduce a candidate cycle and verify validation rejects or bounds it for runtime traversal. BW-015 Registry traceability Select any canonical Bitword and verify it can be traced through manifests to registered Bit IDs. SECTION G Glossary Term Definition Automatic Bitlinking Derived semantic linkage created by reuse of the same Bit ID; runtime state propagation additionally requires a shared state binding/context. Bit An exact bounded semantic primitive identified by a stable Bit ID. Bit Address A local B### position inside a specific Bitword layout. Bit Group A governed reusable conceptual grouping of registered Bits. Bit ID Stable canonical identity of one semantic primitive. Bit State Binding Runtime association of a canonical Bit ID with a value in a particular record, person, event, or authorized context. Bitlink Explicit registered semantic relationship between bounded semantic objects. Bitlink Extension A registered relationship indicating that another semantic structure provides additional resolution of the source context. Bitword A bounded binary semantic word identified by a BitWord ID; may be Pure or Compound. BitWord ID Stable identity of a governed Pure or Compound Bitword definition. BIGFOOT Persistent human-readable semantic viewing/indexing graph over explicit registered relations; in this specification its Bitword identity spine consists of Bits, Bit Groups, Pure Bitwords, and Compound Bitwords registries. Canonical Extension Governed extension route written with ↳. Compound Bitword A bracketed [PREFIX]-### word built from an ordered composition of complete registered Bitwords. Composition Invariance Rule that composition does not rewrite constituent identity, bits, ordering, or interpretation. Composition Manifest Deterministic ordered declaration of a Compound Bitword’s constituents and occurrence sequence. Custom Bitlink Extension Namespaced semantic extension written ↳{NAMESPACE} whose destination is not globally fixed by the source specification. Custom Extension Isolation Rule that namespaced extension bindings cannot redefine the canonical source Bitword. Custom Extension Route Bit A Route Bit whose target is determined by a namespace binding. Epistemic Status Preservation Rule that traversing a relation does not change CIRCLE, FRINGE, FASK, private, or proprietary status. Extension Branch One source with multiple extension destinations, written ↳*. Extension Routing State A bounded state such as EXT meaning that local vocabulary is insufficient and registered extension resolution is required. HEALTH_DATA Compact private physiological/model-input and health-routing Pure Bitword family used as a worked example in this specification. Identity Relation Relationship arising because multiple occurrences resolve to the same canonical Bit ID. Namespace Declared authority/scope controlling a Custom Bitlink Extension binding. Prefix Extension Increase in Pure Bitword resolution that preserves lower-resolution prefix bits and meanings. Prefix Invariance Rule that higher-resolution members preserve established lower-resolution prefixes unchanged. Projection Extraction or rendering of a declared semantic constituent or state. Pure Bitword An unbracketed PREFIX-### word whose entire payload belongs to one canonical prefix lineage. Route Bit A Bit whose canonical function participates in semantic extension routing. Semantic Descent Use of :: to traverse constituent ownership inside nested Compound structures. Semantic Identity Spine The four linked BIGFOOT registries that make Bits, Groups, Pure Bitwords, and Compound Bitwords explicitly addressable. Statebound Bitlink Explicit relation between different Bits that participate in the same declared State transition. Width Conservation Rule that Compound width equals the sum of constituent widths. SECTION I Subject Index by Section Subject References Automatic Bitlinking §§ 4–5, 11, 19, 21; App. C; Glossary BIGFOOT §§ 3–8, 11, 24; Apps. B–C; Glossary Bit address §§ 3, 10–12; Glossary Bit Group / BitGroup ID §§ 3–7; Apps. B–C; Glossary Bit ID §§ 3–7, 11, 19, 21, 24; Apps. B–C; Glossary Bit State Binding §§ 11, 19; App. C; Glossary Bitlink §§ 11–12, 21–24; App. A; Glossary Bitlink Extension §§ 14–16, 20, 22, 24; Apps. A–C; Glossary BitWord ID §§ 3–4, 7–8, 17–18; App. B; Glossary Canonical extension §§ 14, 16, 20; App. A; Glossary Compound Bitword §§ 4, 8–10, 17–18, 20, 25; Apps. A–C; Glossary Composition Manifest §§ 8, 17–18; App. B; Glossary Custom extension §§ 15–16, 20, 22, 24–25; Apps. A–C; Glossary Extension Routing State / EXT § 16; Glossary FASK extension §§ 15, 22, 25; Glossary HEALTH_DATA §§ 7, 13–16, 20, 25; Glossary Identity versus state §§ 3, 5, 11, 19; App. C Minimum semantic depth §§ 14, 20–23 Namespace § 15; Apps. A, C; Glossary Permission separation §§ 14, 22, 24; App. C Prefix Extension §§ 7, 9, 13, 24; Glossary Pure Bitword §§ 4, 7, 9, 13, 17; Apps. A–C; Glossary Route Bit §§ 7, 14–16, 20; Glossary Semantic path § 10; App. A Statebound Bitlink § 12; App. A; Glossary Width Conservation §§ 17–18, 24; App. C; Glossary CLOSING RULE A well-designed Semantic Kernel does not need to predict every future concept. It needs stable reusable semantic identities, deterministic composition, and explicit routes through which specialized or custom meaning can extend without rewriting the core. End of Formal System Specification v2.0