4 - GROOVE_Routing_Semantic_Kernels_Multifactor_Discretization_Formal_AddOn_Specification_v0.1.docx

CERBERUS GROOVE Routing Semantic Kernels Formal Add-On Specification for Multifactor Semantic Discretization, Branch Factorization, Recursive Resolution, and Accretive Corpus Routing CORE SYSTEM STATEMENT A GROOVE application of a Routing Semantic Kernel compiles an Observable Entry into the complete permitted Routing BitWord state, preserves all compatible semantic factors, and may factor active routes into independently traversable branches. Those branches can increase in resolution, accrete into GROOVE Bundles, and correspond to existing Models and FASKs without merging the source corpus into BIGFOOT or implying lineage. ROUTING SKs DO NOT PUT AN ENTRY IN ONE BOX. They discretize the semantic factors present in the Entry. GROOVE preserves the whole and routes the factors. Formal Add-On Specification v0.1 15 August 2026 | CERBERUS / BIGFOOT / GROOVE / Routing Semantic Kernel Architecture Status: Draft companion specification for prototype implementation, corpus experiments, and revision. Document Control Field Value Document GROOVE Routing Semantic Kernels — Formal Add-On Specification Version 0.1 Date 15 August 2026 System CERBERUS Matryoshka / BIGFOOT / GROOVE Specification role Defines the use of Routing SKs as reusable structural semantic templates for GROOVE corpus discretization and branching. Companion foundation CERBERUS Routing Semantic Kernels — Formal Specification v0.1 Primary scope Multifactor Entry routing, branch factorization, recursive resolution, Bundle compilation, co-activation analysis, Model/FASK correspondence, custom GROOVE passes. Canonical boundary GROOVE state is independent corpus interpretation. It does not add source Entries to BIGFOOT, mutate Routing SKs, or establish source lineage. Normative vocabulary MUST, MUST NOT, SHALL, SHALL NOT, SHOULD, SHOULD NOT, MAY Abstract This add-on specification defines why and how GROOVE reuses Routing Semantic Kernels as structural semantic templates over independent corpora. Unlike a single-label classifier, a Routing SK can expose a bounded multi-route mask. GROOVE therefore compiles an Entry into a complete BitWord state such as 0000 0010 0100 0001, preserving several simultaneously applicable semantic factors. Active routes can then be factored into independent branch objects, each of which may be routed through finer-resolution Routing SKs, described in branch-specific language, and accreted into one or more System Understanding Bundles. The architecture preserves a hard boundary between the semantic template and the corpus. A GROOVE Entry does not become a Bit, BitWord constituent, Model input source, or BIGFOOT record merely because its GROOVE state uses the same ordered Routing SK vocabulary. Stable coordinates enable comparison and retrieval: a branch that resolves to a semantic address can surface the corresponding Models, Operators, CIRCLE structures, FRINGE structures, or FASKs for explicit comparison. That correspondence remains non-causal and non-genealogical unless separate provenance evidence establishes otherwise. Core normative laws ID Law GRSK-L01 The Routing SK supplies the structural vocabulary; the GROOVE Projection owns the corpus-specific routing state. GRSK-L02 A GROOVE pass SHOULD preserve every defensible compatible route allowed by the Routing SK contract. GRSK-L03 The complete multifactor BitWord state SHALL be preserved before branch factorization. GRSK-L04 Factored branches are derived traversal objects and SHALL preserve the source Entry identity and parent whole-entry state. GRSK-L05 A source Entry MAY participate in several GROOVE Bundles without source duplication. GRSK-L06 Higher semantic resolution increases available distinction, not epistemic certainty. GRSK-L07 Corpus co-activation patterns are GROOVE observations; they SHALL NOT redefine canonical Routing SK relationships. GRSK-L08 Semantic correspondence enables retrieval and comparison; it does not establish provenance, influence, authorship, or canonical membership. GRSK-L09 Routing SK reuse across non-merging environments SHALL NOT imply shared mutable state or shared storage. GRSK-L10 Custom GROOVE Passes MAY compose Routing SKs, prior GROOVE surfaces, Models, and comparison scopes while preserving lineage and review state. Architectural Summary Routing SKs already distinguish canonical route identity from mutable instance state and support independent route masks, explicit cardinality, nested routing, and bounded traversal. GROOVE uses those structural properties as a corpus-discretization grammar rather than as a live link into the Registry. The same ordered semantic contract can be used in CERBERUS and in independent GROOVE environments without merging their data. ADD-ON SCOPE This document does not redefine Routing SK construction, <R> semantics, BIGFOOT identity, Rules, Operators, or Reader behavior. It defines a new usage pattern: how GROOVE instantiates the Routing SK structure over Observable Entries, preserves multifactor results, derives branch objects, and uses those branches for recursive semantic compilation. Contents Sec. Title Sec. Title Part I Structural Semantic Reuse 1 Purpose and Scope 2 Relationship to Routing SKs and GROOVE 3 Non-Merging Semantic Environments 4 Routing SK as Structural Template 5 Canonical Ownership Boundaries Part II Multifactor Corpus Discretization 6 Entry Routing State 7 Independent Route Masks and Cardinality 8 Multifactor Routing Principle 9 Whole-State Preservation 10 Uncertainty and Review Part III Semantic Branch Factorization 11 Active Route Extraction 12 Semantic Branches 13 Semantic Branch Factorization Principle 14 Shared Entry Identity 15 Polyhierarchical Bundle Membership 16 Branch-Conditioned Entry Descriptions 17 Intra-SK Co-Activation Part IV Recursive Semantic Resolution 18 Branch-Conditioned Routing 19 Resolution Families 20 SCIENCE-16 → SCIENCE-64 → SCIENCE-256 21 Stopping Conditions 22 Resolution vs Certainty Part V GROOVE Bundle Compilation 23 Bundle Accretion 24 00 Creation 25 Relation Sweeps 26 Whole-Entry Recovery 27 Cross-Bundle Links Part VI Accretive Semantic Correspondence 28 Semantic Corpus Neighborhoods 29 Canonical Semantic Correspondence 30 Model / CIRCLE / FRINGE / FASK Retrieval 31 Correspondence vs Lineage 32 Branch-Specific Comparison Part VII Custom Passes and Synthesis 33 Routing SK Pass Builder 34 Co-Activation Semantic Surfaces 35 Cross-GROOVE Intersections 36 Custom Idea-Comb Passes 37 Saved Projections and Re-Sweeps Part VIII Worked Example 38 Cross-Domain Entry 39 Multifactor SCIENCE-16 Compilation 40 Three-Branch Factorization 41 Recursive Resolution and Bundle Placement 42 Canon/FASK Comparison 43 Co-Activation Idea Sweep Part IX Governance and Conformance 44 Permissions and Scope 45 Provenance and Review 46 Failure Modes 47 Conformance Requirements 48 Conclusion Appendix A Reference Interface Objects Appendix B GROOVE Routing Pass Schema Glossary Key Terms PART I — STRUCTURAL SEMANTIC REUSE One ordered Routing SK contract can be reused as a semantic template in many independent GROOVE environments. 1. Purpose and Scope This specification defines the GROOVE-side use of Routing Semantic Kernels. The primary purpose is corpus discretization: an Observable Entry is evaluated against a bounded ordered semantic vocabulary and the resulting Routing SK state is stored in a GROOVE Projection. The Routing SK is reused structurally, like a template or semantic ruler. GROOVE does not need to link the source file into BIGFOOT in order to use the same ordered distinctions. The specification covers multifactor routing, route-state preservation, branch derivation, recursive refinement, Bundle accretion, branch-conditioned descriptions, co-activation analysis, canonical semantic correspondence, and configurable pass construction. It does not require that every corpus use CERBERUS storage, that every Entry be imported into a Registry, or that every GROOVE result become canonical. 2. Relationship to Routing SKs and GROOVE The companion Routing SK specification defines the Router as a bounded Semantic Kernel role whose primary purpose is to organize, select, classify, sort, link, index, or expose registered semantic destinations. It also distinguishes canonical route destination from mutable route state and explicitly supports independent route masks in which several routes can be active. This add-on uses those properties as a semantic compilation contract for external corpora. GROOVE contributes the persistence layer around that contract. It stores which routes were activated for which Entry, under which Routing SK version and Sweep Profile, with what review state, branch descriptions, derived Bundle memberships, and subsequent relations. The Routing SK remains the structural vocabulary; GROOVE remains the corpus-specific interpretation layer. 3. Non-Merging Semantic Environments NON-MERGER PRINCIPLE Using SCIENCE-16 in GROOVE is equivalent to saying “evaluate this Entry using these sixteen ordered semantic distinctions.” It is not equivalent to importing the Entry into the Routing SK Registry, sharing mutable instance state with BIGFOOT, or asserting that the Entry influenced the definition of any Bit. Environment Uses Owns Does not imply CERBERUS / BIGFOOT Canonical Routing SK identity and governed semantic definitions. Bit identities, BitGroups, BitWord contract, registered destinations, linked Models/Rules/Operators. External GROOVE Entries are canonical constituents. GROOVE Projection A structural copy/reference of the ordered Routing SK vocabulary for corpus evaluation. Entry-specific route state, branch objects, descriptions, Bundle membership, review/provenance. Shared storage, shared mutable state, source lineage, or Registry membership. Runtime / AI pass The declared Routing SK + pass configuration. Temporary evaluation context and candidate results. Authority to publish canonical semantic changes. 4. Routing SK as Structural Template The structural template includes the ordered route vocabulary, the allowed cardinality of route groups, any declared meaning of inactive/unknown states, and sufficient version metadata to interpret the resulting BitWord. GROOVE SHOULD use the same semantic positions in the same order so that separate corpora can be compared using stable coordinates. A Routing SK used in GROOVE may be materialized as a local immutable schema snapshot, a compact exported contract, or another implementation that faithfully preserves the registered ordering and meanings. The implementation mechanism is secondary to semantic fidelity. ONE ROUTING SK, TWO NON-MERGING ENVIRONMENTS Structural semantic reuse CERBERUS GROOVE BOUNDARY CERBERUS SCIENCE-16 Bits / destinations / Models Canonical definitions STRUCTURAL REUSE same ordered B01…B16 No shared mutable state No corpus import GROOVE Research Archive A DOC-001…DOC-N Entry routing states Figure 1. One Routing SK used in two non-merging environments. Figure explanation The same ordered SCIENCE-16 semantic contract can be used canonically inside CERBERUS and structurally inside an independent GROOVE corpus. Semantic identity and ordering correspond; source records, runtime state, and ownership do not merge. 5. Canonical Ownership Boundaries Object Owns Must not be inferred from GROOVE use Routing SK Ordered vocabulary, Bit meaning, route contract, version. That GROOVEd Entries are constituents or historical sources of the SK. GROOVE Entry Routing State The corpus-specific BitWord result for one Entry under one Routing SK version. That active routes are canonical claims about the source beyond the declared GROOVE review state. Semantic Branch A derived isolated active route plus lineage to the whole-entry state. That the source Entry is only about that branch. Bundle An accreted semantic neighborhood of branch memberships. That folder/Bundle membership changes source identity or ownership. Model / FASK Its own canonical or speculative semantics and governance. That semantic correspondence proves influence, evidentiary support, or derivation. PART II — MULTIFACTOR CORPUS DISCRETIZATION Compile the Routing SK as a BitWord first; do not collapse a complex Entry into one convenient label. 6. Entry Routing State An Entry Routing State is the GROOVE-owned application result of one Routing SK to one Observable Entry. If the Routing SK exposes sixteen independent semantic routes, the GROOVE result is a sixteen-position BitWord interpreted under that exact version. The state belongs to the Entry × Routing SK evaluation, not to the canonical Bit records. 7. Independent Route Masks and Cardinality When the Routing SK contract permits zero-or-more or one-or-more active routes, GROOVE SHOULD preserve all compatible factors that are defensibly present. A paper about biologically derived food packaging can legitimately activate Materials Science, Biological Science, and Food Sciences simultaneously. Forcing one primary label would discard information that the word was designed to represent. Cardinality GROOVE interpretation zero-or-more Any defensible subset of routes may activate; multifactor state is expected. one-or-more At least one route must activate; several may coexist. exactly-one The Routing SK contract itself requires one route; GROOVE SHALL validate accordingly. at-most-one Zero or one active route is allowed. bounded-many(N) Several routes may activate, up to the declared bound. 8. Multifactor Routing Principle MULTIFACTOR ROUTING PRINCIPLE A GROOVE application of a Routing SK SHOULD preserve every defensible compatible route activation permitted by the Routing SK contract. The complete resulting BitWord is the primary corpus discretization record; any later single-route branches are derived from it. Illustrative SCIENCE-16 result: 0000 0010 0100 0001 In this paper, the active positions are illustratively labeled Materials Science, Biological Science, and Food Sciences. The labels and bit positions are examples only; a production SCIENCE Routing SK must use separately governed definitions and versioned allocations. GROOVE ENTRY COMPILER Corpus: Research Archive A ENTRY ROUTING BRANCHES SOURCE DOC-184 Bio-Derived Active Food Packaging Material Observable source remains one Entry. The GROOVE pass evaluates all compatible SCIENCE-16 factors. OPEN SOURCE Routing Template: SCIENCE-16 v1.0 B03 ○ Physical Sciences B06 ● Materials Science B08 ○ Earth Systems B10 ● Biological Science B13 ○ Behavioral Science B16 ● Food Sciences COMPILED BITWORD 0000 0010 0100 0001 3 Active factors zero-or-more Policy Proposed Review FACTOR BRANCHES Figure 2. Multifactor Entry Compiler interface. Figure explanation The compiler evaluates a single Observable Entry against the complete Routing SK template and preserves every compatible route activation permitted by the word contract. The resulting BitWord is a multifactor semantic reading, not a single-label classification. 9. Whole-State Preservation The complete BitWord SHALL remain inspectable after factorization. The whole state preserves co-occurrence: the fact that several semantic factors were present in one source. That information supports later corpus statistics, intersection discovery, and return from a branch-specific view to the complete Entry context. 10. Uncertainty and Review A GROOVE result SHOULD distinguish reviewed activations from AI-proposed activations. Where the source supports a broad route but not a finer route, the system should preserve the broad factor and stop rather than manufacture precision. Unknown, unresolved, or disputed branch states may be represented by companion review metadata when the Routing SK itself is binary. Review state Meaning PROPOSED AI or automated pass suggests the activation; not yet ratified. REVIEWED A reviewer has inspected the relevant source context and accepted the route for GROOVE use. VERIFIED The route has passed the declared GROOVE evidence/review procedure. DISPUTED Reasonable disagreement exists; preserve both the route proposal and dissent. REJECTED The proposed route SHALL NOT participate in the active GROOVE state. PART III — SEMANTIC BRANCH FACTORIZATION Preserve the multifactor whole, then derive independent semantic continuations for deeper routing and Bundle formation. 11. Active Route Extraction Factorization begins only after a complete Entry Routing State exists. GROOVE identifies every active route permitted by the validated word state and creates a branch record that isolates that route while retaining a pointer to the parent Entry, Routing SK version, and whole-entry BitWord. 12. Semantic Branches A Semantic Branch is a derived GROOVE traversal object representing one active routing factor or explicitly bounded subset of factors from a parent multifactor state. A branch is not another copy of the document. It is a semantic continuation context that allows subsequent passes to ask narrower questions of the same source. 13. Semantic Branch Factorization Principle SEMANTIC BRANCH FACTORIZATION PRINCIPLE A multifactor GROOVE Routing state MAY be decomposed into independently traversable branches for finer Routing SK passes, Bundle construction, branch-conditioned interpretation, and comparison. Decomposition SHALL preserve the original combined state and the stable source Entry identity. GROOVE BITWORD FACTORIZER DOC-184 × SCIENCE-16 WHOLE STATE FACTORED BRANCHES PROVENANCE WHOLE-ENTRY ROUTING STATE 0000 0010 0100 0001 ↓ preserve combined state, then isolate each active factor for traversal ↓ BRANCH 01 0000 0010 0000 0000 Materials Science SCIENCE-16:B06 CONTINUE BRANCH 02 0000 0000 0100 0000 Biological Science SCIENCE-16:B10 CONTINUE BRANCH 03 0000 0000 0000 0001 Food Sciences SCIENCE-16:B16 CONTINUE ✓ Original multifactor state preserved ✓ Source identity preserved: DOC-184 ✓ Branches remain derived GROOVE objects Figure 3. BitWord factorization interface. Figure explanation The whole-entry state remains canonical to the GROOVE Projection while active routes are factored into branch objects. Each branch can be routed independently at higher semantic resolution without erasing the fact that all three factors co-occurred in the same source Entry. 14. Shared Entry Identity Every branch originating from the same document, image, dataset, or other Observable Entry retains the same underlying Entry ID. The branch adds route lineage; it does not mint a competing source identity. This is what makes later cross-Bundle and Cross-GROOVE synthesis possible without duplicating files. 15. Polyhierarchical Bundle Membership A source can legitimately belong to several semantic neighborhoods. GROOVE therefore treats Bundle membership as branch membership rather than as exclusive file ownership. Physical storage can remain a simple tree while the semantic topology above it remains polyhierarchical. ENTRY MEMBERSHIP MAP DOC-184 MEMBERSHIP WHOLE STATE SOURCE One Observable Entry can participate in several GROOVE Bundles through different factored branches. MATERIALS BUNDLE via SCIENCE-16:B06 MATERIALS-64:B21 BIOLOGY BUNDLE via SCIENCE-16:B10 BIOLOGY-64:B44 FOOD SCIENCE BUNDLE via SCIENCE-16:B16 FOOD_SCIENCE-64:B18 DOC-184 — shared source identity 1 source • 3 semantic memberships • 0 source duplication Figure 4. Polyhierarchical Bundle membership. Figure explanation Bundle membership is produced by factored semantic branches, not by duplicating or re-homing the source file. The same Entry identity can therefore participate in several independently compiled Bundles while its physical storage and provenance remain singular. 16. Branch-Conditioned Entry Descriptions Once a branch exists, GROOVE MAY compile a short description explaining why the source belongs in that branch. This description should be written from the branch context and point to relevant source locations. It is distinct from the whole-document summary, which may remain broader. BRANCH-CONDITIONED DESCRIPTION EDITOR DOC-184 MATERIALS BIOLOGY FOOD SCIENCE SCIENCE-16:B06 Branch MATERIALS-64:B21 Next AI Draft Review AI DRAFT Relevant to Materials Science because the Entry evaluates mechanical strength, permeability, and degradation behavior of a bio-derived packaging substrate. This description explains branch membership; it does not replace the source summary for the whole document. GROUNDED LOCATIONS • §3 Material Composition • §5 Barrier Testing • Figure 7 ACCEPT EDIT REJECT Figure 5. Branch-conditioned Entry description. Figure explanation A single document can carry different compact descriptions for different semantic branches. Each description answers why the same source belongs in that Bundle and cites relevant source locations, improving future AI reading without creating separate source documents. 17. Intra-SK Co-Activation Because the whole-entry BitWord is preserved, GROOVE can aggregate which factors repeatedly activate together across a corpus. Co-activation is a property of the GROOVEd corpus under a Routing SK version. It does not create a canonical Bitlink or change the Routing SK. It can, however, identify semantic intersections worth further analysis. SCIENCE-16 CO-ACTIVATION EXPLORER Corpus: 50,000 Entries MATRIX PAIR DETAILS NEW SURFACE 48,713 Entries routed 21,905 Multifactor 73 Active pairs Materials Biology Food Physics Materials — 6,701 3,240 1,182 Biology 6,701 — 4,711 932 Food 3,240 4,711 — 510 Physics 1,182 932 510 — Selected pair: Materials × Biology • 6,701 Entries Corpus co-activation is a GROOVE statistic. It does not redefine the SCIENCE-16 Bit relationships. CREATE SEMANTIC SURFACE Figure 6. Intra-SK co-activation explorer. Figure explanation The preserved whole-entry BitWord makes corpus-level co-activation measurable. Dense factor combinations can seed targeted semantic surfaces and new passes, while remaining explicitly separate from canonical Routing SK relations. PART IV — RECURSIVE SEMANTIC RESOLUTION Each branch can become the bounded input context for a finer semantic routing contract. 18. Branch-Conditioned Routing A finer pass SHOULD receive both the original Observable Entry and the active parent branch context. This avoids repeatedly asking the AI to classify the entire document from scratch. The system instead asks a narrower question: within the semantic factor already identified, which finer distinctions are present? 19. Resolution Families Routing SK families may increase semantic resolution by word width or by nested specialist routers. The naming SCIENCE-16, SCIENCE-64, and SCIENCE-256 is illustrative of increasing available distinction; an implementation may instead use branch-specific words such as MATERIALS-64, BIOLOGY-64, and FOOD_SCIENCE-64. What matters is that the continuation is explicit, versioned, and appropriate to the branch. 20. SCIENCE-16 → SCIENCE-64 → SCIENCE-256 Stage Purpose Example result SCIENCE-16 Coarse multifactor domain detection. Materials + Biology + Food Sciences Branch factorization Isolate each active factor while preserving the whole. Materials branch / Biology branch / Food branch 64-resolution router Distinguish meaningful subdomains inside each branch. Biopolymers / Microbial Degradation / Food Packaging 256-resolution router Pinpoint specialist semantic regions where useful. Specific mechanism, process, or domain specialization SEMANTIC RESOLUTION TREE DOC-184 TREE PASS BUILDER BRANCH DETAILS DOC-184 SCIENCE-16 0000 0010 0100 0001 Materials Biology Food Science MATERIALS-64 BIOLOGY-64 FOOD_SCIENCE-64 Composite Materials Microbial Degradation Food Preservation Biopolymers Packaging [Continue] [Stop: sufficient] [Continue] Branch context constrains the next Routing SK. Finer resolution is applied only where useful and defensible. Figure 7. Recursive semantic resolution tree. Figure explanation Branch-specific Routing SKs refine an Entry independently after multifactor factorization. The tree preserves the broad coordinates, the route lineage, the selected finer word, and explicit stopping points where additional resolution would be unnecessary or speculative. 21. Stopping Conditions A branch SHOULD stop when further routing adds little retrieval value, when no registered finer Routing SK applies, when source evidence is insufficient, when permissions block inspection, or when the next distinction would be speculative. Stopping is a valid result, not a failure. 22. Resolution vs Certainty RESOLUTION-NOT-CERTAINTY PRINCIPLE A higher-width Routing SK offers finer semantic distinctions. It does not make the GROOVE interpretation more certain by itself. Confidence and review status remain separate from classification resolution. PART V — GROOVE BUNDLE COMPILATION Branch memberships accrete into semantic neighborhoods that can be summarized, related, and routed through local 00 manifests. 23. Bundle Accretion A GROOVE Bundle collects branch memberships that resolve into a useful semantic territory. The Bundle can contain documents, images, diagrams, tables, datasets, or other Entry types because routing is based on semantic factors rather than file format. One source may contribute to several Bundles through several branches. 24. 00 Creation Once a Bundle has enough stable membership, GROOVE can compile a local 00 manifest describing the Bundle, its sources, branch lineages, candidate foundation Entries, relations, boundaries, and reading paths. The 00 is a navigation and interpretation artifact, not a replacement for the underlying Entries. GROOVE BUNDLE COMPILER Materials Science ENTRIES RELATIONS 00 PREVIEW WHOLE-ENTRY LINKS 428 Branch entries 371 Unique sources 104 Shared multifactor 612 Candidate relations Entry Routing lineage Branch description Source DOC-184 SCIENCE-16:B06 → MATERIALS-64:B21 Bio-derived packaging substrate OPEN PAPER-311 SCIENCE-16:B06 → MATERIALS-64:B18 Composite fatigue mechanisms OPEN IMG-071 SCIENCE-16:B06 → MATERIALS-64:B09 Layered material diagram OPEN DOC-052 SCIENCE-16:B06 → MATERIALS-64:B21 Biopolymer processing OPEN PREVIEW 00 COMPILE GROOVE BUNDLE Figure 8. Bundle compiler and 00 builder. Figure explanation The Bundle compiler aggregates branch memberships rather than taking ownership of source documents. It preserves route lineage, branch-conditioned descriptions, shared multifactor source links, and candidate relations before generating the local 00 GROOVE manifest. 25. Relation Sweeps After Bundle membership is established, later passes can inspect relations among Entries with a substantially smaller search space and better semantic orientation. Relations may include REQUIRES, EXTENDS, APPLIES, CONTRADICTS, DEPICTS, EXAMPLE_OF, or custom GROOVE vocabularies. Relation inference remains distinct from the Routing SK state that created the Bundle. 26. Whole-Entry Recovery A user reading a Materials Bundle should be able to return from the Materials branch of DOC-184 to the complete Entry Routing State and see that Biology and Food Science were also active. This avoids branch tunnel vision and allows cross-domain synthesis to recover the original multifactor context. 27. Cross-Bundle Links When the same Entry participates in several Bundles, GROOVE may expose those memberships as navigation links. The cross-Bundle relationship comes from shared Entry identity and factored route lineage, not from duplicated source files or forced folder hierarchy. PART VI — ACCRETIVE SEMANTIC CORRESPONDENCE Stable routing coordinates let GROOVE material accumulate around semantic regions and become comparable to existing CERBERUS structures without becoming their provenance. 28. Semantic Corpus Neighborhoods As more Entries are GROOVEd through the same Routing SK positions, each semantic coordinate gains a retrievable corpus neighborhood. The neighborhood is a GROOVE-side index of independently classified material. It is not a new canonical definition of the route and does not alter the semantic contract. 29. Canonical Semantic Correspondence A Routing SK position may correspond to a semantic territory that has Models, Operators, Rules, Readers, CIRCLE knowledge, FRINGE material, or FASKs in CERBERUS. GROOVE can use the stable coordinate to surface those structures for comparison. The relationship is a shared semantic address across non-merging environments. 30. Model / CIRCLE / FRINGE / FASK Retrieval Once an Entry branch is sufficiently resolved, a comparison pass can ask how the branch relates to structures already present in the corresponding territory. The output may identify overlap, extension, contradiction, unrepresented distinctions, or related FASKs. Such outputs are new GROOVE comparison records and must preserve their own review state. SEMANTIC CORRESPONDENCE INSPECTOR SCIENCE-256:B117 GROOVE CERBERUS TERRITORY COMPARE FASKS GROOVE BRANCH DOC-184 SCIENCE-16:B16 → FOOD_SCIENCE-64:B18 → SCIENCE-256:B117 Branch description: microbial fermentation dynamics in active packaging. GROOVE neighborhood: 128 related Entries CORRESPONDING CERBERUS TERRITORY Canonical Models: 3 Operators: 7 Rules: 12 CIRCLE items: 41 FRINGE items: 8 FASKs: 6 SEMANTIC CORRESPONDENCE ≠ SOURCE LINEAGE ≠ CANONICAL MEMBERSHIP COMPARE BRANCH TO MODELS + FASKs Figure 9. Canon and FASK correspondence interface. Figure explanation A stable Routing SK coordinate lets GROOVE surface the corresponding CERBERUS semantic territory for comparison. The interface keeps a hard representational boundary: related corpus Entries are independently GROOVEd material, not sources that defined or influenced the Bits, Models, Operators, Rules, CIRCLE, FRINGE, or FASK records. 31. Correspondence vs Lineage CORRESPONDENCE-NOT-LINEAGE PRINCIPLE If DOC-184 resolves to the same semantic address used by an existing Model, GROOVE may surface that Model for comparison. This does not mean DOC-184 defined, influenced, validated, or historically preceded the Model. Provenance and influence require separate evidence. 32. Branch-Specific Comparison The same Entry can compare differently in different branches. A mechanism may be established in Biology, routine in Materials Science, and novel as an application in Food Science. GROOVE SHOULD preserve those domain-relative results rather than collapse novelty or alignment into one global score. PART VII — CUSTOM PASSES AND SYNTHESIS Routing SKs become modular semantic instruments that can be inserted into user-defined Sweep Profiles over saved GROOVE surfaces. 33. Routing SK Pass Builder GROOVE does not define one universal pass order. A pass configuration declares its input surface, Routing SK, review policy, multifactor policy, branch policy, downstream resolution, comparison targets, and output. This permits general classification sweeps as well as highly targeted idea-combing sweeps. CUSTOM GROOVE PASS BUILDER New Pass INPUT ROUTER FACTOR POLICY COMPARE OUTPUT Input surface SCIENCE-16 co-activation: Materials + Biology Input size 6,701 Entries Apply Routing SK BIOLOGY-256 v2.0 Pass purpose Look for biological transformation patterns within material-science Entries Multifactor policy Preserve all compatible active routes Branch policy Factor active routes and retain whole-entry state Compare against Materials Models + Biology Models + related FASKs Output Bio-Materials Idea GROOVE Review gate Human review required before promoted relations RUN PASS SAVE SWEEP PROFILE Figure 10. Custom idea-comb Pass Builder. Figure explanation Routing SKs become configurable semantic instruments inside GROOVE Sweep Profiles. A pass can begin from a prior co-activation or Bundle surface, apply another Routing SK, preserve multifactor state, factor new branches, compare against existing Models/FASKs, and save the result as a reusable GROOVE Projection. 34. Co-Activation Semantic Surfaces A dense co-activation region such as Materials + Biology can be saved as a Semantic Surface and used as the input set for another Routing SK. The surface is derived from GROOVE statistics and remains traceable to the whole-entry states that produced it. 35. Cross-GROOVE Intersections Cross-GROOVE synthesis differs from intra-SK co-activation. It combines independently applied semantic instruments over shared Entry identities. For example, SCIENCE-16:B16 may be intersected with FOOD-128:B72 to find Entries that independently landed in both coordinates. CROSS-GROOVE INTERSECTION BUILDER Shared Entry identity PROJECTION A OPERATION PROJECTION B FOLLOW-UP A SCIENCE-16:B16 Food Sciences ∩ INTERSECT 2,104 shared Entries B FOOD-128:B72 Fermentation FOLLOW-UP PASS CHEMISTRY-256 → classify + relation sweep → save FOOD-SCIENCE-CHEMISTRY GROOVE SAVE SEMANTIC SURFACE Figure 11. Cross-GROOVE coordinate intersection. Figure explanation Cross-GROOVE synthesis operates over shared Entry identities and independently applied structural coordinates. The resulting Semantic Surface can become the input to another Routing SK or comparison pass without merging the underlying SKs, corpora, or canonical semantic systems. 36. Custom Idea-Comb Passes A custom pass can deliberately search for concepts from one domain inside material previously routed into another. “Look for Biological Ideas within Materials Sciences” becomes a concrete configuration: use a Materials-scoped GROOVE surface as input, apply a Biology Routing SK, factor the resulting routes, and optionally compare them against registered Materials and Biology Models or FASKs. 37. Saved Projections and Re-Sweeps The output of a Routing SK pass MAY be saved as a versioned GROOVE Projection. Future passes can operate on that compact projection first, then selectively reopen source artifacts where needed. This is the accretive property of Semantic Grooving: interpretive work becomes reusable infrastructure rather than disappearing after one AI interaction. GROOVE ROUTING LIFECYCLE Reference flow PIPELINE LOOPS PROVENANCE 1 ENTRY Observable source 2 MULTIFACTOR ROUTING Compile BitWord 3 FACTOR Extract active branches 4 RESOLVE Finer Routing SKs 5 DESCRIBE Branch-conditioned summaries 6 BUNDLE Accrete semantic neighborhoods 7 00 + RELATIONS Compile local GROOVE 8 COMPARE Models / CIRCLE / FASKs 9 DISCOVER Candidate Models / Operators / Rules CO-ACTIVATION → NEW SEMANTIC SURFACE → CUSTOM PASS → back into ROUTING Figure 12. Complete GROOVE Routing SK lifecycle. Figure explanation The lifecycle preserves whole-entry multifactor state, derives branch objects for independent resolution, accretes those branches into Bundles, and uses stable semantic correspondence for comparison and targeted idea discovery. Corpus-derived co-activation can seed new semantic surfaces and custom passes without altering the Routing SK definitions. PART VIII — WORKED EXAMPLE A single cross-domain Entry demonstrates multifactor compilation, factorization, recursive resolution, Bundle placement, correspondence, and idea-combing. 38. Cross-Domain Entry Consider the illustrative document DOC-184, “Bio-Derived Active Food Packaging Material.” It contains material-property testing, biologically produced polymer mechanisms, and food-preservation requirements. The example is intentionally cross-domain so that a single-label classifier would lose useful structure. 39. Multifactor SCIENCE-16 Compilation A SCIENCE-16 GROOVE pass evaluates the Entry against the full sixteen-position routing template and returns: 0000 0010 0100 0001 Active branch Illustrative meaning Why active B06 Materials Science The Entry evaluates strength, permeability, material composition, and degradation behavior. B10 Biological Science The Entry relies on biologically derived polymers and microbial degradation mechanisms. B16 Food Sciences The Entry evaluates packaging performance relative to preservation and storage requirements. 40. Three-Branch Factorization GROOVE preserves the whole state and derives three branches. Each branch retains DOC-184 as the source Entry and records its own route lineage. The same source is therefore available to three Bundle pipelines without copying the document. 41. Recursive Resolution and Bundle Placement Branch 64-resolution continuation Resulting Bundle membership Materials MATERIALS-64 Composite Materials + Biopolymers → Materials Science Bundle Biology BIOLOGY-64 Microbial Degradation → Biology Bundle Food Science FOOD_SCIENCE-64 Food Preservation + Packaging → Food Sciences Bundle 42. Canon/FASK Comparison Branch Comparison outcome Materials Most core material-property concepts overlap established structures; one polymer behavior is unrepresented. Biology The microbial degradation mechanism aligns with established biology semantics and is related to an existing speculative FASK. Food Science The application combines known mechanisms in a way not represented by the current Food Science Model; flag as a candidate extension rather than asserting novelty as fact. 43. Co-Activation Idea Sweep At corpus scale, the Materials + Biology co-activation pair appears frequently. The user creates a Semantic Surface containing all Entries with that pair, then configures a new Biology-256 pass to look for recurring transformation mechanisms within materials-oriented Entries. The output is saved as a Bio-Materials Idea GROOVE, after which candidate Models or Operators can be reviewed and formalized separately. PART IX — GOVERNANCE AND CONFORMANCE GROOVE gains flexibility from reusable routing structure only if representational layers remain explicit, reviewable, and bounded. 44. Permissions and Scope A GROOVE pass SHALL operate only over Entries and semantic structures authorized for the current user or process. Sharing a Routing SK template does not grant access to corpora that used it. Likewise, a correspondence lookup into CERBERUS must respect the visibility rules of the target Models, FASKs, and other records. 45. Provenance and Review Every material GROOVE routing result SHOULD preserve Entry identity, Routing SK identity/version, Sweep Profile identity/version, whole BitWord state, active branch positions, branch lineage, review status, source locations used for justification where available, and downstream derived artifacts. This allows the route interpretation to be revisited as sources or models evolve. 46. Failure Modes Anti-pattern Failure Correction Single-label collapse A multifactor Entry is forced into one broad domain. Use the Routing SK cardinality contract and preserve all compatible factors. Branch replaces whole Only factored branches survive. Preserve the original whole-entry BitWord and link every branch back to it. Global reclassification Every fine pass ignores branch context and rereads the source as if no prior routing occurred. Pass the source plus the active parent branch to the finer router. GROOVE-to-BIGFOOT merge External Entries are treated as canonical SK constituents merely because they use its structure. Keep GROOVE routing state in the GROOVE environment. Co-activation becomes canon Frequent corpus co-occurrence is promoted to a canonical Bit relation. Keep co-activation as a corpus-derived statistic until independently modeled. Correspondence becomes lineage A related Model is presented as if the source created or influenced it. Use explicit correspondence labels and separate provenance evidence. Resolution inflation A system forces every Entry through the highest-resolution router. Stop when finer routing is unsupported or adds little retrieval value. Hidden pass behavior Custom passes silently change factor policy or comparison scope. Persist the Sweep Profile and expose the Pass Builder configuration. 47. Conformance Requirements ID Requirement GRSK-C01 A conforming GROOVE use of a Routing SK preserves the SK order, version, and semantic meaning of each route position. GRSK-C02 Corpus-specific route state is stored outside the canonical Routing SK definition. GRSK-C03 When the Routing SK permits multi-route activation, the system can preserve more than one active factor for one Entry. GRSK-C04 The full Entry Routing State remains recoverable after branch factorization. GRSK-C05 Every branch points to the same underlying source Entry identity and its parent whole-entry state. GRSK-C06 One source Entry may participate in multiple Bundles without source duplication. GRSK-C07 Finer Routing SK passes can be conditioned on one factored branch. GRSK-C08 The system can stop resolution without fabricating a finer classification. GRSK-C09 Corpus co-activation remains distinguishable from canonical Routing SK relations. GRSK-C10 Semantic correspondence to Models/FASKs remains distinguishable from provenance or influence. GRSK-C11 Custom Passes expose input scope, Routing SK, factor policy, comparison scope, and output. GRSK-C12 Saved GROOVE Projections preserve enough lineage to determine which Routing SK versions and source Entries produced them. GRSK-C13 Cross-GROOVE intersections use shared Entry identity or another explicit compatibility bridge. GRSK-C14 Permissions are enforced independently for source corpora and corresponding CERBERUS structures. GRSK-C15 A deterministic interface can show both the whole-entry BitWord and its factored branches without AI reinterpretation. 48. Conclusion Routing Semantic Kernels give GROOVE a compact semantic discretization grammar that is both bounded and reusable. Their value is not that they put each document into one box. Their value is that the whole Routing SK can be compiled as a multifactor word, allowing one Entry to activate several meaningful domains at once. GROOVE preserves that combined state, factors it into independent semantic branches, and increases resolution inside each branch only where useful. This makes semantic organization polyhierarchical without forcing storage duplication. It also creates two valuable forms of synthesis: intra-SK co-activation, where several factors occur together inside one Routing SK state, and Cross-GROOVE intersection, where independently applied semantic instruments resolve the same Entry into compatible coordinates. Both can seed new Semantic Surfaces and custom passes. FINAL ARCHITECTURAL LAW The Routing SK defines the ordered semantic ruler. GROOVE records how an Entry measures against it. The whole BitWord preserves multifactor meaning. Branches provide traversable continuations. Bundles accrete around those branches. Models and FASKs can be surfaced for comparison through shared semantic correspondence — without merging environments or inventing lineage. APPENDIX A — REFERENCE INTERFACE OBJECTS Minimum user-facing objects required to make multifactor routing inspectable and configurable. Interface object Required visibility Routing SK Template Selector Routing SK name/version, route vocabulary, cardinality, applicable scope. Entry Compiler Source Entry, complete route list, active/inactive positions, compiled BitWord, review state. BitWord Factorizer Parent whole state, active branches, source identity, branch continuation controls. Resolution Tree Branch lineage, finer Routing SKs, stopping points, whole-state return path. Branch Description Editor Branch-specific description, source locations, review controls. Bundle Compiler Branch memberships, unique source count, shared multifactor Entries, 00 preview. Co-Activation Explorer Corpus-level pair/multi-factor counts with explicit non-canonical warning. Correspondence Inspector GROOVE branch on one side; corresponding Models/CIRCLE/FRINGE/FASKs on the other; lineage boundary. Pass Builder Input surface, Routing SK, factor policy, branch policy, comparisons, output, review gate. Cross-GROOVE Builder Projection A, operation, Projection B, shared Entry count, follow-up pass. APPENDIX B — GROOVE ROUTING PASS SCHEMA A reference configuration structure for custom semantic grooving. Fields are illustrative and technology-neutral. Field Purpose Pass ID Stable identity for the pass definition. Pass Name Human-readable purpose. Input Surface Corpus, Bundle, Semantic Surface, prior Projection, or branch set. Routing SK Structural semantic template and version. Cardinality Policy Use the Routing SK contract or an explicitly narrower compatible policy. Multifactor Policy Preserve all compatible routes, preserve reviewed-only routes, etc. Branch Policy Factor each active route, factor selected routes, or preserve whole-only. Next Resolution Default or conditional finer Routing SKs for each branch. Description Policy Whether to generate branch-conditioned Entry descriptions. Bundle Policy How resolved branches accrete into Bundles. Comparison Scope Optional Models, CIRCLE, FRINGE, FASKs, or prior GROOVEs. Review Gate Proposed/reviewed/verified requirement before promotion. Output Type GROOVE Projection, Semantic Surface, Bundle, 00 manifest, candidate component set. Reopen Policy When the original source must be inspected rather than relying on prior summaries. Provenance Required source, Routing SK, pass, review, and derived-artifact lineage. Glossary Term Definition Accretive Semantic Correspondence The accumulation of independently GROOVEd Entries around a stable semantic coordinate, enabling retrieval and comparison without changing the Routing SK or implying lineage. Branch-Conditioned Entry Description A compact explanation of why one source Entry participates in one specific semantic branch. Entry Routing State The complete corpus-specific BitWord produced by applying one Routing SK version to one Observable Entry. GROOVE Branch A derived isolated active route or bounded subset of routes used for deeper routing, Bundle compilation, or comparison. GROOVE Routing Pass A configured operation that applies a Routing SK to an input surface and persists declared outputs. Intra-SK Co-Activation Two or more route positions active together in the same Routing SK result for one or more Entries. Multifactor Routing Preservation of several simultaneously applicable routes within one Routing SK state when the contract permits them. Non-Merging Environment An environment that reuses the same semantic structure without sharing canonical storage or mutable state. Polyhierarchical Bundle Membership One source Entry participating in several Bundles through several semantic branches. Recursive Semantic Resolution Application of finer or specialist Routing SKs to a previously factored branch. Semantic Branch Factorization Derivation of independently traversable route branches from a preserved multifactor Entry Routing State. Semantic Corpus Neighborhood The GROOVE-side collection of Entries that resolve to a shared semantic coordinate or compatible branch region. Semantic Surface A bounded set of Entries/branches produced by GROOVE operations and used as input to later passes. Structural Semantic Reuse Use of a registered semantic structure as an immutable interpretive template in another environment without shared mutable state, shared storage, or canonical merger. Reference Architecture Overview REFERENCE ARCHITECTURE Whole → factor → refine → accrete → compare ENTRY ROUTING BUNDLES CORRESPONDENCE ENTRY DOC / IMG / DATA ROUTING SK multifactor BitWord FACTOR semantic branches RESOLVE finer Routing SKs BUNDLE 00 + relations COMPARE Models / FASKs Whole-state co-activation and Cross-GROOVE intersections can seed custom passes at any later stage. Figure 13. GROOVE Routing SK reference architecture. Figure explanation The add-on architecture begins with a complete multifactor Routing SK reading, derives branch continuations, selectively increases semantic resolution, accretes branch memberships into Bundles, and exposes stable correspondence to existing semantic structures for comparison. Whole-state and cross-projection synthesis remain available as inputs to new custom passes.