This document is the public navigation map for the Representation-Induced Mechanics and Evolution (RIME) program. It identifies semantic ownership, typed interfaces, and promotion boundaries across Papers I--XIV. It is not a proof document, release ledger, result record, or substitute for an owning manuscript.
Definitions, hypotheses, theorem statements, and claim boundaries belong to the owning versioned manuscript. Project-specific numerical values and computational certificates belong to their declared inputs, versioned result records, and passing validators.
Public release identities, current versions, DOIs, and repository migration status are maintained in the root Public Release table and accepted release manifests. This map describes semantic ownership and does not redefine release status.
As a maintenance rule, candidate architecture first converges in the owning manuscript and internal planning documents. This public map is normally updated after the relevant ownership boundary has been accepted for release. Earlier changes are reserved for correcting or narrowing an already public description.
Cross-paper citations identify compatible interfaces. They do not import hypotheses, promote evidence, or turn neighboring papers into a dependency chain.
The program moves from represented source structure to typed objects and then to increasingly downstream records:
represented source structure
-> compatible realization and sectorization
-> static typed observable carriers
-> declared deformation charts and trajectories
-> capability-sound claim compilation
-> morphology of admitted wall records
-> realization-relative single reports
-> aligned sparse report comparisons
-> context- and policy-relative interpretation
The arrows indicate interface order, not automatic mathematical implication. Every transition must retain its own hypotheses, conventions, policies, and evidence status.
The program's current organizing principle is:
Source structure bounds the available realization.
Sectorization exposes the observable interface.
Typed carriers record distinct accessibility mechanisms.
Deformations produce policy-relative trajectories and walls.
Every cross-layer promotion requires an explicit certificate.
No line asserts a profile-independent observable invariant or a universal law that uniquely determines behavior.
| Paper | Owned layer | Core object | Reader question |
|---|---|---|---|
| I | block spectral structure | represented averaging operator and spectral layers | What is the blockwise canonical spectrum, and which conditional arithmetic criteria apply? |
| II | direct transport registration | compatible sectors and labelled generator blocks | Which direct sector-to-sector channels are present? |
| III | composition obstruction | support paths and projected matrix products | When does support-graph reachability fail to compose at operator level? |
| IV | fixed collision geometry | finite affine-branch arrangement and collision quotient | How do fixed spectral collisions organize quotient layers? |
| V | local accessibility separation | direct support, routed products, words, commutators, and cutoff depth | Why do support and composition not determine commutator accessibility? |
| VI | spectral admissibility and point registration | linearized commutativity/normality constraints and gated spectral samples | Which tangent directions preserve the declared constraints, and which points pass the spectral gates? |
| VII | incidence and promotion limits | image--kernel incidence and rank-protection conditions | When do nonzero projected factors compose, and what blocks stronger promotion? |
| VIII | static SOF object theory | marked SOF core with independently typed operator/word and Lie/Hall branches | What is the static sectorized observable object? |
| IX | observable dynamics | typed charts, comparison maps, trajectories, wall pullbacks, and response policies | How do selected typed fields change? |
| X | capability-aware compilation | Capability Manifest, Typed SOF IR, Report Profile, and Registry evidence | Which claims may be emitted from declared capabilities and evidence? |
| XI | wall morphology | sparse wall atoms, profile-relative coordinates, multi-label taxonomy, and local-model eligibility | What morphology does an admitted wall record have? |
| XII | single-report protocol | realization-relative .sofreport record |
What does one typed report assert, and where does adapter responsibility remain? |
| XIII | alignment and comparison | Audit Profile, alignment contract, and sparse .sofaudit comparison |
How do two aligned reports differ? |
| XIV | interpretation and bounded candidate semantics | ActionContext, PolicyProfile, InterpretationRecord, and bounded CandidateActionSet |
What can admitted context and policy legitimately support from an aligned difference? |
This table is thematic rather than sequential. A paper may import an object or certificate from another paper while retaining its own hypotheses and claim status.
After sectorization, the operator/word and Lie/Hall branches are independently declared:
operator/word branch:
labelled blocks -> direct support -> routed products -> full words
-> route depth and word depth
Lie/Hall branch:
registered Lie generators -> simple commutators -> Hall filtration
-> Lie depth
A graph path is not a routed product. A routed product is not a full-word sum. An associative word is not a commutator. A positive-word algebra, observable star-closure, and sector-enriched star-closure answer different questions. None supplies another carrier without an explicit bridge.
For parameter-dependent sectorizations, the admissibility order is
Sigma_comm -> Sigma_normal -> Sigma_spec -> {Q_i(w)}.
Commutativity does not imply normality. Pointwise diagonalization does not provide coherent projector continuation. Any moving field must declare its chart, label policy, comparison maps, and continuity assumptions.
Exact finite first-hit depth requires a first-hit certificate: a witness at the
reported level and verified non-hits at every lower level. A finite audit may
instead report a hit by a cutoff or UNREACHED_AT_CUTOFF. Response-time
censoring on a declared trajectory interval is a different dynamic state.
Neither truncated state means mathematical infinity.
Missing capabilities are not numerical zero. They remain omitted or carry an explicit unavailable state under the owning contract.
A finite computation supports only its declared Computational Certificate or Computational Observation. Numerical agreement does not prove equality, a finite atlas does not prove genericity, and a proxy trajectory does not prove a binary support or depth transition without a proxy-to-shadow theorem.
The SOF stack has seven ownership layers:
Paper VIII static marked object and carrier-qualified morphisms
Paper IX typed deformation, trajectories, walls, and response
Paper X capability/evidence guards and sound claim compilation
Paper XI wall records, coordinate profiles, and taxonomy
Paper XII realization-relative single-report protocol
Paper XIII aligned sparse comparison
Paper XIV ActionContext/PolicyProfile interpretation and bounded candidates
Paper VI owns the commutativity and normality gates, their linearized certificates, and normality-gated point registrations. These are pointwise certificates. Paper VI does not establish a general deformation category, coherent moving spectral charts, or a wall-pullback theorem.
Paper IX owns typed deformation charts, fibre comparison maps, selected one-parameter trajectories, typed wall definitions, discriminant pullbacks, pullback-exactness, response policies, and truncated or censored dynamic states. A wall is relative to the declared field, chart or path, comparison policy, and threshold conventions.
Paper XI consumes an admissible Paper IX wall datum. It does not redefine what qualifies as a wall. It records trajectory events and locus samples using different typed atoms, attaches sparse field changes or incident-stratum germs, derives profile-relative coordinates, assigns nonexclusive curation tags, and applies local-model eligibility gates. Static findings do not enter a wall spectrum without wall admission, and diagnostic analogue morphology remains separate from the strict main wall spectrum.
Paper X defines the contracts through which validated declarations and evidence may enter Typed SOF IR, and it gates report claims through a Report Profile. The Registry is a parallel compatible evidence interface; Registry rows do not automatically populate the IR. Paper XII defines what one realization-relative report records; it does not re-own the compiler theorem. Paper XIII begins only after two reports and an explicit alignment contract exist.
SOFAUDIT comparison states are interpreted as follows:
| State | Meaning |
|---|---|
ALIGNED |
the coordinate is aligned and equal, or within the declared comparison tolerance |
MISMATCH |
the coordinate is aligned but unequal, or outside the declared comparison tolerance |
NOT_DECLARED |
a required source field was not declared |
NOT_APPLICABLE |
the requested coordinate does not apply under the declared profile |
INCOMPARABLE |
the declarations exist but no valid comparison map or convention is available |
UNRESOLVED |
comparison was requested but the required check did not reach a conclusion |
Paper XIV is the downstream action-semantics layer. It studies context- and policy-relative
interpretation of aligned coordinates and their conversion into structured
bounded candidate-action records. Difference alone is not defect, and no
candidate follows from a Paper XIII mismatch without an admitted
ActionContext and applicable PolicyProfile. That PolicyProfile is the
sole normative rule input in the current contract; selection and authorization
remain downstream.
Papers I--VII provide two broad families of reusable input interfaces:
- spectral and sector interfaces: represented averaging operators, joint spectral data, compatible sectorizations, collision arrangements, and commutativity/normality gates;
- transport and accessibility interfaces: labelled generator blocks, direct support, projected composition, word and commutator carriers, image--kernel incidence, and promotion limits.
These are input families, not two universal routes through every paper. Their detailed ownership and promotion boundaries are maintained in PRE_SOF_INTERFACE_MAP.md.
The Rubik cube is a finite represented-system laboratory. Its registered operators, sectors, support records, collision data, and validation artifacts provide reproducible examples and counterexamples.
The general theory concerns typed constructions such as compatible sectorization, projected composition, words, commutators, incidence, deformation charts, walls, report compilation, and alignment. A Rubik result becomes a general theorem only when the abstract hypotheses and the promotion step are stated and proved.
This map therefore names the logical role of project certificates without copying their numerical payloads. Numerical values remain with the owning manuscript and source-addressed result record.
RIME uses four reader-facing evidence levels:
| Level | Meaning |
|---|---|
| Theorem | exact result proved from declared hypotheses |
| Computational Certificate | reproducible finite computation tied to declared inputs |
| Computational Observation | bounded numerical pattern without theorem promotion |
| Research Program | open problem, conjectural bridge, or proposed extension |
Local theorem claims require proofs. Project-specific computational, numerical, census, or sampled claims require an owning result record and a passing validator. Imported results require accurate citation and ownership attribution. Interpretations must use explicit non-theorem language unless a separate theorem supports them.
The owning manuscript fixes the meaning of a computational claim; the owning result record and validator fix its public numerical value. A disagreement blocks release rather than being resolved by prose precedence.
| Document | Scope |
|---|---|
| PRE_SOF_INTERFACE_MAP.md | Papers I--VII interfaces and promotion boundaries |
| PROGRAM_VOCABULARY.md | controlled typed vocabulary and deprecated shorthand |
| SOF_OBJECTS.md | static SOF objects, carriers, closures, and filtrations |
| SOF_DEFORMATIONS.md | deformation charts, trajectories, walls, and response diagnostics |
| SOF_REGISTRY.md | Registry evidence architecture and capability routing |
| PAPER_SCOPE.md | detailed paper ownership and scope |
| experiments/README.md | source-addressed artifact and validator map |
| schemas/README.md | versioned public data contracts |
RIME studies how represented source structure becomes typed observable data, how declared deformations change that data, and how evidence-preserving interfaces carry the resulting records into reports, comparisons, and context-relative interpretation without crossing undeclared boundaries.