Representation-Induced Mechanics and Evolution
RIME studies spectral, transport, accessibility, and deformation structures in finite-dimensional represented systems. The Rubik cube is used as a concrete finite representation laboratory, not as a puzzle-solving problem.
The current public release contains Papers I--XIV. CCS v2 is published separately as an optional non-paper Computational Companion Archive; the immutable first combined record retains its historical predecessor.
| Component | Topic | DOI / source |
|---|---|---|
| Paper I | block spectral structure and a conditional rationality criterion | https://doi.org/10.5281/zenodo.21571403 |
| Paper II | sector non-invariance, direct support, and transport channels | https://doi.org/10.5281/zenodo.21581072 |
| Paper III | support-graph reachability and matrix-composition obstructions | https://doi.org/10.5281/zenodo.21583070 |
| Paper IV | collision geometry of joint spectra | https://doi.org/10.5281/zenodo.21972335 |
| Paper V | Boolean support and commutator accessibility | https://doi.org/10.5281/zenodo.21634007 |
| Paper VI | linearized commutativity geometry, normality gates, and typed spectral registrations | https://doi.org/10.5281/zenodo.21973224 |
| Paper VII | incidence geometry, rank protection, and composition-promotion limits | https://doi.org/10.5281/zenodo.21976516 |
| Paper VIII | sectorized observable framework | https://doi.org/10.5281/zenodo.21977464 |
| Paper IX | observable dynamics of sectorized observable frameworks | https://doi.org/10.5281/zenodo.21713306 |
| Paper X | capability-aware compilation for Sectorized Observable Frameworks and Registry evidence | https://doi.org/10.5281/zenodo.21768257 |
| Paper XI | typed wall morphology for Sectorized Observable Frameworks | https://doi.org/10.5281/zenodo.21801722 |
| Paper XII | SOF diagnostic protocol and report specification | https://doi.org/10.5281/zenodo.21870368 |
| Paper XIII | Audit Profiles, SOF Report Alignment, and sparse typed comparison maps | https://doi.org/10.5281/zenodo.21870778 |
| Paper XIV | context- and policy-relative interpretation and bounded candidate dispositions | https://doi.org/10.5281/zenodo.21880943 |
| CCS v2 | optional reproducibility, observation, open-problem, and history archive | https://doi.org/10.5281/zenodo.21616956 |
| Historical combined Papers I--III + CCS release | immutable first-version archive; current papers are maintained independently | https://doi.org/10.5281/zenodo.21108197 |
This is the repository's canonical DOI index. It identifies immutable published records; other public documents link here instead of duplicating the list. Papers VII--XIV now match their published versioned records. Their listed DOIs identify immutable published versions, and frozen historical contracts remain unchanged.
| If you want to... | Start with |
|---|---|
| browse the public documentation | docs/README.md |
| get the program overview | docs/overview.md |
| understand the paper architecture | docs/PROGRAM_MAP.md |
| understand the Rubik-as-laboratory philosophy | docs/PROGRAM_PHILOSOPHY.md |
| check paper boundaries | docs/PAPER_SCOPE.md |
| inspect canonical Rubik invariants | docs/CORE_INVARIANTS.md |
| check geometry and move conventions | docs/conventions.md |
| inspect reproducibility scripts | experiments/README.md |
| inspect published SOF data contracts | schemas/README.md |
| run domain adapters, plugins, and capability-aware compilation | sof-runtime |
| inspect optional reproducibility data, observations, open problems, and history | ccs/canonical_specification.md |
| Paper | Source | Main question | |
|---|---|---|---|
| I | paper1_arxiv.pdf |
Paper I.md |
What is the blockwise canonical spectrum, and which conditional arithmetic criteria apply? |
| II | paper2_arxiv.pdf |
Paper II.md |
Why does the nine-sector transport graph have its observed sparse structure? |
| III | paper3_arxiv.pdf |
Paper III.md |
When does a path in the direct support graph represent a nonzero projected matrix composition? |
| IV | paper4_arxiv.pdf |
Paper IV.md |
How do fixed affine-branch collisions form quotient layers, and when may a numerical realization inherit that quotient? |
| V | paper5_arxiv.pdf |
Paper V.md |
Why does Boolean support fail to determine commutator accessibility? |
| VI | paper6_arxiv.pdf |
Paper VI.md |
Which linearized directions preserve the constraints, and which samples pass the spectral gates? |
| VII | paper7_arxiv.pdf |
Paper VII.md |
When do nonzero projected factors compose, and what limits stronger promotions? |
| VIII | paper8_arxiv.pdf |
Paper VIII.md |
What is the marked static sectorized observable object? |
| IX | paper9_arxiv.pdf |
Paper IX.md |
How do comparable typed SOF fields evolve under a declared deformation? |
| X | paper10_arxiv.pdf |
Paper X.md |
Under which contracts can typed claims be compiled without manufacturing evidence or crossing carriers? |
| XI | paper11_arxiv.pdf |
Paper XI.md |
How can admitted wall data be recorded as sparse typed changes and organized by profile-relative morphology? |
| XII | paper12_arxiv.pdf |
Paper XII.md |
What does a compiled report represent, and where do adapter adequacy and reporting authority end? |
| XIII | paper13_arxiv.pdf |
Paper XIII.md |
How can two SOF Reports be aligned and compared without conflating difference with defect? |
| XIV | paper14_arxiv.pdf |
Paper XIV.md |
How can an immutable audit be interpreted under admitted context and policy without promoting candidates into decisions or effects? |
| CCS v2 Archive | ccs_arxiv.pdf |
canonical_specification.md |
Optional Paper I--III reproducibility pointers, computational observations, open problems, and historical records |
Thematic index, not a paper dependency order:
Arithmetic
Transport
Support-graph/matrix-composition separation
Collision geometry
Local support and commutator separation
Linearized commutativity and normality-gated registration
Incidence geometry and promotion limits
SOF object theory
Observable dynamics
Capability-aware compilation for Sectorized Observable Frameworks and Registry evidence
Typed wall morphology and multi-label taxonomy
SOF diagnostic reporting
SOF Report Alignment and comparison geometry
Context- and policy-relative interpretation and bounded candidate semantics
Papers I--VII are independently readable. Their neighboring results connect through typed inputs and outputs; every receiving paper restates its objects, hypotheses, and missing promotion conditions.
rime-lite/
|-- rime/ core representation and spectral computation
|-- experiments/ paper support scripts and diagnostics
|-- tests/ invariant checks
|-- papers/ manuscript sources
|-- ccs/ Computational Companion and Status Archive source
|-- docs/ public overview, program map, and companion notes
|-- schemas/ versioned SOFRS, SOFAUDIT, SOFAction, and Registry contracts
|-- registry/ immutable v1 and frozen typed v2 Registry snapshots
`-- figures/ manuscript figures and presentation-only renderers
This repository is the normative source for papers, mathematical objects,
theorems, versioned contracts, accepted evidence, and publication identities.
The separate sof-runtime
repository provides the Python reference runtime, domain adapters, execution
plugins, evidence generation, compiler operation, and application examples.
Runtime protocol conformance or a passing extension validator does not by itself add a carrier, theorem, claim status, or public result to RIME. Stable extensions return here as source-addressed promotion proposals; accepted semantics are versioned here before the runtime refreshes its upstream lock. Existing paper-local experiments remain with their owning releases.
Install the package in editable mode:
pip install -e .Run fast invariant checks:
python tests/run_all_tests.pyRepresentative support scripts:
python experiments/paper1/validation/spectral_ladder.py
python experiments/paper2/validation/primitive_sectors.py
python experiments/paper3/validation/composition_obstruction.py
python experiments/paper4/validation/rubik_collision_quotient.py
python experiments/paper5/validation/matrix_nondegeneracy.py
python experiments/paper6/validation/tangent_commutator_map.py
python experiments/paper7/validation/rank_protected_bridge_audit.py
python experiments/paper9/validation/validate_results.py
python experiments/paper10/validation/validate_results.py
python experiments/paper11/validation/typed_wall_record_census.py
python experiments/paper12/validation/validate_sofrs_v2.py
python experiments/paper13/validation/validate_sofaudit_v2.py
python experiments/paper14/action_workbench.py
python experiments/paper14/validate_sofaction.pyFor the full experiment map, see experiments/README.md.
This is not a cube-solving repository. It does not implement Kociemba's algorithm, pruning tables, scramble search, sticker rendering, or neural solvers. The cube is used as a finite representation-theoretic testbed.
Repository maintenance and editorial workflows have used ChatGPT/Codex, Claude, and Gemini/Continue for bounded assistance with code, document restructuring, language suggestions, and consistency review. These tools are not authors or authorities on mathematical claims. All mathematical judgments, accepted edits, verification choices, releases, and scholarly responsibility remain with WuJun Chen.
Code: MIT License. See LICENSE.
Papers and manuscript sources: Creative Commons Attribution 4.0 International
(CC BY 4.0). See LICENSE-PAPERS.
Please cite the individual paper DOI when referring to a specific result. Use the canonical DOI index above to select the immutable record. Cite CCS v2 only for archive-specific material, and cite the historical combined record only when referring to that immutable first-version package.