RIME

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.

Public Release

The current public release contains Papers I--XV, the independently scoped Paper XVI computational case study, and Papers XX--XXIX mathematical lines. CCS v2.1 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.21991080
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.22006816
Paper XIII	Audit Profiles, SOF Report Alignment, and sparse typed comparison maps	https://doi.org/10.5281/zenodo.22010220
Paper XIV	context- and policy-relative interpretation and bounded candidate dispositions	https://doi.org/10.5281/zenodo.22024158
Paper XV	evidence-bound revision, supersession, and revalidation of current commitments	https://doi.org/10.5281/zenodo.22043124
Paper XVI	structural and dynamic descent in the Male Drosophila CNS	https://doi.org/10.5281/zenodo.22931881
Paper XX	all-depth carrier accessibility, survivor recursion, and image--kernel obstructions	https://doi.org/10.5281/zenodo.22076736
Paper XXI	finite-field route profiles, prefix-pole semantics, and characteristic-aware stability	https://doi.org/10.5281/zenodo.22078884
Paper XXII	fixed-deficit rational dynamics, anchored Farey classification, and Catalan-Fibonacci envelopes	https://doi.org/10.5281/zenodo.22109140
Paper XXIII	pair hitting, marked-kernel corridors, Schreier waiting, and exact binary clean depth	https://doi.org/10.5281/zenodo.22136087
Paper XXIV	finite typed-context descent, semantic visibility, relational acyclicity, and comparison reconstruction	https://doi.org/10.5281/zenodo.22140377
Paper XXV	aligned diagnostic transport, carrier-local perturbation, and minimax information bounds	https://doi.org/10.5281/zenodo.22429890
Paper XXVI	pair-chain transfer operators, random synchronization, and sharp reset-word waiting envelopes	https://doi.org/10.5281/zenodo.22637317
Paper XXVII	entry sections, source-addressed completion relations, and fixed-scope relation-valued descent	https://doi.org/10.5281/zenodo.22853891
Paper XXVIII	finite mechanism structure, exact credit composition, and fixed-scope recursive return	https://doi.org/10.5281/zenodo.22980858
Paper XXIX	cyclic lineage dynamics and rank-five raw first-exit frontiers	https://doi.org/10.5281/zenodo.23028361
CCS v2.1	optional reproducibility, observation, open-problem, and history archive	https://doi.org/10.5281/zenodo.21988041
RIME Lite v2.1 repository snapshot	accepted papers, contracts, Registry evidence, release tools, and exact-byte historical inputs	Zenodo DOI / GitHub Release
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--XVI and Papers XX--XXIX now match their published records. Their listed DOIs identify immutable published versions, and frozen historical contracts remain unchanged.

The repository v2.1 release content is commit 005e2453d508ba5e12136bf9005050ac72185ae5. The annotated tag points to the release-manifest commit 69b33d60ac729eeff45dfe42e79e68197cdd7f68. This DOI propagation is a later metadata-only update and is not part of the tagged release closure.

Start Here

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

Papers

Paper	PDF	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?
XV	paper15_arxiv.pdf	Paper XV.md	How can current commitments be revised without rewriting historical artifacts or granting feedback operational authority?
XVI	paper16_arxiv.pdf	Paper XVI.md	Which structural and dynamic properties survive declared coarse representations of the MaleCNS connectome?
CCS v2.1 Archive	ccs_arxiv.pdf	canonical_specification.md	Optional Paper I--III reproducibility pointers, computational observations, open problems, and historical records

Independent Case Study and Post-Protocol Mathematical Lines

Paper XVI is an independently scoped computational connectome case study. It does not continue the SOF protocol authority chain closed by Paper XV. Papers XVII--XIX remain intentionally unused in the public numbered sequence. Paper XX begins an independently scoped post-protocol mathematical line, and Paper XXI develops its finite-field route branch. Paper XXII develops the fixed-deficit rational branch through anchored Farey classification and Catalan-Fibonacci envelopes. Paper XXIII begins a separate synchronizing- automata line built from rank escape, marked-kernel corridors, and Schreier waiting. Paper XXIV begins a separate finite contextual/descent line. None continues the SOF protocol authority chain. Paper XXV develops a separate finite-dimensional methods layer for aligned generator-resolved diagnostics. Paper XXVI develops the stochastic pair-transfer branch, separating deterministic reset scales from random pair absorption and proving a sharp reset-word waiting envelope. Paper XXVII develops fixed-scope entry sections and source-addressed relation-valued completion interfaces for single-defect circular automata. Paper XXVIII develops finite mechanism quotients, exact credit composition, five fixed-scope recursive-return surfaces, and canonical path alignment while leaving Projectable-Origin Supply open at arbitrary ambient size. Paper XXIX develops an independent all-n classification of the raw rank-five first-exit frontier for the canonical single-defect circular family. Its raw lineage geometry does not establish the typed transfer or projectability bridge left open by Paper XXVIII. Published release identities are maintained in the canonical DOI index above.

Paper	Manuscript	Evidence	Scope
XVI	Paper XVI.md	experiments/paper16/	source-addressed MaleCNS audits of structural liftability, signed dynamics, observation visibility, and coarse-state closure
XX	Paper XX.md	experiments/paper20/	all-depth carrier accessibility, survivor recursion, and exact shared-carrier controls
XXI	Paper XXI.md	experiments/paper21/	prefix-pole route classification, finite-field automata, and characteristic-aware stability
XXII	Paper XXII.md	experiments/paper22/	fixed-deficit rational dynamics, anchored Farey classification, and Catalan-Fibonacci envelopes
XXIII	Paper XXIII.md	experiments/paper23/	pair hitting, marked-kernel corridors, Schreier waiting, and exact binary clean depth
XXIV	Paper XXIV.md	experiments/paper24/	semantic visibility for typed section descent, imported relational acyclicity, and fixed-alignment comparison reconstruction
XXV	Paper XXV.md	experiments/paper25/	aligned unitary transport, carrier-local perturbation, minimax information bounds, and typed semantic-lift boundaries
XXVI	Paper XXVI.md	experiments/paper26/	pair-chain transfer operators, random pair absorption, Perron asymptotics, and sharp reset-word waiting envelopes
XXVII	Paper XXVII.md	experiments/paper27/	intrinsic entry sections, source-addressed completion relations, and fixed-scope relation-valued descent
XXVIII	Paper XXVIII.md	experiments/paper28/	finite mechanism quotients, exact credit composition, fixed-scope recursive return, and canonical path alignment
XXIX	Paper XXIX.md	experiments/paper29/	cyclic lineage dynamics, spectator-safe reachability, and the all-n raw rank-five first-exit frontier

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
Corrigible structural interfaces and evidence-bound epistemic revision
All-depth carrierwise route obstruction
Finite-field route profiles and prefix-pole stability
Fixed-deficit rational dynamics and anchored Farey classification
Rank escape, marked-kernel corridors, and Schreier waiting
Finite typed-context descent and comparison reconstruction
Aligned diagnostic transport and carrier-local stability
Pair-chain transfer operators and random synchronization
Entry sections and source-addressed relation-valued descent
Raw packet-lineage dynamics and rank-five first-exit frontiers

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.

Repository Structure

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 Registry releases and versioned candidates
|-- release-snapshots/    exact-byte historical release inputs
|-- tools/                read-only release and evidence-closure verification
`-- figures/              manuscript figures and presentation-only renderers

Runtime and Application Boundary

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.

Reproducibility

Install the package in editable mode:

pip install -e .

Run fast invariant checks:

python tests/run_all_tests.py verify

The runner executes in a temporary copy and fails with VERIFICATION_SIDE_EFFECT if the source checkout's tracked state changes. Artifact rebuilding and promotion are separate explicit operations; active verification does not rewrite historical result directories. See tests/README.md for active-test handling and tools/README.md for snapshot, evidence-graph, release manifest, and external-anchor checks.

Validate the frozen v2.0 snapshot and the current v2.1 receipt graph with:

python tools/validate_release_snapshot.py release-snapshots/rime-lite-v2.0/manifest.json
python tools/release/validate_evidence_graph.py

Paper-local validation commands are maintained with their owning evidence packages. See the experiments/ routing index and the corresponding experiments/paperN/README.md.

Scope

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.

Acknowledgements

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.

License

Code: MIT License. See LICENSE.

Papers and manuscript sources: Creative Commons Attribution 4.0 International (CC BY 4.0). See LICENSE-PAPERS.

Citation

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 v2.1 only for archive-specific material, and cite the historical combined record only when referring to that immutable first-version package.