# Rainbow Raccoon Compiler Integration Date: 2026-05-08 Status: integration shim with one proof-backed fixed-point lowering lane. Runner: ```text 4-Infrastructure/shim/rainbow_raccoon_compiler.py ``` Receipt: ```text 4-Infrastructure/shim/rainbow_raccoon_compiler_receipt.json ``` Curriculum: ```text 4-Infrastructure/shim/rainbow_raccoon_compiler_curriculum.jsonl ``` Receipt hash: ```text 3507d55ae2d6e40a76a36b44466fe69a312c16e8110a3f65fdd815f053487759 ``` ## Primary Read The Rainbow Raccoon Compiler is now represented as a small manifold-indexed type-checker boundary for the current stack: ```text object -> manifold projection -> nearest lawful shape -> type witness -> field equation -> invariant receipt ``` This first pass is intentionally conservative. It emits `CANDIDATE` only when the object has enough declared projection, witness, and scale evidence to be admissible for a next-stage proof. It emits `HOLD` when the object is underspecified or has weak receipt axes. ## Manifold Axes The shim projects each object into a 16-axis vector: ```text semantic_entropy geometric_mass compression_pressure topology_torsion receipt_density field_energy hardware_affinity proof_readiness residual_risk shape_closure history_depth negative_control_strength projection_declared decoder_declared witness_declared scale_band_declared ``` These axes are not proof terms yet. They are a routing surface for deciding which proof, receipt, or hold policy should apply next. ## Proof-Backed Fixed-Point Lowering Lane The first proof-backed RRC compiler lane is the MetaManifoldProver Q16_16 fixed-point lowering certificate: ```text 0-Core-Formalism/lean/Semantics/Semantics/MetaManifoldProver.lean 2-Search-Space/FAMM/docs/lemma_proof_space_mapping.md ``` This lane lets RRC treat the following lowering rules as proof-bearing compiler facts rather than heuristic rewrite hints: ```text weighted_term_bounded: (E * alpha) / 65536 <= E shiftRight_eq_div: x >>> 16 = x / 65536 shiftRight_monotone: a <= b -> a >>> 16 <= b >>> 16 div_le_div_of_lt: x >= 0, a > b, b > 0 -> x / a <= x / b ``` Compiler interpretation: ```text Q16_16 expression -> fixed-point lowering certificate -> shift/division rewrite -> bounded weighted-term rewrite -> monotone projection witness -> invariant receipt ``` Boundary: ```text The Lean proof closes only the named Q16_16 arithmetic surface. It does not prove arbitrary RRC projections, geometry claims, compression gains, or network topology claims. ``` ## Canonical Projectable Geometry Representation For projectable-geometry objects, the RRC route should treat the 16-axis vector as the signed routing/witness envelope over a lower-dimensional replay chain: ```text 16D signed envelope -> 12D source/residual plane -> 4D primitive keel -> genus-3 residual boat -> 0D closure ``` The RRC projection is lawful only when it preserves the replay equations: ```text source_12D = lift(project(source_12D)) + residual_12D ``` and: ```text packet_local + shear_torsion + spectral_field = residual_12D ``` The shell closure prior is priced in twelfths: ```text visible_4d = 4/12 shadow_3d = 3/12 closure_0d = 1/12 lawbound = 4/12 unresolved = 0/12 ``` RRC must emit `HOLD` when the 16D axes are untyped, the residual handles do not sum to the 12D residual, or the shell leaves unresolved mass debt. The reference Lean gate is: ```text 0-Core-Formalism/lean/Semantics/Semantics/ProjectableGeometryCanonical.lean ``` ## Lawful Shape Prototypes The initial lawful-shape set is: ```text SignalShapedRouteCompiler ProjectableGeometryTopology CognitiveLoadField CadForceProbeReceipt LogogramProjection LanguageSetManifoldGraph FixedPointLoweringCertificate HoldForUnlawfulOrUnderspecifiedShape ``` Each shape has a prototype vector and a field equation. The compiler compares the projected object to these prototypes and records the nearest shape plus the distance. ## Current Compile Results ```text rrc_obj_signal_route_compiler label: Compression Signal Shaping Synthesis shape: SignalShapedRouteCompiler distance: 0.07146 status: HOLD reason: scale_band_declared is weak rrc_obj_projectable_geometry label: Projectable Geometry Topology Receipt shape: ProjectableGeometryTopology distance: 0.107275 status: CANDIDATE rrc_obj_cognitive_load label: Connectome Protective Cognitive Load Receipt shape: CognitiveLoadField distance: 0.101187 status: CANDIDATE rrc_obj_cad_force_probe label: CAD Force Probe Experiment Matrix Receipt shape: CadForceProbeReceipt distance: 0.165749 status: HOLD reason: scale_band_declared is weak rrc_obj_underspecified label: Underspecified raw object negative control shape: HoldForUnlawfulOrUnderspecifiedShape distance: 0.240924 status: HOLD reason: projection, witness, and scale are weak rrc_obj_language_set_ithkuil label: Ithkuil Language Set Manifold Graph Typing shape: LanguageSetManifoldGraph distance: 0.051138 status: HOLD reason: scale_band_declared is weak rrc_obj_q16_16_lowering_certificate label: MetaManifoldProver Q16_16 Fixed-Point Lowering Certificate shape: FixedPointLoweringCertificate distance: 0.093118 status: CANDIDATE lean_boundary: proved_by_MetaManifoldProver reason: no weak required axes ``` The current pass uses both manifold-feature distance and a declared-kind prior. That keeps geometry receipts in geometry type-space even when their text also contains route/cost language. ## Field Equations Signal-shaped route compiler: ```text r* = argmin_r LB(r | phi_signal(c), semantic_regime(c), history_state) promote iff exact decode hash closes and total bytes beat incumbent ``` Projectable geometry topology: ```text close iff mass_delta_q == 0 and horizon_hash matches and nan0_flag == 0 ``` Cognitive load field: ```text L_total = C_domain * response_family(S; theta) * phi_gain * B_gate * overflow_gate ``` CAD force-probe receipt: ```text sum_j q_ij * (x_i - x_j) + p_i = 0 residual must stay under declared tolerance ``` Hold shape: ```text HOLD iff projection, decoder, witness, scale, or residual accounting is missing ``` Logogram projection: ```text logogram_cell -> canonical_hash -> glyph_payload -> projection_lane admit iff cell hash, payload bound, substitution receipt, and regime guard close ``` Language-set manifold graph: ```text language_set -> category_inventory -> typed_graph -> surface_views admit iff graph schema, replay law, residual policy, negative controls, and scale band close ``` Fixed-point lowering certificate: ```text Q16_16 lowering admits iff shift-right/division, weighted-term bounds, shift monotonicity, and denominator antitonicity close in Lean ``` ## Promotion Rules ```text CANDIDATE is not a Lean proof; it is only admissible for next-stage proving. HOLD is emitted when projection, witness, decoder, residual, or scale is weak. No object may be promoted as lawful without a replayable invariant receipt. Compression gain must still count residual, witness, decoder, sidecar, and container bytes. Geometry or force claims require calibrated physical measurement receipts. Fixed-point lowering claims may cite MetaManifoldProver only for the closed Q16_16 arithmetic lemmas. ``` ## Next Integration Steps ```text 1. Add a Lean RRCShape enum and witness-gate theorem surface. 2. Wire RRC classifications into the compression route classifier from E1/E2. 3. Use RRC HOLD status as a fail-closed gate for semantic tokenbook merges. 4. Map CAD force-probe receipts through RRC before four-force geometry claims. 5. Add calibrated scale-band metadata to release CAD and compression holds. 6. Keep [[RRC Logogram Projection Bridge]] as the projection gate for logogram surfaces. 7. Type whole language sets as `LanguageSetManifoldGraph` objects before using them as compression surfaces. 8. Use the Q16_16 lowering certificate as the first proof-backed RRC compiler lane. ``` ## Claim Boundary RRC is now an executable integration boundary. It is not yet a verified compiler. The current value is that it turns abstract type-shape language into a receipt-bearing, inspectable pipeline with explicit `CANDIDATE` and `HOLD` states.