RRC (Rainbow Raccoon Compiler) — Library Placement

What RRC Actually Is

From PVGS_DQ_Bridge_fixed.lean §4:

structure RRCEvidence where
  typeWitness        : ℚ
  projectionWitness  : ℚ
  mergeWitness       : ℚ
  typeAdmissible     : Prop      -- gate 1: type check
  projectionAdmissible : Prop    -- gate 2: projection check
  mergeAdmissible    : Prop      -- gate 3: merge check

def kernelEvidence (x m y n : ℕ) : RRCEvidence

theorem goormaghtigh_passes_rrc  -- known solutions pass
theorem unknown_fails_rrc        -- unknown solutions fail (Goormaghtigh)

RRC is a receipt compiler — it takes receipts and compiles them through three gates. Each gate is a semantic validation:

Gate	What it checks	Physical meaning
Type	`	witness
Projection	`	witness
Merge	`	R1-R2

Where It Fits: Its Own Library

RRC is NOT AuditLib. AuditLib checks receipt format (well-formedness). RRC checks receipt semantics (mathematical validity through polynomial gates).

                    SilverSightCore.lean
                          │
              ┌───────────┼───────────┐
              │           │           │
          LexLib    SearchLib   StructureLib
              │           │           │
              └───────────┼───────────┘
                          │
                    Receipt produced
                          │
              ┌───────────┼───────────┐
              │           │           │
          AuditLib    RRCLib      EventLib
          (format)   (semantics)   (count)
              │           │           │
              └───────────┴───────────┘
                          │
                   Core.accept / reject

RRCLib — Rainbow Raccoon Compiler Library

Type signature:

-- RRCLib.lean
import SilverSightCore

-- Compile a receipt through RRC gates
def RRCLib.compile (r : Receipt) : RRCResult

-- Gate verdicts
structure RRCResult where
  typeGate        : GateVerdict
  projectionGate  : GateVerdict
  mergeGate       : GateVerdict
  compiled        : Bool  -- all gates pass
  deriving Repr

inductive GateVerdict
  | Pass   -- witness below threshold
  | Fail   -- witness above threshold
  | Borderline  -- within 10% of threshold (needs human)
  deriving DecidableEq, Repr

What RRCLib does NOT do:

Does NOT produce the initial receipt (that's SearchLib/LexLib)
Does NOT count TIC (that's EventLib)
Does NOT check receipt format (that's AuditLib)
Does NOT compute the Finsler metric (that's MetricLib)

What RRCLib DOES do:

Takes an existing receipt
Evaluates the H-KdF polynomial at the receipt's parameters
Checks three gate thresholds
Returns Pass/Fail/Borderline for each gate
The receipt is admissible only if all three gates Pass

The Key Insight

RRC is a compiler because:

Input: receipt (source code)
Process: three-pass gate evaluation (compilation passes)
Output: compiled result with verdicts (executable decision)

The "Rainbow" part: each gate filters a different color (aspect) of the receipt:

Type = red channel (structural validity)
Projection = green channel (manifold fit)
Merge = blue channel (collision freedom)

All three must be clear for the receipt to be white (valid).

RRC as Meta-Library

RRC can also validate receipts ABOUT receipts (meta-recursion):

-- Receipt from RRCLib about another receipt
def RRCLib.metaCompile (r : Receipt) (rrcReceipt : Receipt) : RRCResult

This is how you get the self-indexing property: RRC receipts about RRC receipts, forming a hash chain (which is what pvgs_receipt_hash.py implements).

Current Code Location

Your PVGS_DQ_Bridge_fixed.lean §4 (hermitianRRCKernel through rrc_characterizes_goormaghtigh) becomes:

SilverSight/
├── Core/
│   └── SilverSightCore.lean        ← 200 lines, never changes
├── Library/
│   ├── LexLib.lean                 ← your token work
│   ├── SearchLib.lean              ← your chaos game work
│   ├── MetricLib.lean              ← your Finsler work
│   ├── QUBOLib.lean                ← your QUBO/QAOA work
│   ├── StructureLib.lean           ← your ChiralitySpace work
│   ├── PVGSLib.lean                ← your PVGS bridge work
│   ├── EventLib.lean               ← your TIC counting work
│   ├── AuditLib.lean               ← format validation
│   └── RRCLib.lean                 ← §4 of PVGS_DQ_Bridge_fixed.lean
│       ├── RRCGates.lean           -- gate definitions
│       ├── RRCKernel.lean          -- hermitianRRCKernel
│       ├── RRCEvidence.lean        -- RRCEvidence structure
│   └── RRCLib/                     -- NEW: RRC as standalone library
│       ├── RRCReceipt.lean         -- receipt validation
│       ├── RRCMeta.lean            -- meta-receipt validation
│       └── RRCHashChain.lean       -- from pvgs_receipt_hash.py
└── Orchestrator/
    └── SilverSight.lean            -- composes everything

Summary

Question	Answer
Is RRC AuditLib?	No — AuditLib checks format, RRC checks semantics
Is RRC SearchLib?	No — SearchLib finds basins, RRC validates receipts
Is RRC its own library?	Yes — RRCLib, importing only Core
What does RRC compile?	Receipts through 3 polynomial gates
Why "Rainbow"?	3 gates = 3 color channels = white if all pass
Why "Raccoon"?	Because raccoons wash everything before accepting it
Why "Compiler"?	Source receipt → gate passes → compiled verdict

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