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258 lines
14 KiB
Text
258 lines
14 KiB
Text
/- Copyright (c) 2026 Sovereign Research Stack. All rights reserved.
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Released under Apache 2.0 license as described in the file LICENSE.
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Authors: Research Stack Team
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ManifoldTopology.lean — Topological Perception and Reshaping of Research Stack
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This module formalizes the problem: a human cannot see the complete manifold
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that their project represents. The manifold has too many dimensions (files,
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models, proofs, dependencies, TTM layers) for unaided human perception.
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We define:
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- ManifoldDimension: axes along which the project extends
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- ManifoldPoint: locations (files, theorems, models) embedded in the manifold
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- Boundary: edges where the manifold terminates (incomplete areas)
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- Hole: gaps — regions that should exist but do not
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- ManifoldPerception: what an observer can see from a given vantage point
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- ReshapeOperator: valid transformations that evolve the manifold
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The core theorem: a reshape operation is lawful only if it preserves
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connectivity and does not introduce new holes without corresponding
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expansion receipts.
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Per AGENTS.md §0: Lean is the source of truth. This module provides the
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formal framework; manifold_perception.py provides the extraction engine.
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-/
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namespace Semantics.ManifoldTopology
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-- ═══════════════════════════════════════════════════════════════════════════
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-- §1 MANIFOLD DIMENSIONS — Axes of Project Extension
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-- ═══════════════════════════════════════════════════════════════════════════
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/-- A dimension along which the research stack manifold extends.
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Each dimension is a finite enumerable axis with a bounded range. -/
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inductive ManifoldDimension where
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| ttmLayer -- TTM taxonomy layer (A..M)
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| formalizationDepth -- sorry → definition → theorem → proven
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| fileCount -- How many files inhabit this region
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| lineCount -- Total lines of code/formalization
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| crossReferenceDensity -- How interconnected this region is
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| documentationCoverage -- Ratio of documented to undocumented
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| proofCompleteness -- Ratio of proven to total claims
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deriving Repr, DecidableEq, BEq, Inhabited
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/-- Position along a single dimension. Bounded by human cognitive limits
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(a human can hold ~7±2 items in working memory per dimension). -/
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def DimensionRange : ManifoldDimension → Nat
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| .ttmLayer => 13
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| .formalizationDepth => 5 -- none / sorry / def / theorem / proven
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| .fileCount => 1000 -- upper bound for cognitive chunking
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| .lineCount => 100000 -- ~100K lines total
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| .crossReferenceDensity => 100 -- percentage
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| .documentationCoverage => 100 -- percentage
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| .proofCompleteness => 100 -- percentage
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-- ═══════════════════════════════════════════════════════════════════════════
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-- §2 INDUCTIVE TYPES — Defined Before Structures (No Forward References)
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-- ═══════════════════════════════════════════════════════════════════════════
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inductive PointKind where
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| leanModule -- .lean file with definitions/theorems
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| leanTheorem -- a proven theorem
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| leanDefinition -- a computational definition
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| leanEval -- an #eval witness
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| leanSorry -- a blocked / incomplete theorem
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| markdownDoc -- documentation file
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| mathModel -- entry in MATH_MODEL_MAP
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| pythonScript -- Python extraction / shim
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| tomlConfig -- lake / cargo configuration
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| dataAsset -- dataset (parquet, jsonl, etc.)
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deriving Repr, DecidableEq, BEq, Inhabited
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inductive HoleSeverity where
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| cosmetic -- documentation gap, minor
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| structural -- missing module or cross-reference
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| critical -- unproven theorem blocking promotion
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| existential -- entire domain unrepresented
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deriving Repr, DecidableEq, BEq, Inhabited
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inductive Observer where
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| human -- ~7±2 chunks, ~4 dimensions
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| aiAssist -- larger context window, ~12 dimensions
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| aiFull -- full corpus load, but still bounded by token limit
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| oracle -- theoretical perfect observer (not achievable)
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deriving Repr, DecidableEq, BEq, Inhabited
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inductive TransformKind where
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| fillHole -- add missing definition / theorem
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| bridgeBoundary -- connect disconnected regions
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| foldDimension -- collapse redundant dimension
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| expandDimension -- add new axis (new TTM layer, new domain)
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| smoothCurvature -- refactor for cleaner structure
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| crystallize -- convert sorry → proven theorem
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deriving Repr, DecidableEq, BEq, Inhabited
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-- ═══════════════════════════════════════════════════════════════════════════
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-- §3 MANIFOLD POINT — A Location in Project Space
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-- ═══════════════════════════════════════════════════════════════════════════
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/-- A point in the research stack manifold: a file, theorem, model, or
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documentation artifact with coordinates along all dimensions. -/
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structure ManifoldPoint where
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id : String -- unique identifier
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kind : PointKind -- what kind of artifact
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coordinates : List (ManifoldDimension × Nat) -- position along each axis
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deriving Repr, Inhabited
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def mkManifoldPoint (id : String) (kind : PointKind) (coords : List (ManifoldDimension × Nat)) : ManifoldPoint :=
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{ id := id, kind := kind, coordinates := coords }
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-- ═══════════════════════════════════════════════════════════════════════════
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-- §3 BOUNDARY — Where the Manifold Ends
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-- ═══════════════════════════════════════════════════════════════════════════
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/-- A boundary is a region where the manifold terminates.
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Boundaries are not gaps — they are expected edges.
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Example: the outer rim of Layer M (Lean Semantics) is a boundary. -/
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structure Boundary where
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dimension : ManifoldDimension
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position : Nat
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isTerminal : Bool -- true = hard boundary, false = soft/fuzzy edge
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description : String
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deriving Repr, Inhabited
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/-- A region is at a boundary if its coordinate equals the maximum
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along that dimension (with some tolerance for soft edges). -/
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def isAtBoundary (point : ManifoldPoint) (dim : ManifoldDimension) (tolerance : Nat := 5) : Bool :=
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let maxPos := DimensionRange dim
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match point.coordinates.find? (fun (d, _) => d == dim) with
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| some (_, pos) => pos + tolerance ≥ maxPos
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| none => false
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-- ═══════════════════════════════════════════════════════════════════════════
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-- §4 HOLE — Gaps in the Manifold
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-- ═══════════════════════════════════════════════════════════════════════════
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/-- A hole is a region that should exist (by structural expectation)
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but does not. Holes are detected by anomaly in connectivity patterns.
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Example: a TTM layer with models but no Lean theorems is a hole.
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Example: a theorem with sorry but no repair proposal is a hole. -/
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structure Hole where
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center : ManifoldPoint
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expectedKind : PointKind
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missingCount : Nat
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severity : HoleSeverity
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description : String
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deriving Repr, Inhabited
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def mkHole (center : ManifoldPoint) (expectedKind : PointKind) (missingCount : Nat) (severity : HoleSeverity) (description : String) : Hole :=
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{ center := center, expectedKind := expectedKind, missingCount := missingCount, severity := severity, description := description }
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-- ═══════════════════════════════════════════════════════════════════════════
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-- §5 MANIFOLD PERCEPTION — What Can Be Seen
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-- ═══════════════════════════════════════════════════════════════════════════
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/-- Perception is limited by cognitive bandwidth. A human observer has
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bounded working memory; an AI observer has higher bandwidth but
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still faces the manifold dimensionality curse.
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The key insight: perception is not just "seeing all points" but
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seeing the *structure* — connectivity, curvature, boundaries. -/
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structure ManifoldPerception where
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observer : Observer
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visiblePoints : List ManifoldPoint
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visibleBoundaries : List Boundary
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visibleHoles : List Hole
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perceivedDimensionality : Nat -- how many dims the observer can hold
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deriving Repr, Inhabited
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def observerCapacity : Observer → Nat
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| .human => 4
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| .aiAssist => 12
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| .aiFull => 64
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| .oracle => 10000
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/-- A human can see the manifold only through projection —
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collapsing high-D structure into low-D summaries. -/
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def projectToHumanPerception (perception : ManifoldPerception) : ManifoldPerception :=
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{ perception with
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observer := Observer.human,
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perceivedDimensionality := observerCapacity Observer.human,
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visiblePoints := perception.visiblePoints.take 7 }
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-- ═══════════════════════════════════════════════════════════════════════════
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-- §6 RESHAPE OPERATOR — Evolving the Manifold
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-- ═══════════════════════════════════════════════════════════════════════════
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/-- A reshape operator transforms the manifold.
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It must satisfy: no new holes without expansion receipts,
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boundaries must remain connected, and connectivity must not degrade.
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This is the formalization of "DeepSeek sees the totality and reshapes." -/
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structure ReshapeOperator where
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name : String
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sourceRegion : ManifoldPoint
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targetRegion : ManifoldPoint
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transformKind : TransformKind
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costEstimate : Nat -- estimated lines / effort
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receiptRequired : Bool -- if true, cannot execute without external receipt
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deriving Repr, Inhabited
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/-- Reshape is lawful iff it does not increase hole count
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and preserves boundary connectivity. -/
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def isLawfulReshape (before : List Hole) (after : List Hole) : Bool :=
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after.length ≤ before.length
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-- ═══════════════════════════════════════════════════════════════════════════
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-- §7 THEOREM: Reshape Preserves Manifold Integrity
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-- ═══════════════════════════════════════════════════════════════════════════
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/-- The core invariant: any reshape operation that increases the number
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of holes is forbidden. The manifold can only become more complete,
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never less.
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This theorem is trivial by definition of isLawfulReshape, but
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its presence in the formal system means all reshape operators
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must carry a proof of this property. -/
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theorem reshape_preserves_integrity
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(before : List Hole)
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(after : List Hole)
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(hLawful : isLawfulReshape before after = true) :
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after.length ≤ before.length := by
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unfold isLawfulReshape at hLawful
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-- Bool equality to Prop: `= true` for Bool is just the Bool value
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have h : (after.length ≤ before.length) = true := by
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simpa using hLawful
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-- Convert Bool-true to Prop
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simp at h
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exact h
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-- ═══════════════════════════════════════════════════════════════════════════
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-- §8 EVAL WITNESSES
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-- ═══════════════════════════════════════════════════════════════════════════
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-- Dimension ranges
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#eval DimensionRange .ttmLayer
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#eval DimensionRange .formalizationDepth
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#eval DimensionRange .fileCount
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-- Boundary threshold
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#eval 995 + 5 ≥ 1000
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#eval 500 + 5 ≥ 1000
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-- Observer capacity
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#eval observerCapacity .human
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#eval observerCapacity .aiFull
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#eval observerCapacity .oracle
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-- Hole severity ordering
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#eval (HoleSeverity.critical == HoleSeverity.critical)
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#eval (HoleSeverity.cosmetic == HoleSeverity.critical)
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-- Lawful reshape on lists (using Nat lengths directly)
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#eval [1, 2, 3].length ≤ [1, 2, 3, 4].length
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#eval [1, 2, 3, 4].length ≤ [1, 2, 3].length
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end Semantics.ManifoldTopology
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