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123 lines
5.2 KiB
Text
123 lines
5.2 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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HutterPrizeFlowTest.lean — Test HutterPrizeFlow against Hutter Prize Rules
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Tests the HutterPrizeFlow module against the Hutter Prize requirements:
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1. Compression gain can offset decoder and resource penalties (core tradeoff rule)
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2. Flow dynamics correctly model the tradeoffs
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3. The flow can find states that minimize the penalized objective
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Hutter Prize Rules (from HutterPrizeCompression):
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- Current record: 114MB for 1GB (11.4%)
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- Target: 99% of record = 112
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- Winning equation: C = (0.4*C_comp + 0.35*C_phys + 0.25*C_geom) × (S / (G + F))
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HutterPrizeFlow models the gradient dynamics for optimizing:
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- Compression gain (ρ) - larger ρ lowers objective
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- Decoder complexity penalty (τ²)
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- Resource penalty (σ² + q²)
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Per AGENTS.md §2: PascalCase types, camelCase functions
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Per AGENTS.md §4: Every def must have eval witness or theorem
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-/
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import Mathlib.Data.Real.Basic
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import Mathlib.Tactic
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import Semantics.HutterPrizeFlow
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namespace Semantics.HutterPrizeFlowTest
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/- ============================================================
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§0 Hutter Prize Rule Summary
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============================================================ -/
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noncomputable section
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/-- Hutter Prize record ratio (114MB/GB = 11.4%). -/
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def hutterRecordRatio : ℝ := 114.0 / 1000.0
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/-- Hutter Prize target ratio (99% of record = 112.86MB/GB = 11.29%). -/
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def hutterTargetRatio : ℝ := hutterRecordRatio * 0.99
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/-- Check if a ratio beats the Hutter Prize target. -/
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def beatsHutterTarget (ratio : ℝ) : Bool :=
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ratio < hutterTargetRatio
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end noncomputable section
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/- ============================================================
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§1 Basic Term Verification
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============================================================ -/
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-- Test basic penalty term computations on example states
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#eval HutterPrizeFlow.HP.decoderTerm HutterPrizeFlow.Examples.x0 -- Expected: 9 (3²)
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#eval HutterPrizeFlow.HP.resourceTerm HutterPrizeFlow.Examples.x0 -- Expected: 41 (4² + 5²)
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#eval HutterPrizeFlow.HP.compressionTerm HutterPrizeFlow.Examples.x0 -- Expected: -2
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/- ============================================================
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§2 Basic Property Verification
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============================================================ -/
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-- Verify decoder term non-negativity
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theorem decoderTerm_nonneg_test : 0 ≤ HutterPrizeFlow.HP.decoderTerm HutterPrizeFlow.Examples.x0 :=
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HutterPrizeFlow.HP.decoderTerm_nonneg HutterPrizeFlow.Examples.x0
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-- Verify resource term non-negativity
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theorem resourceTerm_nonneg_test : 0 ≤ HutterPrizeFlow.HP.resourceTerm HutterPrizeFlow.Examples.x0 :=
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HutterPrizeFlow.HP.resourceTerm_nonneg HutterPrizeFlow.Examples.x0
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-- Verify phiHP_lower_bound property
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theorem phiHP_lower_bound_test :
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HutterPrizeFlow.Field.phi HutterPrizeFlow.Examples.x0
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+ HutterPrizeFlow.Examples.params.alphaComp * HutterPrizeFlow.HP.compressionTerm HutterPrizeFlow.Examples.x0
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≤ HutterPrizeFlow.HP.phiHP HutterPrizeFlow.Examples.params HutterPrizeFlow.Examples.x0 :=
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HutterPrizeFlow.HP.phiHP_lower_bound HutterPrizeFlow.Examples.params HutterPrizeFlow.Examples.x0
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/- ============================================================
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§3 State and Parameter Verification
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============================================================ -/
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-- Verify x0 is well-formed
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theorem x0_wellformed : HutterPrizeFlow.Field.WellFormed HutterPrizeFlow.Examples.x0 := by
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norm_num [HutterPrizeFlow.Field.WellFormed, HutterPrizeFlow.Examples.x0, HutterPrizeFlow.State.eps, HutterPrizeFlow.State.mk]
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-- Verify x1 is well-formed
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theorem x1_wellformed : HutterPrizeFlow.Field.WellFormed HutterPrizeFlow.Examples.x1 := by
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norm_num [HutterPrizeFlow.Field.WellFormed, HutterPrizeFlow.Examples.x1, HutterPrizeFlow.State.eps, HutterPrizeFlow.State.mk]
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-- Verify parameter constraints
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theorem params_alphaComp_nonneg : 0 ≤ HutterPrizeFlow.Examples.params.alphaComp :=
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HutterPrizeFlow.Examples.params.h_alphaComp
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theorem params_alphaDec_nonneg : 0 ≤ HutterPrizeFlow.Examples.params.alphaDec :=
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HutterPrizeFlow.Examples.params.h_alphaDec
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theorem params_alphaRes_nonneg : 0 ≤ HutterPrizeFlow.Examples.params.alphaRes :=
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HutterPrizeFlow.Examples.params.h_alphaRes
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/- ============================================================
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§4 Cross-Reference with HutterPrizeCompression
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============================================================ -/
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-- Hutter Prize record: 114MB/GB = 11.4%
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-- HutterPrizeCompression.hutterRecordRatio = 114 (as Nat)
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-- Our hutterRecordRatio = 0.114 (as Real)
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-- Both represent the same target
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-- Hutter Prize goal: beat 99% of current record = 112.86MB/GB = 11.286%
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-- Target compression must be better than current record
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-- HutterPrizeFlow aligns with Hutter Prize rules through:
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-- 1. Compression gain (ρ) - larger ρ lowers the penalized objective
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-- 2. Decoder penalty (τ²) - models decoder complexity cost
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-- 3. Resource penalty (σ² + q²) - models computational resource cost
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-- The tradeoff theorem (sufficient_compression_gain_can_offset_penalties)
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-- formalizes the Hutter Prize rule that compression gain must exceed
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-- the sum of decoder and resource penalties to be worthwhile.
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end
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