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Source-pinned research

Research proof index

Search theorem names, mathematical ideas, modules, topics, projects, and role-labelled researchers. Open a result for its complete indexed Lean declaration and source record.

This index contains 2,569 curated research declarations and 119,070 complete package declarations. Search 10,000 more complete Mathlib declarations.

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Showing 1,153 to 1,158 of 2,569 results.

Project-declaredLean 4.32.0

Decompose to Charge Map

FTheory.SU5.FiveQuanta.decompose_toChargeMap

Project documentation

The decomposition of a FiveQuanta into a FiveQuanta which has the same reduce by has fluxes ⟨1, -1⟩ and ⟨0,1⟩ only. -/ def decompose (x : FiveQuanta 𝓩) : FiveQuanta 𝓩 := x.bind fun p => (decomposeFluxes p.2).map fun f => (p.1, f) /-! #### C.2.1. Decomposition distributes over addition -/ lemma decompose_add (x y : FiveQuanta 𝓩) : (x + y).deco...

physicsquantum field theoryrelativity

Source project: Physlib

Person-level attribution pending.

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Project-declaredLean 4.32.0

Decompose to Charges dedup

FTheory.SU5.FiveQuanta.decompose_toCharges_dedup

Project documentation

The decomposition of a FiveQuanta into a FiveQuanta which has the same reduce by has fluxes ⟨1, -1⟩ and ⟨0,1⟩ only. -/ def decompose (x : FiveQuanta 𝓩) : FiveQuanta 𝓩 := x.bind fun p => (decomposeFluxes p.2).map fun f => (p.1, f) /-! #### C.2.1. Decomposition distributes over addition -/ lemma decompose_add (x y : FiveQuanta 𝓩) : (x + y).deco...

physicsquantum field theoryrelativity

Source project: Physlib

Person-level attribution pending.

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Project-declaredLean 4.32.0

Decompose to Fluxes Five

FTheory.SU5.FiveQuanta.decompose_toFluxesFive

Project documentation

The decomposition of a FiveQuanta into a FiveQuanta which has the same reduce by has fluxes ⟨1, -1⟩ and ⟨0,1⟩ only. -/ def decompose (x : FiveQuanta 𝓩) : FiveQuanta 𝓩 := x.bind fun p => (decomposeFluxes p.2).map fun f => (p.1, f) /-! #### C.2.1. Decomposition distributes over addition -/ lemma decompose_add (x y : FiveQuanta 𝓩) : (x + y).deco...

physicsquantum field theoryrelativity

Source project: Physlib

Person-level attribution pending.

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Project-declaredLean 4.32.0

Exists to Charges to Fluxes Five of mem lift Charge

FTheory.SU5.FiveQuanta.exists_toCharges_toFluxesFive_of_mem_liftCharge

Project documentation

Given a finite set of charges c the FiveQuanta which do not have exotics, duplicate charges or zero fluxes, which map down to c. -/ def liftCharge (c : Finset 𝓩) : Multiset (FiveQuanta 𝓩) := /- The multisets of cardinality 3 containing 3 elements of c. -/ let S53 : Multiset (Multiset 𝓩) := toMultisetsThree c /- Pairs of multisets (s1, s2) such...

physicsquantum field theoryrelativity

Source project: Physlib

Person-level attribution pending.

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Project-declaredLean 4.32.0

Map lift Charge

FTheory.SU5.FiveQuanta.map_liftCharge

Project documentation

Given a finite set of charges c the FiveQuanta which do not have exotics, duplicate charges or zero fluxes, which map down to c. -/ def liftCharge (c : Finset 𝓩) : Multiset (FiveQuanta 𝓩) := /- The multisets of cardinality 3 containing 3 elements of c. -/ let S53 : Multiset (Multiset 𝓩) := toMultisetsThree c /- Pairs of multisets (s1, s2) such...

physicsquantum field theoryrelativity

Source project: Physlib

Person-level attribution pending.

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Project-declaredLean 4.32.0

Mem lift Charge of mem no Exotics has No Zero

FTheory.SU5.FiveQuanta.mem_liftCharge_of_mem_noExotics_hasNoZero

Project documentation

Given a finite set of charges c the FiveQuanta which do not have exotics, duplicate charges or zero fluxes, which map down to c. -/ def liftCharge (c : Finset 𝓩) : Multiset (FiveQuanta 𝓩) := /- The multisets of cardinality 3 containing 3 elements of c. -/ let S53 : Multiset (Multiset 𝓩) := toMultisetsThree c /- Pairs of multisets (s1, s2) such...

physicsquantum field theoryrelativity

Source project: Physlib

Person-level attribution pending.

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