mirror of
https://github.com/allaunthefox/Research-Stack.git
synced 2026-07-31 03:05:21 +00:00
allaun
b038778361
- SDPVerify.lean: certificate verification engine (714 lines, compiles cleanly) - GoormaghtighCert.lean: Goormaghtigh conjecture SDP certificate - HachimojiManifoldAxiom/HachimojiSubstitution: Hachimoji DNA encoding - GeneticBraidBridge.lean: genetic algorithm braid bridge - load_dependency_graph/load_module_graph: Gremlin Cosmos DB graph loaders - test_graph_queries/rrc_math_xref: graph verification queries - Gremlin mathblob DB provisioned and accessible - Branch cleanup: deleted 11 stale remote branches Build: 3297 jobs, 0 errors (lake build Semantics.SDPVerify)
242 lines
8.4 KiB
Text
242 lines
8.4 KiB
Text
/-
|
|
GeneticBraidBridge.lean -- Genetic Sequence to BraidState Translation
|
|
|
|
Maps any supported genetic alphabet (DNA, RNA, mRNA, Hachimoji, XNA, 6-state)
|
|
to a BraidState via braid word composition on the 8-strand BraidStorm topology.
|
|
|
|
Each symbol is assigned to a primary strand (0-7) based on its ordinal within
|
|
the alphabet. The crossing generator crosses the primary strand with its XOR-1
|
|
pair. Codons compose into a braid word applied sequentially.
|
|
|
|
The resulting BraidState inherits all existing compressor theorems:
|
|
- eigensolid_convergence (BraidEigensolid.lean)
|
|
- receipt_invertible (BraidEigensolid.lean)
|
|
-/
|
|
|
|
import Semantics.GeneticCode
|
|
import Semantics.GeneticGroundUp
|
|
import Semantics.BraidEigensolid
|
|
import Semantics.BraidCross
|
|
import Semantics.BraidStrand
|
|
import Semantics.BraidBracket
|
|
|
|
namespace Semantics.GeneticBraidBridge
|
|
|
|
open Semantics.GeneticCode
|
|
open Semantics.GeneticGroundUp
|
|
open Semantics.BraidEigensolid
|
|
open Semantics.BraidCross
|
|
open Semantics.BraidStrand
|
|
open Semantics.BraidBracket
|
|
|
|
-- ============================================================
|
|
-- SS1. ALPHABET TAXONOMY
|
|
-- ============================================================
|
|
|
|
/-- The supported genetic alphabets. -/
|
|
inductive AlphabetType
|
|
| dna -- 4 bases: A, C, G, T
|
|
| rna -- 4 bases: A, C, G, U
|
|
| mrna -- mRNA: same as RNA
|
|
| hachimoji -- 8 bases: A, C, G, T, Z, P, S, B
|
|
| xna -- 16 symbols: 0-9, A-F (hex)
|
|
| genetic6 -- 6-state: A, C, G, T, U, X
|
|
deriving Repr, DecidableEq, BEq
|
|
|
|
/-- Canonical symbol count per alphabet type. -/
|
|
def alphabetSize : AlphabetType -> Nat
|
|
| .dna => 4
|
|
| .rna => 4
|
|
| .mrna => 4
|
|
| .hachimoji => 8
|
|
| .xna => 16
|
|
| .genetic6 => 6
|
|
|
|
/-- Canonical codon length per alphabet type. -/
|
|
def codonLength : AlphabetType -> Nat
|
|
| .dna => 3
|
|
| .rna => 3
|
|
| .mrna => 3
|
|
| .hachimoji => 3
|
|
| .xna => 2
|
|
| .genetic6 => 3
|
|
|
|
/-- Number of codons = alphabetSize ^ codonLength. -/
|
|
def numCodons (a : AlphabetType) : Nat :=
|
|
(alphabetSize a) ^ (codonLength a)
|
|
|
|
-- ============================================================
|
|
-- SS2. HACHIMOJI SYMBOLS
|
|
-- ============================================================
|
|
|
|
/-- Hachimoji 8-symbol alphabet (Benner et al.): natural pairs
|
|
(A,T), (C,G), (Z,P), (S,B). -/
|
|
inductive HachimojiSym
|
|
| A | C | G | T | Z | P | S | B
|
|
deriving Repr, DecidableEq, BEq
|
|
|
|
-- ============================================================
|
|
-- SS3. GENETIC SYMBOL DISPATCH
|
|
-- ============================================================
|
|
|
|
/-- A unified genetic symbol covering all supported alphabets. -/
|
|
inductive GeneticSymbol
|
|
| base (b : EventType) -- DNA/RNA base
|
|
| nuc (n : Nucleotide) -- 6-state nucleotide
|
|
| a8 (a : HachimojiSym) -- Hachimoji
|
|
| hex (v : UInt8) -- XNA hex digit (0-15)
|
|
deriving Repr, DecidableEq, BEq
|
|
|
|
/-- Ordinal index within the alphabet: determines strand assignment. -/
|
|
def symbolOrdinal (sym : GeneticSymbol) (alphabet : AlphabetType) : Nat :=
|
|
match sym, alphabet with
|
|
| .base b, .dna =>
|
|
match b with
|
|
| .a => 0 | .g => 1 | .c => 2 | .t => 3
|
|
| .base b, .rna =>
|
|
match b with
|
|
| .a => 0 | .g => 1 | .c => 2 | .t => 3
|
|
| .base b, .mrna =>
|
|
match b with
|
|
| .a => 0 | .g => 1 | .c => 2 | .t => 3
|
|
| .nuc n, .genetic6 =>
|
|
match n with
|
|
| .A => 0 | .T => 1 | .C => 2 | .G => 3 | .U => 4 | .X => 5
|
|
| .a8 a, .hachimoji =>
|
|
match a with
|
|
| .A => 0 | .C => 1 | .G => 2 | .T => 3
|
|
| .Z => 4 | .P => 5 | .S => 6 | .B => 7
|
|
| .hex v, .xna => v.toNat
|
|
| _, _ => 0
|
|
|
|
/-- Proof that ordinal % 8 < 8. -/
|
|
private lemma ordinal_mod_lt (sym : GeneticSymbol) (alphabet : AlphabetType) :
|
|
symbolOrdinal sym alphabet % 8 < 8 :=
|
|
Nat.mod_lt _ (by decide)
|
|
|
|
/-- Primary strand index (0-7): ordinal % 8. -/
|
|
def symbolToStrand (sym : GeneticSymbol) (alphabet : AlphabetType) : Fin 8 :=
|
|
⟨symbolOrdinal sym alphabet % 8, ordinal_mod_lt sym alphabet⟩
|
|
|
|
-- ============================================================
|
|
-- SS4. DEFAULT SIDON LABELS
|
|
-- ============================================================
|
|
|
|
/-- Default Sidon labels: powers of two (1, 2, 4, 8, 16, 32, 64, 128). -/
|
|
def defaultSidonLabels (i : Fin 8) : UInt32 :=
|
|
match i.val with
|
|
| 0 => 1 | 1 => 2 | 2 => 4 | 3 => 8
|
|
| 4 => 16 | 5 => 32 | 6 => 64 | 7 => 128
|
|
| _ => 1
|
|
|
|
-- ============================================================
|
|
-- SS5. GENETIC WORD -> BRAID STATE
|
|
-- ============================================================
|
|
|
|
/-- Initial BraidState: 8 strands with default Sidon labels, zero phase. -/
|
|
def initialState : BraidState :=
|
|
{ strands := fun i => BraidStrand.zero (defaultSidonLabels i)
|
|
, step_count := 0
|
|
}
|
|
|
|
/-- Pair strand: XOR-1 of the given strand index.
|
|
For v in [0,7], v ^ 1 is always in [0,7] (swaps each adjacent pair). -/
|
|
def pairStrand (i : Fin 8) : Fin 8 :=
|
|
match i with
|
|
| 0 => ⟨1, by decide⟩
|
|
| 1 => ⟨0, by decide⟩
|
|
| 2 => ⟨3, by decide⟩
|
|
| 3 => ⟨2, by decide⟩
|
|
| 4 => ⟨5, by decide⟩
|
|
| 5 => ⟨4, by decide⟩
|
|
| 6 => ⟨7, by decide⟩
|
|
| 7 => ⟨6, by decide⟩
|
|
|
|
/-- Apply a single genetic symbol crossing to a BraidState.
|
|
|
|
The symbol's assigned strand crosses with its XOR-1 pair strand.
|
|
The merged strand replaces the primary strand. -/
|
|
def applySymbol (s : BraidState) (sym : GeneticSymbol) (alphabet : AlphabetType) : BraidState :=
|
|
let i := symbolToStrand sym alphabet
|
|
let j := pairStrand i
|
|
let (merged, _) := braidCross (s.strands i) (s.strands j)
|
|
{ strands := fun k =>
|
|
if k = i then merged
|
|
else s.strands k
|
|
, step_count := s.step_count + 1
|
|
}
|
|
|
|
/-- Apply a list of genetic symbols (a braid word) to the initial BraidState. -/
|
|
def applyGeneticWord (word : List GeneticSymbol) (alphabet : AlphabetType) : BraidState :=
|
|
List.foldl (fun s sym => applySymbol s sym alphabet) initialState word
|
|
|
|
-- ============================================================
|
|
-- SS6. GENETIC RECEIPT
|
|
-- ============================================================
|
|
|
|
/-- Produce a BraidReceipt from a genetic braid state.
|
|
|
|
Delegates to BraidEigensolid.encodeReceipt.
|
|
Inherits all properties proven there. -/
|
|
def geneticReceipt (state : BraidState) : BraidReceipt :=
|
|
encodeReceipt state
|
|
|
|
-- ============================================================
|
|
-- SS7. BRIDGE THEOREMS
|
|
-- ============================================================
|
|
|
|
/-- Eigensolid convergence for genetic sequences. Follows directly
|
|
from eigensolid_convergence. -/
|
|
theorem genetic_eigensolid_convergence
|
|
(s : BraidState)
|
|
(h_eig : IsEigensolid (crossStep s)) :
|
|
∀ i : Fin 8, (crossStep (crossStep s)).strands i = (crossStep s).strands i :=
|
|
eigensolid_convergence s h_eig
|
|
|
|
/-- Receipt invertibility for genetic sequences. Follows directly
|
|
from receipt_invertible. -/
|
|
theorem genetic_receipt_invertible
|
|
(s1 s2 : BraidState)
|
|
(h_eig1 : IsEigensolid s1) (h_eig2 : IsEigensolid s2)
|
|
(h_rec : encodeReceipt s1 = encodeReceipt s2) :
|
|
((∀ i : Fin 8, (s1.strands i).residue = (s2.strands i).residue) ∧
|
|
(s1.strands ⟨0, by decide⟩).bracket = (s2.strands ⟨0, by decide⟩).bracket ∧
|
|
(s1.strands ⟨7, by decide⟩).slot = (s2.strands ⟨7, by decide⟩).slot ∧
|
|
s1.step_count = s2.step_count) :=
|
|
receipt_invertible s1 s2 h_eig1 h_eig2 h_rec
|
|
|
|
-- ============================================================
|
|
-- SS8. HELPER CONSTRUCTORS
|
|
-- ============================================================
|
|
|
|
/-- Build a genetic word from a DNA/RNA string (A, C, G, T, U). -/
|
|
def stringToWord (s : String) : List GeneticSymbol :=
|
|
let toSym (c : Char) : Option GeneticSymbol :=
|
|
match c.toUpper with
|
|
| 'A' => some (.base .a)
|
|
| 'C' => some (.base .c)
|
|
| 'G' => some (.base .g)
|
|
| 'T' => some (.base .t)
|
|
| 'U' => some (.base .t)
|
|
| _ => none
|
|
s.toList.filterMap toSym
|
|
|
|
-- ============================================================
|
|
-- SS9. WITNESSES
|
|
-- ============================================================
|
|
|
|
-- A simple DNA word: ATGCGTAA (8 symbols)
|
|
def testWord : List GeneticSymbol :=
|
|
[.base .a, .base .t, .base .g, .base .c, .base .g, .base .t, .base .a, .base .a]
|
|
|
|
-- #eval testWord.length
|
|
-- expect: 8
|
|
|
|
def testState : BraidState := applyGeneticWord testWord .dna
|
|
|
|
-- #eval (testState.strands ⟨0, by decide⟩).slot
|
|
-- Slot of strand 0 after first crossing (A -> strand 0, crosses with strand 1)
|
|
|
|
-- #eval (geneticReceipt testState).step_count
|
|
-- expect: 8 (one crossing per symbol)
|
|
|