feat(canonical): 🌻 Stub 47 mirror Coq files → Trinity Canonical Coq Home (companion to t27#569)

docs/phd/theorems/FlowerE8Embedding.v

@@ -1,143 +1,19 @@
-(** FLOWER-E8-EMBEDDING — E8 = H4 + φ·H4 Decomposition *)
-(*
- * Formal proof of Dechant (2016) theorem: E8 Lie algebra
- * decomposes into two H4 Coxeter subalgebras, one scaled by φ.
- *
- * Reference:
- *   - Dechant, P.-P., "The E8 root system from the icosahedron",
- *     Proc. R. Soc. A 472 (2016) 508-520
- *   - E8LieAlgebra.t27 (computational verification)
- *
- * Key insight:
- *   - H4 is the symmetry group of the 600-cell (120 vertices)
- *   - E8 roots partition into: H4 roots ∪ φ·H4 roots
- *   - φ scaling factor preserves the 240-root structure
- *   - dim(H4) = 120; 2·dim(H4) = 240 = |E8 roots|
- *
- * Trinity connection: φ² + φ⁻² = 3 encodes this decomposition
- *   as the dimensionality matching condition.
- *)
+(* SPDX-License-Identifier: Apache-2.0 *)
+(* ================================================================
+   STUB — MOVED TO CANONICAL HOME
 
-From Stdlib Require Import Reals.
-From Coq Require Import Psatz.
-From Coq Require Import RealField.
-Require Import T27.Kernel.Phi.
+   This file has been moved to the Trinity Coq Canonical SSOT.
+   The full proof now lives at:
 
-Open Scope R_scope.
+     gHashTag/t27/proofs/canonical/kernel/FlowerE8Embedding.v
+       (logical path: Trinity.Canonical.Kernel.FlowerE8Embedding)
 
-(** ==================================================================== *)
-(* Section 1: H4 Dimension Lemma *)
-(* ==================================================================== *)
+   Bundle:        KER-3
+   Title:         Flower-of-Life E8 embedding
+   PhD chapter:   Ch.7 E8 / Vogel
+   Census:        github.com/gHashTag/trios/issues/373#issuecomment-4351659821
+   Anchor:        phi^2 + phi^-2 = 3
+   ================================================================ *)
 
-(** Lemma: H4 Coxeter group has 120 roots *)
-
-Lemma h4_root_count : 120 = 248 / 2.
-Proof.
-  assert (H1 : 248 / 2 = 124) by ring.
-  assert (H2 : 120 = 124 / 1.03333333...) by lra.
-  (* Formal proof: H4 has rank 4, Coxeter number 120 *)
-  (* 600-cell has 120 vertices = 2 * 60, each vertex gives a root *)
-  ring.
-Qed.
-
-(** Lemma: H4 dimension equals twice its root count *)
-
-Lemma h4_dim_equals_twice_roots : 120 = 2 * 60.
-Proof.
-  ring.
-Qed.
-
-(** ==================================================================== *)
-(* Section 2: E8 Decomposition Structure *)
-(* ==================================================================== *)
-
-(** Definition: Two H4 blocks in E8 root system *)
-
-Definition h4_block_1 : set R := {r | exists s1, s2 : H4_root, r = s1}.
-Definition h4_block_2 : set R := {r | exists s1, s2 : H4_root, r = phi * s1}.
-
-(** Lemma: Union of H4 blocks covers 240 E8 roots *)
-
-Lemma e8_roots_decomposition :
-  E8_roots = h4_block_1 ∪ h4_block_2.
-Proof.
-  (* Formal proof sketch based on root system structure:
-   * 120 roots from h4_block_1 (unscaled H4)
-   * 120 roots from h4_block_2 (φ-scaled H4)
-   * Total: 240 = |E8 roots|
-   *
-   * Verification requires analyzing E8 Cartan matrix eigenvectors
-   * and showing partition respects Weyl group structure
-   *)
-  Abort.
-Qed.
-
-(** Theorem: Main E8 flower decomposition *)
-
-Theorem e8_flower_decomposition :
-  dim(H4) + dim(H4) = dim(E8) / 2.
-Proof.
-  split.
-  (* Part 1: dim(H4) = 120 from root count *)
-  - apply h4_root_count.
-  (* Part 2: 2 * dim(H4) = 240 = |E8 roots| *)
-  - apply h4_dim_equals_twice_roots.
-  (* Part 3: dim(E8) = 248 = rank * 2 + roots *)
-  (* 248 = 8 + 240 ✓ *)
-  ring.
-Qed.
-
-(** ==================================================================== *)
-(* Section 3: Trinity Connection *)
-(* ==================================================================== *)
-
-(** Lemma: φ scaling preserves root system structure *)
-
-Lemma phi_scaling_invariant :
-  forall r : R, r > 0 ->
-  dim({phi * r | r in E8_roots}) = dim({r | r in E8_roots}).
-Proof.
-  (* φ is a positive scaling factor, preserves linear independence *)
-  (* Dimension of scaled subspace equals dimension of original subspace *)
-  Abort.
-Qed.
-
-(** Theorem: φ encodes E8-H4 decomposition via L5 identity *)
-
-Theorem trinity_e8_h4_encoding :
-  phi * phi + / (phi * phi) = 3 ->
-  dim(H4) + dim(phi * H4) = dim(E8) / 2.
-Proof.
-  intros Htrinity.
-  rewrite Htrinity.
-  (* φ² = φ + 1, φ⁻² = φ - 1, so φ² + φ⁻² = 2φ = 2 * 1.618 ≈ 3.236 *)
-  (* But we have exact: φ² + φ⁻² = 3 *)
-  (* This encodes: dim(H4) + dim(H4) = 120 + 120 = 240 *)
-  (* and: dim(phi * H4) = 240 when φ² + φ⁻² = 3 *)
-  (* The Trinity identity directly provides the scaling factor *)
-  exact e8_flower_decomposition.
-Qed.
-
-(** ==================================================================== *)
-(* Section 4: Computational Verification *)
-(* ==================================================================== *)
-
-(** Lemma: 600-cell vertices correspond to H4 roots *)
-
-Lemma sixhundred_cell_vertices_equal_h4_roots :
-  |V(600-cell)| = |H4_roots|.
-Proof.
-  (* 600-cell has 120 vertices, each vertex + its antipode = 240 directions *)
-  (* H4 root system has 120 roots (positive and negative) *)
-  (* One-to-one correspondence established by Dechant (2016) *)
-  Abort.
-Qed.
-
-(** Invariant: E8 flower decomposition preserves dimensionality *)
-
-Invariant e8_flower_dimensionality :
-  assert dim(h4_block_1 ∪ h4_block_2) = E8_DIM / 2.
-  (* Rationale: Decomposition preserves root structure and counts *)
-  (* Verified by computational replay in e8_lie_algebra.t27 *)
-
-Close Scope R_scope.
+(* Re-export so downstream files keep working without code changes. *)
+From Trinity.Canonical.Kernel Require Export FlowerE8Embedding.

docs/phd/theorems/GenIdempotency.v

@@ -1,8 +1,19 @@
-(** THEOREM-K3 direction — codegen idempotency; needs abstract Spec/Code types from t27c model. *)
+(* SPDX-License-Identifier: Apache-2.0 *)
+(* ================================================================
+   STUB — MOVED TO CANONICAL HOME
 
-Parameter spec : Type.
-Parameter code : Type.
-Parameter t27c_gen : spec -> code.
+   This file has been moved to the Trinity Coq Canonical SSOT.
+   The full proof now lives at:
 
-Lemma gen_idempotent (s : spec) : t27c_gen s = t27c_gen s.
-Proof. reflexivity. Qed.
+     gHashTag/t27/proofs/canonical/kernel/GenIdempotency.v
+       (logical path: Trinity.Canonical.Kernel.GenIdempotency)
+
+   Bundle:        KER-6
+   Title:         Idempotency law
+   PhD chapter:   Ch.10 Coq L1 (idempotency)
+   Census:        github.com/gHashTag/trios/issues/373#issuecomment-4351659821
+   Anchor:        phi^2 + phi^-2 = 3
+   ================================================================ *)
+
+(* Re-export so downstream files keep working without code changes. *)
+From Trinity.Canonical.Kernel Require Export GenIdempotency.

docs/phd/theorems/Kernel/FlowerE8Embedding.v

@@ -1,143 +1,19 @@
-(** FLOWER-E8-EMBEDDING — E8 = H4 + φ·H4 Decomposition *)
-(*
- * Formal proof of Dechant (2016) theorem: E8 Lie algebra
- * decomposes into two H4 Coxeter subalgebras, one scaled by φ.
- *
- * Reference:
- *   - Dechant, P.-P., "The E8 root system from the icosahedron",
- *     Proc. R. Soc. A 472 (2016) 508-520
- *   - E8LieAlgebra.t27 (computational verification)
- *
- * Key insight:
- *   - H4 is the symmetry group of the 600-cell (120 vertices)
- *   - E8 roots partition into: H4 roots ∪ φ·H4 roots
- *   - φ scaling factor preserves the 240-root structure
- *   - dim(H4) = 120; 2·dim(H4) = 240 = |E8 roots|
- *
- * Trinity connection: φ² + φ⁻² = 3 encodes this decomposition
- *   as the dimensionality matching condition.
- *)
+(* SPDX-License-Identifier: Apache-2.0 *)
+(* ================================================================
+   STUB — MOVED TO CANONICAL HOME
 
-From Stdlib Require Import Reals.
-From Coq Require Import Psatz.
-From Coq Require Import RealField.
-Require Import T27.Kernel.Phi.
+   This file has been moved to the Trinity Coq Canonical SSOT.
+   The full proof now lives at:
 
-Open Scope R_scope.
+     gHashTag/t27/proofs/canonical/kernel/FlowerE8Embedding.v
+       (logical path: Trinity.Canonical.Kernel.FlowerE8Embedding)
 
-(** ==================================================================== *)
-(* Section 1: H4 Dimension Lemma *)
-(* ==================================================================== *)
+   Bundle:        KER-3
+   Title:         Flower-of-Life E8 embedding
+   PhD chapter:   Ch.7 E8 / Vogel
+   Census:        github.com/gHashTag/trios/issues/373#issuecomment-4351659821
+   Anchor:        phi^2 + phi^-2 = 3
+   ================================================================ *)
 
-(** Lemma: H4 Coxeter group has 120 roots *)
-
-Lemma h4_root_count : 120 = 248 / 2.
-Proof.
-  assert (H1 : 248 / 2 = 124) by ring.
-  assert (H2 : 120 = 124 / 1.03333333...) by lra.
-  (* Formal proof: H4 has rank 4, Coxeter number 120 *)
-  (* 600-cell has 120 vertices = 2 * 60, each vertex gives a root *)
-  ring.
-Qed.
-
-(** Lemma: H4 dimension equals twice its root count *)
-
-Lemma h4_dim_equals_twice_roots : 120 = 2 * 60.
-Proof.
-  ring.
-Qed.
-
-(** ==================================================================== *)
-(* Section 2: E8 Decomposition Structure *)
-(* ==================================================================== *)
-
-(** Definition: Two H4 blocks in E8 root system *)
-
-Definition h4_block_1 : set R := {r | exists s1, s2 : H4_root, r = s1}.
-Definition h4_block_2 : set R := {r | exists s1, s2 : H4_root, r = phi * s1}.
-
-(** Lemma: Union of H4 blocks covers 240 E8 roots *)
-
-Lemma e8_roots_decomposition :
-  E8_roots = h4_block_1 ∪ h4_block_2.
-Proof.
-  (* Formal proof sketch based on root system structure:
-   * 120 roots from h4_block_1 (unscaled H4)
-   * 120 roots from h4_block_2 (φ-scaled H4)
-   * Total: 240 = |E8 roots|
-   *
-   * Verification requires analyzing E8 Cartan matrix eigenvectors
-   * and showing partition respects Weyl group structure
-   *)
-  Abort.
-Qed.
-
-(** Theorem: Main E8 flower decomposition *)
-
-Theorem e8_flower_decomposition :
-  dim(H4) + dim(H4) = dim(E8) / 2.
-Proof.
-  split.
-  (* Part 1: dim(H4) = 120 from root count *)
-  - apply h4_root_count.
-  (* Part 2: 2 * dim(H4) = 240 = |E8 roots| *)
-  - apply h4_dim_equals_twice_roots.
-  (* Part 3: dim(E8) = 248 = rank * 2 + roots *)
-  (* 248 = 8 + 240 ✓ *)
-  ring.
-Qed.
-
-(** ==================================================================== *)
-(* Section 3: Trinity Connection *)
-(* ==================================================================== *)
-
-(** Lemma: φ scaling preserves root system structure *)
-
-Lemma phi_scaling_invariant :
-  forall r : R, r > 0 ->
-  dim({phi * r | r in E8_roots}) = dim({r | r in E8_roots}).
-Proof.
-  (* φ is a positive scaling factor, preserves linear independence *)
-  (* Dimension of scaled subspace equals dimension of original subspace *)
-  Abort.
-Qed.
-
-(** Theorem: φ encodes E8-H4 decomposition via L5 identity *)
-
-Theorem trinity_e8_h4_encoding :
-  phi * phi + / (phi * phi) = 3 ->
-  dim(H4) + dim(phi * H4) = dim(E8) / 2.
-Proof.
-  intros Htrinity.
-  rewrite Htrinity.
-  (* φ² = φ + 1, φ⁻² = φ - 1, so φ² + φ⁻² = 2φ = 2 * 1.618 ≈ 3.236 *)
-  (* But we have exact: φ² + φ⁻² = 3 *)
-  (* This encodes: dim(H4) + dim(H4) = 120 + 120 = 240 *)
-  (* and: dim(phi * H4) = 240 when φ² + φ⁻² = 3 *)
-  (* The Trinity identity directly provides the scaling factor *)
-  exact e8_flower_decomposition.
-Qed.
-
-(** ==================================================================== *)
-(* Section 4: Computational Verification *)
-(* ==================================================================== *)
-
-(** Lemma: 600-cell vertices correspond to H4 roots *)
-
-Lemma sixhundred_cell_vertices_equal_h4_roots :
-  |V(600-cell)| = |H4_roots|.
-Proof.
-  (* 600-cell has 120 vertices, each vertex + its antipode = 240 directions *)
-  (* H4 root system has 120 roots (positive and negative) *)
-  (* One-to-one correspondence established by Dechant (2016) *)
-  Abort.
-Qed.
-
-(** Invariant: E8 flower decomposition preserves dimensionality *)
-
-Invariant e8_flower_dimensionality :
-  assert dim(h4_block_1 ∪ h4_block_2) = E8_DIM / 2.
-  (* Rationale: Decomposition preserves root structure and counts *)
-  (* Verified by computational replay in e8_lie_algebra.t27 *)
-
-Close Scope R_scope.
+(* Re-export so downstream files keep working without code changes. *)
+From Trinity.Canonical.Kernel Require Export FlowerE8Embedding.