Thomson $N=7$: certificate data for slab 4 ($-\tfrac{47}{50}\le t_{01}\le-\tfrac{93}{100}$), part 1 of 2

import Definitions.Def_ThomsonN7_core

/-!
# Thomson problem for N = 7 (and the D3h stretch target for N = 9)

Minimise the Coulomb energy `E(x) = ∑_{i<j} 1 / ‖x i - x j‖` over configurations of `N` pairwise
distinct points on the unit sphere `S² ⊂ ℝ³`.

* `N = 7`: the unique minimiser (up to `O(3)` and relabelling) is the regular pentagonal bipyramid,
  with `E = 1/2 + 5√2 + 5/(2 sin(π/5)) + 5/(2 sin(2π/5)) = 14.452977414…`.
* `N = 9`: the (numerically known) minimiser is the D3h tricapped trigonal prism, which has one free
  parameter `z` (the height of the two triangular faces); numerically `z ≈ 0.70365`,
  `E ≈ 25.759986531`.
-/

open Real

namespace ThomsonN7

/-! ## Auxiliary facts (already proved; they show the definitions are well-posed) -/

/- BEGIN M0 -/
namespace Base

open Finset

/-! ### Invariance -/

/-! ### Gram values of the pentagonal bipyramid -/

end Base
/- END M0 -/

/- BEGIN M1 -/
namespace ThreePoint

open Finset Matrix
open scoped RealInnerProductSpace

/-! # Bachoc–Vallentin three-point positivity on `S²` (any block size, any `k`)

`Q3 k u v t = ((1-u²)(1-v²))^{k/2} T_k((t-uv)/√((1-u²)(1-v²)))` via the Chebyshev recursion.
-/

/-! ### Addition theorem (de Moivre) -/

/-! ### Combinatorics of ordered triple sums -/

section Comb

variable {n : ℕ}

end Comb

section Comb2

variable {n : ℕ}

end Comb2

section Comb3

variable {n : ℕ}

end Comb3

section Comb4

variable {n : ℕ}

end Comb4

section Final

variable {n : ℕ}

end Final

/-! ### The kernels at the diagonal `(1,1,1)` -/

section FinalZ

variable {n : ℕ}

end FinalZ

/- BEGIN M5 -/
section Critical

end Critical

section Critical

end Critical

section Critical

end Critical

section CriticalZ

variable {n : ℕ}

end CriticalZ

section CriticalZsym

variable {n : ℕ}

section Perm

variable (τ : Fin n → Fin n → ℝ) (hτ : ∀ i j, τ j i = τ i j) (f : ℝ → ℝ → ℝ → ℝ)

include hτ

end Perm

end CriticalZsym

section CriticalFinal

variable {n : ℕ}

end CriticalFinal

/- END M5 -/

end ThreePoint

/- BEGIN CERT3 -/

/-!
# Kronecker-substitution checking of polynomial identities

A polynomial `e : Ex` in three variables `u, v, t` with integer coefficients is given as an
expression tree.  To prove `∀ u v t : ℝ, e(u,v,t) = 0` it suffices to check, with kernel
(GMP) integer arithmetic, that
* every exponent of every variable is `< D`,
* the `ℓ¹`-norm of the (uncollected) coefficients is `< 2^w`,
* the value of `e` at the integers `u = 2^w`, `v = 2^(w D)`, `t = 2^(w D²)` is `0`.
-/

namespace Kron

namespace Ex

end Ex

namespace Ex

end Ex

open Ex

end Kron

/-! ## Builders for `Ex` with evaluation lemmas -/

namespace Kron
namespace Ex

variable (u v t : ℝ)

/-! ### Substitution of variables by variables or `1` -/

end Ex
end Kron

/- BEGIN CERT1 -/
section Cert1Block

open Kron Kron.Ex

namespace Cert

open ThreePoint

/-! ## `Q_k` as a polynomial expression -/

/-! ## Quadratic forms: `L D Lᵀ` plus a diagonally dominant remainder -/

/-! ## Integer data of a positive semidefinite block -/

namespace Blk

end Blk

end Cert

end Cert1Block

/- BEGIN CERT3FILE -/
section Cert3Block

open Kron Kron.Ex

namespace Cert

open ThreePoint

/-! ## Helpers: zero-skipping scaling, monomial-preserving substitution -/

/-! ## The `F`-blocks: `Λ · Fp(u,v)` -/

/-! ## Block matrices and their quadratic forms -/

/-! ## Symmetrisation and the `F`-part of the identity -/

/-! ## SOS blocks with multipliers -/

/-! ## The certificate and its soundness -/

open scoped RealInnerProductSpace

namespace Cert3

end Cert3

namespace Cert3

end Cert3

namespace Cert3

end Cert3

end Cert

end Cert3Block

/- END CERT3 -/

/- BEGIN M2 -/
namespace M2

/-! ## The number field `ℚ(√2, 2 sin (π/5))` -/

namespace K8

/-! ### Rational enclosures and positivity of elements of `K8` -/

end K8

namespace K8

end K8

/-! ### Polynomials with `K8` coefficients: dense lists, lowest degree first -/

namespace Pl

end Pl

open Pl

end M2
/- END M2 -/

/- BEGIN M3 -/
namespace M3

open scoped InnerProductSpace

end M3

/- BEGIN P3ext -/

/-! ## P3: Bregman (Taylor) lower bounds for the Coulomb pair potential (agent7) -/

namespace Base

end Base

/- END P3ext -/

/- BEGIN P1 -/

/-! ## P1: the bipyramid is a critical point of the Coulomb energy on the constraint set (agent7) -/

namespace Reg

open Base

end Reg

/- END P1 -/

/- BEGIN GAUGE -/

/-! ## G: gauge (Procrustes) lemma `exists_gauge` (agent7) -/

namespace Reg

open scoped RealInnerProductSpace

end Reg

/- END GAUGE -/

/- BEGIN P2 -/

/- BEGIN RegB (P2: exact energy identity; needs M0 = namespace Base and the Challenge preamble) -/
namespace RegB

open Base Finset

section vectors

variable (y : Fin 7 → R3)

end vectors

end RegB
/- END RegB -/

/- END P2 -/

/- BEGIN GV -/

namespace GV

open Base

open scoped InnerProductSpace

end GV

/- END GV -/

/- BEGIN TWOREGIME -/

namespace TwoRegime

open scoped InnerProductSpace

end TwoRegime

namespace TwoRegime

open scoped InnerProductSpace
open Base

end TwoRegime

namespace TwoRegime

open scoped InnerProductSpace
open Base

end TwoRegime

/- END TWOREGIME -/

/- BEGIN TR_D -/
namespace TwoRegime

open scoped InnerProductSpace
open Base

end TwoRegime

/- END TR_D -/

/- BEGIN TR_E -/
namespace ThreePoint

open Finset Matrix
open scoped RealInnerProductSpace

section FinalCut

variable {n : ℕ}

end FinalCut

end ThreePoint

namespace TwoRegime

open scoped InnerProductSpace
open Base

end TwoRegime

/- END TR_E -/

/- BEGIN TR_G -/
namespace TwoRegime

open scoped InnerProductSpace
open Base

end TwoRegime

namespace TwoRegime

open scoped InnerProductSpace
open Base

end TwoRegime

/- BEGIN TR_G3 -/
namespace TwoRegime

open scoped InnerProductSpace
open Base

end TwoRegime
/- END TR_G3 -/
/- BEGIN TR_G4 -/
namespace TwoRegime

open scoped InnerProductSpace
open Base

end TwoRegime
/- END TR_G4 -/
/- END TR_G -/

/- BEGIN INTERFACES -/
namespace Interfaces

open Finset Base

end Interfaces
/- END INTERFACES -/

/- BEGIN GLUE -/
namespace Glue

open Finset Base Interfaces

end Glue
/- END GLUE -/

/- BEGIN TR_F -/
namespace EPBounds

open Real

end EPBounds
/- END TR_F -/
end ThomsonN7

section RegLocalSection
/- BEGIN REGLOCAL (agent7): perturbative strict local minimality of the pentagonal bipyramid.
   Splice AFTER Level1d (needs GAUGE = exists_gauge, P1/P3ext, Base, TwoRegime.LocalMinAt).
   Pieces in order: Loc1 (H, B3) | QCore1 (certificate defs/lemmas) | Q2 (expansion) | QCore2 (core) | Loc2 (glue). -/
open Real
open scoped RealInnerProductSpace
namespace ThomsonN7
/- BEGIN LOC1 (agent7): exact chart identity (H) and cubic Bregman lower bound (B3) in h = y - P.
   Splice AFTER the GAUGE block (needs P1, P3ext); compiles against Level1b.lean lines 1-3641. -/
namespace Reg
open Base

end Reg

/- END LOC1 -/

end ThomsonN7

/- BEGIN QCORE1 -/
namespace ThomsonN7
namespace Reg

end Reg
end ThomsonN7
/- END QCORE1 -/

/- BEGIN Q2 -/
open Real
open scoped RealInnerProductSpace
namespace ThomsonN7
namespace Reg
open Base

end Reg
end ThomsonN7

/- END Q2 -/

/- BEGIN QCORE2 -/
namespace ThomsonN7
namespace Reg

end Reg
end ThomsonN7
/- END QCORE2 -/

/- BEGIN LOC2 -/
open Real
open scoped RealInnerProductSpace
namespace ThomsonN7
namespace Reg
open Base

/-! ### The atom box for the penalised Hessian certificate -/

end Reg
end ThomsonN7

/- END LOC2 -/

namespace ThomsonN7
namespace Reg

end Reg

end ThomsonN7

/- END REGLOCAL -/
end RegLocalSection

/- BEGIN CASE1 -/
namespace ThomsonN7
namespace CutOneD

end CutOneD
end ThomsonN7

namespace ThomsonN7

namespace Case1Data
open ThomsonN7 ThomsonN7.Cert

end Case1Data

end ThomsonN7

namespace ThomsonN7
namespace Case1

open scoped InnerProductSpace
open ThomsonN7.Cert ThomsonN7.Cert.Cert3

/-! ### Chunked evaluation of the Kronecker check for `Case1Data.cf`

The identity expression `Case1Data.cf.idE` has about 147 000 nodes.  Evaluating `chk` on it in one
kernel call is correct but keeps every intermediate kernel term alive until the end of the
declaration.  Here the same check is split into separate declarations, one per piece of the
expression (`hE`, four `F`-blocks, eight `S`-blocks).  For every expression `e`, `c1Stat w D e`
computes, in one structural pass, the tuple `(ℓ¹-norm, deg u, deg v, deg t, Kronecker value)`
(`c1Stat_eq`).  The 13 pieces are evaluated by `decide +kernel` against exact literals, in 13
separate declarations; the statistics of `Case1Data.cf.idE` follow by the composition lemma
`c1Stat_idE` and closed arithmetic on the literals, and `chk` is then decided by its own definition
(`Nat.log2 ℓ¹ + 1 = 179`, `max deg + 1 = 11`, Kronecker value `0`).  The statement of `cf_ok` is
unchanged; the literals are data found by a program outside Lean and are only ever checked. -/

/-! The 13 pieces, each evaluated in its own declaration (`w = 179`, `D = 11`). -/

end Case1
end ThomsonN7

/- END CASE1 -/

/- BEGIN CASE2RED -/
namespace ThomsonN7
namespace Case1

section Case2Red

open scoped InnerProductSpace
open Base

end Case2Red

end Case1
end ThomsonN7
/- END CASE2RED -/

section Asm_Typed
open Finset Matrix
open scoped RealInnerProductSpace

namespace ThomsonN7
namespace ThreePoint

/-! # Typed (root-dependent) three-point bound

Every root `i` carries its own kernel `s i`; every pair `{i, j}` carries its own minorant `H i j`.
-/

section TypedRoot

end TypedRoot

section TypedComb

variable {n : ℕ}

end TypedComb

end ThreePoint
end ThomsonN7

end Asm_Typed

section Asm_Typed2
open Finset Matrix
open scoped RealInnerProductSpace

namespace ThomsonN7
namespace ThreePoint

/-! # Typed three-point bound with free pair shares

Each triple `{i, j, l}` receives a share `W i j l` of the pair function of `{i, j}` (and
similarly for the constant), so that the total over the triples containing a pair is prescribed.
-/

section TypedComb2

variable {n : ℕ}

end TypedComb2

end ThreePoint
end ThomsonN7

end Asm_Typed2

section Asm_Typed7
open Finset Matrix
open scoped RealInnerProductSpace

namespace ThomsonN7
namespace ThreePoint

section Sym

end Sym

/-! # The `n = 7` typed instance: two poles (indices `0, 1`) and five ring points (`2..6`) -/

section Typed7

end Typed7

end ThreePoint
end ThomsonN7

end Asm_Typed7

section Asm_T4
namespace ThomsonN7
namespace M6

/-! ### Integer interval arithmetic (exact, no rounding) -/

/-! ### Homogeneous Gram determinants and their interval enclosures -/

/-! ### Boxes, bisection and the two refutation checkers -/

end M6
end ThomsonN7

open scoped InnerProductSpace

namespace ThomsonN7
namespace T4

open M6

/-! ### Combinatorics of the ring: a 2-colouring of `K₅` without monochromatic triangle is a pentagon -/

/-! ### The ring colouring of a configuration -/

/-! ### The relabelling of the bipyramid -/

/-! ### Nominal Gram entries of the relabelled bipyramid -/

/-! ### Ring rigidity -/

end T4
end ThomsonN7

end Asm_T4

section Asm_Glue1
/-!
# Glue for the near-antipodal case (Case 2)

Abstract, numerics-independent assembly:

* `Glue.exists_minpair_perm`: every 7-configuration is a relabelling of one whose pair `(0,1)` has the
  smallest inner product;
* `Glue.RootedClaim`, `Glue.case2_of_rooted`, `Glue.seven_of_rooted`: the rooted claim implies both
  Challenge statements (through `Case1.seven_of_case2`);
* `Glue.rooted_of_cap_slabs`: a cap certificate plus finitely many slab certificates give the rooted
  claim;
* `Glue.slab_of_typed`, `Glue.cap_of_typed`: a typed pair-minorant bound gives the slab / cap claims
  (with the equality analysis through `M3.contact_rigidity`).
-/

namespace ThomsonN7
namespace Glue

section Rooted

open scoped InnerProductSpace
open Base

end Rooted

section Typed

open scoped InnerProductSpace
open Base

end Typed

end Glue
end ThomsonN7

end Asm_Glue1

section Asm_Glue2
/-!
# Glue for the near-sharp (tube) cap certificate, route S2

A typed pair-minorant bound `e <= sum_{i<j} H_cls(<y_i, y_j>)` which is only *near*-sharp
(`E(P) <= e + delta`) still gives the cap claim, provided

* the pair slacks `phi - H_cls` control the distance to the nodes (`slack <= delta` puts the inner
  product within `tau` of a node of its class);
* the tube rigidity `TubeRigid tau` (closeness of all 21 inner products to the class nodes gives a
  relabelling of the pentagonal bipyramid within `tau` in every Gram entry);
* the local statement `LocalGramA` holds on the window `tau` (Regime B).

The proof is: `E(y) <= E(P)` implies `sum of slacks <= delta`, hence every slack `<= delta`, hence the
tube, hence the window, hence the local statement.
-/

namespace ThomsonN7
namespace Glue

section Tube

open scoped InnerProductSpace
open Base

end Tube

end Glue
end ThomsonN7

end Asm_Glue2

section Asm_Glue2b
namespace ThomsonN7
namespace Glue
section TubeFromT4
open scoped RealInnerProductSpace

end TubeFromT4
end Glue
end ThomsonN7

end Asm_Glue2b

section Asm_Glue3
/-!
# Glue3: the typed three-point bound (`Typed7`) feeds the cap / slab glue (`Glue1`, `Glue2`)

`ThreePoint.typed7_bound` bounds `e` by the typed double sum `∑ i<j, H7 HA HB HC i j ⟪x i, x j⟫`.
Here we identify `H7` with the class selector `Glue.cls3` (poles are the indices `0, 1`) and
restate the bound in exactly the shape needed by `Glue.cap_of_typed`, `Glue.cap_of_typed_tube`
and `Glue.slab_of_typed`.
-/

namespace ThomsonN7
namespace Glue

section Bridge

open scoped InnerProductSpace
open Base

end Bridge

section Assembly

open scoped InnerProductSpace
open Base

end Assembly

end Glue
end ThomsonN7

end Asm_Glue3

section Asm_Glue4
/-!
# Glue4: the final interface (`CapSpec`, `SlabSpec`) and the assembly `seven_of_specs`

The near-sharp cap and the margin slabs are certified by *typed* three-point data
(`Typed7`): PSD blocks `FP FR`, class minorants `HA HB HC`, multipliers `ψBa ψCb`, constants
`cal cbe`, together with one-dimensional facts on the minorants.  `CapSpec a0` (resp.
`SlabSpec lo hi`) is the proposition "such data exist"; every certificate producer has to prove
one of these propositions and nothing else.  `seven_of_specs` is the assembly: a cap spec at
`a 0` and slab specs on `[a k, a (k+1)]` for `k < K`, with `a K ≥ -9/10`, give both Challenge
statements for `N = 7`.

The tube-rigidity hypothesis of the near-sharp cap and the local (Regime B) statement are
discharged here once and for all (`Glue.tubeRigid_of_le`, `Glue.localGramA_of_le`).
-/

namespace ThomsonN7
namespace Glue

section Final

open scoped InnerProductSpace
open Base

end Final

end Glue
end ThomsonN7

end Asm_Glue4

section Asm_EPEnc
/-!  agent9: 40-digit enclosure of the minimal energy `E(P)` (for the near-sharp cap route).  -/

namespace ThomsonN7
namespace Glue
section EPEnc
open Real

end EPEnc
end Glue
end ThomsonN7

end Asm_EPEnc

section Asm_Coerce
/-!
# One-dimensional facts for the typed cap / slab certificates (CoerceCert)

The typed three-point bound uses class minorants `H_cls ≤ phi` of the pair potential
`phi t = (√(2 - 2t))⁻¹`.  For a polynomial `H = Q / Dq` write `y = √(2 - 2t) / 2 ∈ (0, 1]`, so
`t = 1 - 2 y²`, `phi = 1 / (2 y)` and

  `phi t - H t = F(y) / (2 y Dq)`,   `F(y) = Dq - 2 y Q(1 - 2 y²)`,

a *polynomial* in `y` (no square roots, no sign case split).  Hence

* `H ≤ phi` on a `y`-interval is the polynomial inequality `F ≥ 0` (`PlainCert`);
* exact double contact at a rational node `y = p / q` is the factorisation `F = (q y - p)² G`
  (`Contact1`; two nodes: `Contact2`; simple contact at the boundary `y = 1`: `ContactA`), and
  `G ≥ g0 > 0` gives *coercivity*: `phi - H ≤ δ` forces `y` (hence `t`) close to the node.

Positivity of a polynomial on a rational `y`-interval is certified by exact Bernstein pieces
(`BPiece`), checked by list arithmetic in the kernel (no SDP data, no rounding).
-/

namespace ThomsonN7
namespace Glue
namespace Coerce

open CutOneD Base

/-! ## A. Polynomial helpers and Bernstein pieces -/

/-! ## B. The substitution `y = √(2 - 2t) / 2` -/

/-! ## C. Plain certificates: `H ≤ phi` on a `y`-interval -/

/-! ## D. Contact certificates with coercivity -/

/-! ## E. Shapes of the hypotheses `hA hB hC` of `cap_of_typed_tube7` and closeness of the nodes -/

end Coerce
end Glue
end ThomsonN7

end Asm_Coerce

section Asm_Coerce2
/-!
# Relaxed contact certificates (Coerce2)

`Coerce.Contact1` / `Contact2` need an *exact* double root of `F` at a rational node, which integer
SDP data cannot provide.  Here the factorisation is relaxed to

  `s · F = (q y - p)² · G + R`   (resp. `(q1 y - p1)² (q2 y - p2)² · G + R`)

with integers `s > 0`, polynomials `G, R` with `G ≥ g0 > 0` and `R ≥ 0` on `[0, 1]` (both by exact
Bernstein chains).  Then `F ≥ 0` on `[0, 1]` (so `H ≤ phi`), and `F ≤ 2 Dq δ` forces
`g0 (q y - p)² ≤ 2 s Dq δ`, i.e. the same coercivity as in the exact case with `Dq` replaced by
`s Dq`.
-/

namespace ThomsonN7
namespace Glue
namespace Coerce

open CutOneD Base

/-! ## A. One node -/

/-! ## B. Two nodes -/

end Coerce
end Glue
end ThomsonN7

end Asm_Coerce2

section Asm_CertF
/-! # Fast (linear-traversal) checking of sum-of-squares blocks

The blocks `⟨d, l, Δ⟩` of `Cert1` are read by random access (`List.getD`), which costs `O(r³)`
kernel steps per block.  Here the same quadratic form and the same positivity check are
implemented by traversing the coefficient lists once, and proved equivalent to the random-access
versions.  Also: packed integer data (one natural-number literal per array, decoded in the kernel).
-/

namespace ThomsonN7

open Kron Kron.Ex
namespace Cert

open ThreePoint

/-! ## Packed integer data -/

/-! ## The quadratic form of a block, by list traversal -/

/-! ## The positivity check, by list traversal -/

end Cert
end ThomsonN7

end Asm_CertF

section Asm_CertT
namespace ThomsonN7

open Kron Kron.Ex
namespace Cert

open ThreePoint

/-! ## Multiplier atoms of the typed certificates -/

/-! ## Kronecker values of the quadratic form of a block -/

/-! ## Size bounds of packed blocks -/

/-! ### Degrees -/

/-! ## Analytic bounds of typed blocks -/

/-! ## Sums of expressions -/

/-! ## The hybrid check -/

end Cert
end ThomsonN7

namespace ThomsonN7

open Kron Kron.Ex
namespace Cert

/-! # Flat (Nat-only inner loops) evaluation of the quadratic form of a packed block -/

end Cert
end ThomsonN7

namespace ThomsonN7

open Kron Kron.Ex
namespace Cert

open ThreePoint
open scoped RealInnerProductSpace

/-! ## One-variable polynomials, marginals, kernel sums -/

/-! ## The three type slacks, scaled to integer polynomials -/

section RealSide

variable (K : ℕ) (m : ℕ → ℕ) (Lam : ℕ) (blP blR : ℕ → Blk)

end RealSide

/-! ## The certificate -/

namespace TCert

variable (cf : TCert)

/-! ### The real data of a certificate -/

end TCert

end Cert
end ThomsonN7

end Asm_CertT

section Asm_SlabHead
/-!
# One-dimensional facts for the typed slab certificates: `H ≤ φ` on an interval

`φ(t) = (√(2 - 2t))⁻¹`.  For `t < 1` put `y = √((1 - t)/2) > 0`, so that `t = 1 - 2 y²` and
`φ(t) = 1/(2y)`.  A polynomial `H(t) = Q(t)/Lam` satisfies `H ≤ φ` iff `q(y) = Lam - 2 y Q(1 - 2y²) ≥ 0`.

A certificate for `q ≥ 0` on `{ν₂ y² ≤ μ₂}` (i.e. `t ≥ lo`) or `{ν₂ y² ≤ μ₂, μ₁ ≤ ν₁ y²}`
(i.e. `lo ≤ t ≤ hi`) is an exact polynomial identity

  `m · Lam · q(y) = Σ_T mult_T(y) · Σ (weight · square)`

where `mult_T` is a product of a subset of the atoms `y`, `μ₂ - ν₂ y²`, `ν₁ y² - μ₁`, and all
weights are natural numbers.  The identity is checked by kernel evaluation of integer polynomials.
-/

namespace ThomsonN7
namespace SlabOneD

/-! ## Fast check by evaluation at a large integer point (Kronecker substitution)

If an integer polynomial `R` satisfies `R(X) = 0` and all its coefficients have absolute value
`< X`, then `R = 0`.  The coefficient bound is obtained from `ℓ¹`-norm majorants along the same
expression tree as the identity, so the kernel only evaluates a few hundred big-integer operations
instead of expanding all polynomial products. -/

end SlabOneD
end ThomsonN7

end Asm_SlabHead

section Asm_Bridge
/-!
# Bridge: the certificate checker `Cert.TCert.sound_lo` feeds `Glue.SlabSpec` / `Glue.CapSpec`

`TCert.sound_lo` bounds `ef` by the typed double sum `∑ i<j, H7 HAf HBf HCf i j ⟪x i, x j⟫`.
Here we restate it with the class selector `Glue.cls3` (via `Glue3.sum_H7_eq_sum_cls3`) and, for a
certificate whose four boolean checks hold, produce the final interface of `Glue4`.  The remaining
inputs are the one-dimensional facts about the minorants (`HAf ≤ phi`, ...) and the numerical
comparison of `ef` with the energy `E(P)`.
-/

namespace ThomsonN7
namespace Glue

section Bridge

open scoped InnerProductSpace
open Base

end Bridge

end Glue
end ThomsonN7

end Asm_Bridge

section Asm_Bridge1D
/-!
# Bridge1D: agent2's one-dimensional slab facts (`SlabOneD`) feed `Bridge`

`SlabOneD.peval Q t / Lam` is the polynomial `polyR Lam Q t` of `CertT`; a generated slab
`SlabOneD.Slab_x.HA_le_phi` therefore gives `HAf ≤ phi` on the slab of a certificate whose
`HA`, `Lam` are the data of `Slab_x.certHA`.
-/

namespace ThomsonN7
namespace Glue

section Bridge1D

open scoped InnerProductSpace
open Base

end Bridge1D

end Glue
end ThomsonN7

end Asm_Bridge1D

section Asm_Bridge2
/-!
# Bridge2: near-sharp cap specification from a certificate and its contact factorisations

`Bridge.capSpec_of_tcert` asks for coercive one-dimensional facts about the three minorants
`HAf, HBf, HCf` of a cap certificate.  `Coerce` produces exactly these facts from an exact
factorisation of `F = Dq - 2 y Q(1 - 2 y²)` at rational `y`-nodes (`ContactA`, `Contact1`,
`Contact2`).  Here the two are glued: the contact data are attached to a certificate `cf` by the
equalities `c.Q = cf.HX`, `c.Dq = cf.Lam`.
-/

namespace ThomsonN7
namespace Glue

section Bridge2

open scoped InnerProductSpace
open Base

end Bridge2

end Glue
end ThomsonN7

end Asm_Bridge2

section Asm_Bridge3
/-!
# Bridge3: near-sharp cap specification with relaxed contacts

Same as `Bridge2.capSpec_of_contacts`, but the pole--ring and ring--ring minorants come with the
*relaxed* factorisations `s F = (q y - p)² G + R` (`Coerce.Contact1R`, `Coerce.Contact2R`), which
integer SDP data can satisfy; the pole--pole minorant keeps the exact simple contact at `y = 1`.
-/

namespace ThomsonN7
namespace Glue

section Bridge3

open scoped InnerProductSpace
open Base

end Bridge3

end Glue
end ThomsonN7

end Asm_Bridge3

section Asm_cap_tc
namespace ThomsonN7
open Kron Kron.Ex
namespace Cert
open ThreePoint

end Cert
end ThomsonN7

end Asm_cap_tc

section Asm_cap_ct
namespace ThomsonN7
namespace Final

end Final
end ThomsonN7

end Asm_cap_ct

section Asm_cap_capspec
namespace ThomsonN7
namespace Final

end Final
end ThomsonN7

end Asm_cap_capspec

section Asm_s99_98_tc
namespace ThomsonN7
open Kron Kron.Ex
namespace Cert
open ThreePoint

end Cert
end ThomsonN7

end Asm_s99_98_tc

section Asm_s99_98_1d
namespace ThomsonN7
namespace SlabOneD

namespace Slab_s99_98

end Slab_s99_98

end SlabOneD
end ThomsonN7

end Asm_s99_98_1d

section Asm_s99_98_spec
namespace ThomsonN7
namespace Final

end Final
end ThomsonN7

end Asm_s99_98_spec

section Asm_s98_96_tc
namespace ThomsonN7
open Kron Kron.Ex
namespace Cert
open ThreePoint

end Cert
end ThomsonN7

end Asm_s98_96_tc

section Asm_s98_96_1d
namespace ThomsonN7
namespace SlabOneD

namespace Slab_s98_96

end Slab_s98_96

end SlabOneD
end ThomsonN7

end Asm_s98_96_1d

section Asm_s98_96_spec
namespace ThomsonN7
namespace Final

end Final
end ThomsonN7

end Asm_s98_96_spec

section Asm_s96_94_tc
namespace ThomsonN7
open Kron Kron.Ex
namespace Cert
open ThreePoint

end Cert
end ThomsonN7

end Asm_s96_94_tc

section Asm_s96_94_1d
namespace ThomsonN7
namespace SlabOneD

namespace Slab_s96_94

end Slab_s96_94

end SlabOneD
end ThomsonN7

end Asm_s96_94_1d

section Asm_s96_94_spec
namespace ThomsonN7
namespace Final

end Final
end ThomsonN7

end Asm_s96_94_spec

section Asm_s94_93_tc
namespace ThomsonN7
open Kron Kron.Ex
namespace Cert
open ThreePoint

def tc_s94_93_FP0 : Blk := mkBlk 6 36 36 80
  0xed41dd66fd9ec02042c22ce3aafc447c5745b57c7f90cda43f4f82
  0x8040000008000000008000000008000000008000000008000000007fde306058010000008000000008000000008000000008000000008000391858001649ff8080000008000000008000000008000000007f06165467fcaa624280138c7ba804000000800000000800000000838469ba182076ec557d3dc82cb7e167b76b88000000080000000077f5492cf7d029f90e7df93f73181b387ede807141a02808000000
  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

def tc_s94_93_FP1 : Blk := mkBlk 5 36 36 84
  0xe49799c6ef3c7174a2d25c5f879ab95a4f93b65fb2ceb
  0x80080000080000000080000000080000000080000000080393936980400000080000000080000000080000000087f84b25b8a590408084000000080000000080000000074c6e0d9c754bc7b267fb3a67c08800000008000000007fd663d7d7ef033b297cc995b427eb1a784a880000000
  0x8cc27958340af995ecada800010751743bc148bb3980000d2ca30f10cc8198280000442bbf773b6ef9827ffff2b9101a258c17fe8800010751743bc148bb398cc2aacfd749f1b12643980001033490c9fe29da227ffffe5dfdf79e7bbb84a800001ab9803744a85a8080000d2ca30f10cc8198280001033490c9fe29da228cc288d12c5de7d99f9b47ffff9b6044df666a69747ffff3de861f9b478760880000442bbf773b6ef9827ffffe5dfdf79e7bbb84a7ffff9b6044df666a69748cc27e9da22e3e5b4542480000a1ec0c55706e0fd87ffff2b9101a258c17fe8800001ab9803744a85a807ffff3de861f9b478760880000a1ec0c55706e0fd88cc27fe889665fe65ec18

def tc_s94_93_FP2 : Blk := mkBlk 4 36 32 80
  0xaa5012fc6a62fa8243dc69b587fbe28df135
  0x8100000080000000800000008000000086af4646840000008000000080000000724d5163788195ac8100000080000000863feb28602c037e7504ee0cc0000000
  0xe196ee0809fc2827dcdd7fffd7dae6d8c13bb0847ffffa184f47ea045f9880004e35e78e619094f87fffd7dae6d8c13bb084e196f3174501f1e901047fffe04dd6dec7514f987fffe2e46e2a8f7275f07ffffa184f47ea045f987fffe04dd6dec7514f98e196c109ffeeb9f1f008800047b50394db67202880004e35e78e619094f87fffe2e46e2a8f7275f0800047b50394db672028e196e6a373ed665d8e98

def tc_s94_93_FP3 : Blk := mkBlk 3 36 32 80
  0xea2cb4bc8bd2da8659bb72a0e16
  0x820000008000000080000000bf8ae8e08800000080000000822ab190712a063aa0000000
  0xd6cca8c07cf4f9080f287ffff7b8e1814553a0507ffffe2d30fdd828e6287ffff7b8e1814553a050d6cd469e25295139aac880000d43692d833123987ffffe2d30fdd828e62880000d43692d83312398d6cd562034f24f8fa7e8

def tc_s94_93_FP4 : Blk := mkBlk 2 36 28 80
  0xd95711b17d684641f9
  0x880000080000007dcf2088400000
  0xcf227bb58780ccb368c07fffff807ba1b59524507fffff807ba1b5952450cf227b29c461477dbe60

def tc_s94_93_FP5 : Blk := mkBlk 1 36 24 80
  0xcf09b4a6d
  0xc00000
  0xcf09b4a6d1d2d5462000

def tc_s94_93_FR0 : Blk := mkBlk 6 36 36 80
  0xd601749d7b9e95213fdefadcdbca58a5df2ca79c9346cb46d05a93
  0x800800000800000000800000000800000000800000000800000000800b1eed38010000008000000008000000008000000008000000007ff1eb10280035e08c8020000008000000008000000008000000007d5a43ca77de36290d804a2186682000000080000000080000000077d5bd37f79c2ef61e81d0bc1ae85d58d2cb82000000080000000080d5d37a980695214f814c4d9f17e057380284e45ef3e808000000
  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

def tc_s94_93_FR1 : Blk := mkBlk 5 36 32 80
  0xc740a3415eca51034db8754cadfe97b15db1d4b92fb53
  0x808000008000000080000000800000008000000081e6f1ec82000000800000008000000080000000c82ec4a6f1551d88c00000008000000080000000467ec48e5e596d15b07091e3c0000000800000007d6fa354735123dd6346d8246d28c262c0000000
  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

def tc_s94_93_FR2 : Blk := mkBlk 4 36 32 80
  0xf67008fb6a432b33e3ad495ef0fa153f565a
  0x8080000080000000800000008000000086d0da698400000080000000800000003cee78d759e8a146840000008000000089c8ff35619200cb7696627fc0000000
  0xd87c2d525c838a255d947fffaf248e1df091093c80000e30ca600516bb3a7fffd3fdef7dbb1f67607fffaf248e1df091093cd87c478b961280dbed2a7ffff60ebc8f8dc7fdde7fffd8d6b2f2e2a052a880000e30ca600516bb3a7ffff60ebc8f8dc7fdded87c712f10629ee7d0c68000287ff49b9a27e3b07fffd3fdef7dbb1f67607fffd8d6b2f2e2a052a88000287ff49b9a27e3b0d87c8917e2bd6d84d6e0

def tc_s94_93_FR3 : Blk := mkBlk 3 36 32 80
  0xc8e319620ab5548d55dc9672a86
  0x820000008000000080000000b5c76d0788000000800000008c0d646b79939b1790000000
  0xd01c337b6789853ef6e580001a8cc8f652c5742a7fffe07319e7a05b5b2880001a8cc8f652c5742ad01c7b31d8153eeec6e28000160dd6d3b9d6c6f87fffe07319e7a05b5b288000160dd6d3b9d6c6f8d01c8db2b959cff60d28

def tc_s94_93_FR4 : Blk := mkBlk 2 36 28 80
  0xc7307aeefd234bc120
  0x880000080000007ec023b8400000
  0xcf1eb21a596a6f49628080000043bddce2191d5880000043bddce2191d58cf1eb2448956b92bbfb8

def tc_s94_93_FR5 : Blk := mkBlk 1 36 24 80
  0xcea27135b
  0xc00000
  0xcea27135b6575f4b3b08

def tc_s94_93_SA0 : TBlk :=
  ⟨[], [(0, 0, 0), (0, 0, 1), (0, 1, 0), (1, 0, 0), (0, 0, 2), (0, 1, 1), (0, 2, 0), (1, 0, 1), (1, 1, 0), (2, 0, 0), (0, 0, 3), (0, 1, 2), (0, 2, 1), (0, 3, 0), (1, 0, 2), (1, 1, 1), (1, 2, 0), (2, 0, 1), (2, 1, 0), (3, 0, 0), (0, 0, 4), (0, 1, 3), (0, 2, 2), (0, 3, 1), (0, 4, 0), (1, 0, 3), (1, 1, 2), (1, 2, 1), (1, 3, 0), (2, 0, 2), (2, 1, 1), (2, 2, 0), (3, 0, 1), (3, 1, 0), (4, 0, 0), (0, 0, 5), (0, 1, 4), (0, 2, 3), (0, 3, 2), (0, 4, 1), (0, 5, 0), (1, 0, 4), (1, 1, 3), (1, 2, 2), (1, 3, 1), (1, 4, 0), (2, 0, 3), (2, 1, 2), (2, 2, 1), (2, 3, 0), (3, 0, 2), (3, 1, 1), (3, 2, 0), (4, 0, 1), (4, 1, 0), (5, 0, 0)], 56, 52, 36, 96,
  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,
  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def tc_s94_93_SA1 : TBlk :=
  ⟨[10, 4], [(0, 0, 0), (0, 0, 1), (0, 1, 0), (1, 0, 0), (0, 0, 2), (0, 1, 1), (0, 2, 0), (1, 0, 1), (1, 1, 0), (2, 0, 0), (0, 0, 3), (0, 1, 2), (0, 2, 1), (0, 3, 0), (1, 0, 2), (1, 1, 1), (1, 2, 0), (2, 0, 1), (2, 1, 0), (3, 0, 0), (0, 0, 4), (0, 1, 3), (0, 2, 2), (0, 3, 1), (0, 4, 0), (1, 0, 3), (1, 1, 2), (1, 2, 1), (1, 3, 0), (2, 0, 2), (2, 1, 1), (2, 2, 0), (3, 0, 1), (3, 1, 0), (4, 0, 0)], 35, 48, 36, 92,
  0x873221b193888d56d023437485de7593d0608945587ec380870a6d51d5788b9f8c78f76c8ba7331cf04486656248b0848ac9afdc967c87b16053ced887818b85a45883f7f412be4484a48954ba7884c35e61e40c8d163f09637c8a87c77cdff48f2e90a775b08f2e930de2a8849b7553f90c86cf2377260084a2550860dc847b850a846c86a7b3840da886c5d24e0360849d8e89b8d8841ed25045708590500239348591a73afa2885c1cc79256487a39c5b361885c28cd62de884af185db7d885c4fb91fe9085c76023db9c83eca400d090,
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def tc_s94_93_SA2 : TBlk :=
  ⟨[11, 6], [(0, 0, 0), (0, 0, 1), (0, 1, 0), (1, 0, 0), (0, 0, 2), (0, 1, 1), (0, 2, 0), (1, 0, 1), (1, 1, 0), (2, 0, 0), (0, 0, 3), (0, 1, 2), (0, 2, 1), (0, 3, 0), (1, 0, 2), (1, 1, 1), (1, 2, 0), (2, 0, 1), (2, 1, 0), (3, 0, 0), (0, 0, 4), (0, 1, 3), (0, 2, 2), (0, 3, 1), (0, 4, 0), (1, 0, 3), (1, 1, 2), (1, 2, 1), (1, 3, 0), (2, 0, 2), (2, 1, 1), (2, 2, 0), (3, 0, 1), (3, 1, 0), (4, 0, 0)], 35, 48, 36, 92,
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def tc_s94_93_SA3 : TBlk :=
  ⟨[12, 8], [(0, 0, 0), (0, 0, 1), (0, 1, 0), (1, 0, 0), (0, 0, 2), (0, 1, 1), (0, 2, 0), (1, 0, 1), (1, 1, 0), (2, 0, 0), (0, 0, 3), (0, 1, 2), (0, 2, 1), (0, 3, 0), (1, 0, 2), (1, 1, 1), (1, 2, 0), (2, 0, 1), (2, 1, 0), (3, 0, 0), (0, 0, 4), (0, 1, 3), (0, 2, 2), (0, 3, 1), (0, 4, 0), (1, 0, 3), (1, 1, 2), (1, 2, 1), (1, 3, 0), (2, 0, 2), (2, 1, 1), (2, 2, 0), (3, 0, 1), (3, 1, 0), (4, 0, 0)], 35, 48, 36, 92,
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def tc_s94_93_SA4 : TBlk :=
  ⟨[3], [(0, 0, 0), (0, 0, 1), (0, 1, 0), (1, 0, 0), (0, 0, 2), (0, 1, 1), (0, 2, 0), (1, 0, 1), (1, 1, 0), (2, 0, 0), (0, 0, 3), (0, 1, 2), (0, 2, 1), (0, 3, 0), (1, 0, 2), (1, 1, 1), (1, 2, 0), (2, 0, 1), (2, 1, 0), (3, 0, 0)], 20, 52, 36, 96,
  0xab456e40a78e0a80a0e45fc2a89c61979e887f8915aa2d9936b09b13770e418a892e75784d03389adffb28ebbb8911f781063e58934884d3b1568a27d4258cb6309fa0dc6e98fe8abdc43a3f1a38ac9f8352844089069af7b80c389901c6f240028931d8adbb7070a6de2ab0a1ee88ee88e9fa8f788f1b58469c9a0a3c623fd422b0,
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def tc_s94_93_SA5 : TBlk :=
  ⟨[13, 10], [(0, 0, 0), (0, 0, 1), (0, 1, 0), (1, 0, 0), (0, 0, 2), (0, 1, 1), (0, 2, 0), (1, 0, 1), (1, 1, 0), (2, 0, 0), (0, 0, 3), (0, 1, 2), (0, 2, 1), (0, 3, 0), (1, 0, 2), (1, 1, 1), (1, 2, 0), (2, 0, 1), (2, 1, 0), (3, 0, 0), (0, 0, 4), (0, 1, 3), (0, 2, 2), (0, 3, 1), (0, 4, 0), (1, 0, 3), (1, 1, 2), (1, 2, 1), (1, 3, 0), (2, 0, 2), (2, 1, 1), (2, 2, 0), (3, 0, 1), (3, 1, 0), (4, 0, 0)], 35, 40, 36, 100,
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def tc_s94_93_SB0 : TBlk :=
  ⟨[], [(0, 0, 0), (0, 0, 1), (0, 1, 0), (1, 0, 0), (0, 0, 2), (0, 1, 1), (0, 2, 0), (1, 0, 1), (1, 1, 0), (2, 0, 0), (0, 0, 3), (0, 1, 2), (0, 2, 1), (0, 3, 0), (1, 0, 2), (1, 1, 1), (1, 2, 0), (2, 0, 1), (2, 1, 0), (3, 0, 0), (0, 0, 4), (0, 1, 3), (0, 2, 2), (0, 3, 1), (0, 4, 0), (1, 0, 3), (1, 1, 2), (1, 2, 1), (1, 3, 0), (2, 0, 2), (2, 1, 1), (2, 2, 0), (3, 0, 1), (3, 1, 0), (4, 0, 0), (0, 0, 5), (0, 1, 4), (0, 2, 3), (0, 3, 2), (0, 4, 1), (0, 5, 0), (1, 0, 4), (1, 1, 3), (1, 2, 2), (1, 3, 1), (1, 4, 0), (2, 0, 3), (2, 1, 2), (2, 2, 1), (2, 3, 0), (3, 0, 2), (3, 1, 1), (3, 2, 0), (4, 0, 1), (4, 1, 0), (5, 0, 0)], 56, 44, 36, 88,
  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,
  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def tc_s94_93_SB1 : TBlk :=
  ⟨[10, 4], [(0, 0, 0), (0, 0, 1), (0, 1, 0), (1, 0, 0), (0, 0, 2), (0, 1, 1), (0, 2, 0), (1, 0, 1), (1, 1, 0), (2, 0, 0), (0, 0, 3), (0, 1, 2), (0, 2, 1), (0, 3, 0), (1, 0, 2), (1, 1, 1), (1, 2, 0), (2, 0, 1), (2, 1, 0), (3, 0, 0), (0, 0, 4), (0, 1, 3), (0, 2, 2), (0, 3, 1), (0, 4, 0), (1, 0, 3), (1, 1, 2), (1, 2, 1), (1, 3, 0), (2, 0, 2), (2, 1, 1), (2, 2, 0), (3, 0, 1), (3, 1, 0), (4, 0, 0)], 35, 40, 32, 84,
  0x8c003a1100953edc6e8c8f125172788edb0b3cd48aa4e43b0888851a16c49d8fd92e688b799bd3c88aea381ab09f0b4e3d388b24417acc9c4f3402588f8db639d88de63e4a8889fb322d8c9e3594671892f3124ea8964216a66893189002348f7f03204092988d1438884de2339495adc0d18093a53ae494941a771a888e3f52d5a89869f7957c933b66f544971042cea89647e37a588b8b8d92748fa3fd825c891542ebc08b273c851c949d36f10c,
  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def tc_s94_93_SB2 : TBlk :=
  ⟨[11, 6], [(0, 0, 0), (0, 0, 1), (0, 1, 0), (1, 0, 0), (0, 0, 2), (0, 1, 1), (0, 2, 0), (1, 0, 1), (1, 1, 0), (2, 0, 0), (0, 0, 3), (0, 1, 2), (0, 2, 1), (0, 3, 0), (1, 0, 2), (1, 1, 1), (1, 2, 0), (2, 0, 1), (2, 1, 0), (3, 0, 0), (0, 0, 4), (0, 1, 3), (0, 2, 2), (0, 3, 1), (0, 4, 0), (1, 0, 3), (1, 1, 2), (1, 2, 1), (1, 3, 0), (2, 0, 2), (2, 1, 1), (2, 2, 0), (3, 0, 1), (3, 1, 0), (4, 0, 0)], 35, 40, 32, 84,
  0x891dc515448d39a9875c8bd58f2f149186e42128892743d0d088b743eae88932a8d7d08c5f2a8e08892382252c9fbf6500d0901941893089a418cd80917a0ba7708e31aab63c89fb331d7099120fc39091e97e6f1c90504bac3894f48caa6c8faef848a090ea32d308896ec00ca09dc4b4b54495af40e470941a73c38c947b32331c96fc104f148d258b6ca0999393ed9095b796bb288b8b8ca20488f2e1ad388fe01446d88b273ceddc949d36993c,
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def tc_s94_93_SB3 : TBlk :=
  ⟨[12, 8], [(0, 0, 0), (0, 0, 1), (0, 1, 0), (1, 0, 0), (0, 0, 2), (0, 1, 1), (0, 2, 0), (1, 0, 1), (1, 1, 0), (2, 0, 0), (0, 0, 3), (0, 1, 2), (0, 2, 1), (0, 3, 0), (1, 0, 2), (1, 1, 1), (1, 2, 0), (2, 0, 1), (2, 1, 0), (3, 0, 0), (0, 0, 4), (0, 1, 3), (0, 2, 2), (0, 3, 1), (0, 4, 0), (1, 0, 3), (1, 1, 2), (1, 2, 1), (1, 3, 0), (2, 0, 2), (2, 1, 1), (2, 2, 0), (3, 0, 1), (3, 1, 0), (4, 0, 0)], 35, 40, 36, 84,
  0x89ae4c993c8d64f666e894c325c2c08d4d07071895ecd068309a8b8d96a48c7285e27c99c6c97e089ea368bc648e375b48dc8e60b560f09183f5b46c960ea9571c8f27e394a0881a3089c09fc3d1c9e89fd658cbd894e2bb1c1c8989f0ebd491164da63c8a271b66548987d8d3309f3be78ab88c5d9dd2208b33fbbefc9d57af1fe88d159d02c099953bea688806aa93589ff353ad5488c2fe78449d0c51e1f89b3bdf94588f56dd5bbc8947dd3314,
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end Cert
end ThomsonN7

end Asm_s94_93_tc

section Asm_s94_93_1d
namespace ThomsonN7
namespace SlabOneD

namespace Slab_s94_93

end Slab_s94_93

end SlabOneD
end ThomsonN7

end Asm_s94_93_1d

section Asm_s94_93_spec
namespace ThomsonN7
namespace Final

end Final
end ThomsonN7

end Asm_s94_93_spec

section Asm_s93_90_tc
namespace ThomsonN7
open Kron Kron.Ex
namespace Cert
open ThreePoint

end Cert
end ThomsonN7

end Asm_s93_90_tc

section Asm_s93_90_1d
namespace ThomsonN7
namespace SlabOneD

namespace Slab_s93_90

end Slab_s93_90

end SlabOneD
end ThomsonN7

end Asm_s93_90_1d

section Asm_s93_90_spec
namespace ThomsonN7
namespace Final

end Final
end ThomsonN7

end Asm_s93_90_spec

section Asm_Final
namespace ThomsonN7
namespace Final

end Final
end ThomsonN7

end Asm_Final

namespace ThomsonN7

end ThomsonN7