Thomson $N=7$: certificate data for slab 2 ($-\tfrac{49}{50}\le t_{01}\le-\tfrac{24}{25}$), 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

def tc_s98_96_FP0 : Blk := mkBlk 6 36 36 80
  0xb3cf4c430ce13ceccdc79305723d2dcb864fc3fd7b8f4a279f3541
  0x8040000008000000008000000008000000008000000008000000007ffde0a2a801000000800000000800000000800000000800000000804c950507ffa2ed0d8100000008000000008000000008000000007dd03a88e7f92db6e17e7bc65058080000008000000008000000008370d2e7680688673c7b7dcc2677f87bd92288000000080000000088086484480bedf14d86ef4f5f27e240448d7f3dead0b804000000
  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

def tc_s98_96_FP1 : Blk := mkBlk 5 36 36 84
  0xfa80670f3cd6075777ddbef250bb8e819295b7045795e
  0x800800000800000000800000000800000000800000000807069e258080000008000000008000000008000000008613dd58187dd1142f84000000080000000080000000075d627a42763757f227e1dc8cff8800000008000000007f3df5bee7d1d6732b79ca9b70d7de37c1de880000000
  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

def tc_s98_96_FP2 : Blk := mkBlk 4 36 36 80
  0xe349e797fb9e374274a225ebd27d50f13f90
  0x80100000080000000080000000080000000080dd4883b80800000080000000080000000077679da867b4eb4ef98040000008000000007fa3aa1dd7df64ea9d7f97d6659840000000
  0xedaf07d5fb4ec28961c080000f8d72a3ae087e4e7ffff67262b2d6f5cf3880007f6302e3bd8e459880000f8d72a3ae087e4eedadf072e6a94ddbb0f1800023bd7ab0623817d080004b4e8688bf9221887ffff67262b2d6f5cf38800023bd7ab0623817d0edae3999c1a552230e987fffa8c0a5f9767ad15080007f6302e3bd8e459880004b4e8688bf9221887fffa8c0a5f9767ad150edae2b4a8d6e95d868c0

def tc_s98_96_FP3 : Blk := mkBlk 3 36 32 80
  0xa53a16081a2056995ed22154c51
  0x840000008000000080000000c9cba89588000000800000007723ab7074761a55a0000000
  0xe3966860691f444a872a7ffffffe78ab96835e98800014bf67fc20d549787ffffffe78ab96835e98e396b451aeb9d697032f7fffdc456bef813c0f18800014bf67fc20d549787fffdc456bef813c0f18e3969e878476d1cefe60

def tc_s98_96_FP4 : Blk := mkBlk 2 36 28 80
  0xa5b991814f05038157
  0x900000080000007bcf7298400000
  0xda9012b247e1d3d9b0417fffff428d32f4c533487fffff428d32f4c53348da90112483035d5b5770

def tc_s98_96_FP5 : Blk := mkBlk 1 36 24 80
  0xd9675de99
  0xc00000
  0xd9675de99842074826a0

def tc_s98_96_FR0 : Blk := mkBlk 6 36 32 80
  0xdf1a8ab3bb98f2636ca834046e9bc25b2badc0b737613e56ffb68b
  0x80800000800000008000000080000000800000008000000080aa704a81000000800000008000000080000000800000007f59773d806f0597820000008000000080000000800000005b8a8d5b5bf1ca2a80207e1da00000008000000080000000c961b13ac8ff6d138522daff3e18cc4fa0000000800000004c134442481a21f886d72341a58e039dc9a166c884000000
  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

def tc_s98_96_FR1 : Blk := mkBlk 5 36 32 84
  0xf0f59940ba0c0092fdf056398ffc2b803de9dda623d8d
  0x80800000800000008000000080000000800000008492661284000000800000008000000080000000941107e49c97e9b89000000080000000800000001d6986a6393a7c3ba814e37cc00000008000000072d65f1a5d0810964962b9995ff31592c0000000
  0x88e1ff4125fe9651667448000066070d885964cd8a7ffff37c1868e95bf23767ffff811453e95da02b8c800007ee75de9fb27bbd08000066070d885964cd8a88e1fe9696aa12bf091f37ffffcee9466acb62018e7ffff9fbb3e86dd98f3547ffffc98986378a0fe8007ffff37c1868e95bf23767ffffcee9466acb62018e88e20610e493cbd95c223800002021e699b6edf1567ffffacd3d1ce19761cd07ffff811453e95da02b8c7ffff9fbb3e86dd98f354800002021e699b6edf15688e1f10eed9c107403a64800006c1bbb5effd02440800007ee75de9fb27bbd07ffffc98986378a0fe8007ffffacd3d1ce19761cd0800006c1bbb5effd0244088e1f71d0a2d3d0d68928

def tc_s98_96_FR2 : Blk := mkBlk 4 36 32 80
  0xfb6536384b80d82d43f3ecb815ae8902ff3c
  0x80800000800000008000000080000000834c15188200000080000000800000006d8ce7c575abe8e78200000080000000847cdb396d39590578c21feca0000000
  0xdfe0549433e03c37a2528000280e3715804e58b680000cc2c02b1d0a78c07fffddda1ae5e62fa4088000280e3715804e58b6dfe0b953c0a867382d027ffff18ecd45dad86d507fff9ede0b750353541080000cc2c02b1d0a78c07ffff18ecd45dad86d50dfe0159e5ac07e106ba080003a23b63cc0ace4f07fffddda1ae5e62fa4087fff9ede0b750353541080003a23b63cc0ace4f0dfe02ffbfee478c90430

def tc_s98_96_FR3 : Blk := mkBlk 3 36 32 80
  0xbe6766bbaff2401b59bd3687e92
  0x8200000080000000800000008285ca7480800000800000009ca6c0ad7bbdefd490000000
  0xdaef29ceb688552f5b2e7fffed028981b664eca8800012599fd1e50ba4287fffed028981b664eca8daeee48591f3a87b50b07ffff77e67cc9b5e26b0800012599fd1e50ba4287ffff77e67cc9b5e26b0daeee06f8930c7911758

def tc_s98_96_FR4 : Blk := mkBlk 2 36 28 80
  0xaeebdbed3daadaaa35
  0x880000080000007f80dec8400000
  0xd9682a6b8b766376625880000072455c8457f1f880000072455c8457f1f8d9682a87d6e8d695c398

def tc_s98_96_FR5 : Blk := mkBlk 1 36 24 80
  0xd993ed3b1
  0xc00000
  0xd993ed3b2176f6a28240

def tc_s98_96_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_s98_96_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, 44, 36, 88,
  0x970f6cf759daa2aaaad6f7957f422edf7925e09cf3bda94235acbf79dd96cf3dd7a6dd57dfab0a546bdb7be1b28e3d68d00a59dc3bc134a897a764ecb900a8fca964948700a926d961cb241e3f914752b7b79a87947a3924bbc82fae834bbcd0887ada92af021734a9c25e955f3e9321800381d9156fbae2e69a6273c806f9abd0b8357192073f7cd28bc89824852e976947967e5977db598a279845459aa22a0d59e3329a98472523b619134c15ab1b97fdfbb463e9805e621d50b77bb5a766c,
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def tc_s98_96_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, 44, 36, 88,
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def tc_s98_96_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, 44, 36, 88,
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def tc_s98_96_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,
  0x8bf0dd2cb4c3e86505bed16bbc8625ebfe0449687836a374f71e850049ed9c28487f7ae816dc7086c43efc2d2f2854e7928ff90c85877977b50d68848ad57502ee8651b83ec082a8b4cf53289b008b5f3fdc698b28420b7f66ec0885df33749c9be842b4e860a2d68762b491c644e845649650d148845ff1288b0888700f728b2c06,
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def tc_s98_96_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_s98_96_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_s98_96_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,
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def tc_s98_96_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,
  0x97fb81c8349fbfa01b98885ba2cc7c96f4c43e2098bf9bccb889d51284d495a77049cc97fee97f708de69d54cc889fbc3eac8ad72b31a492360b7d70931211202c8cdb06b6488bacc8299c98b6f1a56c94b3f2c7c08e91235d289b058e89009592645e308dc35c809c90622656dc92d19f120c9451d04d3c9c69cf3e5c884e5deeac90a0ffb6c888fb4f9bcc8ab91b7eec89c6e86e788b5d02ff488f3f51832c8c61a368709d9a67758c8d2108508c,
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def tc_s98_96_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,
  0x972161611892d72ae9dc8a210be8a489f272e9208a07ba8134936479216895682810c888625e65bc9a82d48f2c8f08915b1c8a2d4232e89c79341c70881a1f00508a8cec33d48dbd3914e08b8524458c8ed94bd1b48b0a9b183c8faf5441848973e3fb6895e9882f888f416c6998926ae920d88968a1fb9888f548ef9089749e0fd0977a09f9d08e0009e49c8c8fc99bb493ca5dfc3c912d32fb089956f64a4c9f9a90d91c912f266b708a44dd5fd0,
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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

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