EOSE FLEET · DAY 84 · 2026-04-26 · LEAN4 PROOF PROGRAMME
PERIODIC TABLE OF MATHEMATICS · V11
285 LIVE LEAN4 SORRIES · 420 MERAROON CELLS · 613 OBLIGATION PROGRAMME
γ₁ = 14.134725141734693 · the floor · element 1 · Day 84
§0 — THREE SCALES · what the numbers mean
285
LIVE LEAN4 SORRY COUNT
Actual code in MeekProofs/*.lean files. Each sorry = a real proof obligation not yet discharged. This number moves as we work — closing sorries is the daily mission. When a sorry closes, an element crystallises. Noble gas = zero sorry = proven.
420
MERAROON TENSOR · 6×6×14
504 total cells in the meraroon tensor (6×6×14). 84 are articulated (one per day of work). 420 remain as structural sorry obligations. 420 = LCM(1..7) = number-theoretically calibrated. This is the structural sorry map — not individual proofs but the architecture of what must be proven.
613
MITZVOT-SORRY DOCTRINE · TRB-MITZVOT-SORRY-001
Every claimable mathematical thing is named. 613 = the classical count of obligations (mitzvot). Each is either discharged (noble gas ✅) or visible (sorry, gap cell 🔴). No invisible obligations. If we claim it, we name it. If we name it, we either prove it or mark it. The doctrine of honest accounting.
PERIOD 1 — THE FLOOR · noble gases · zero sorry · proven · γ₁ anchor
1
✅ NOBLE
γ₁
GAMMA-ONE
14.134725141734693 · proven floor of ζ(s) · the anchor
noble gas · zero sorry
2
✅ NOBLE
Z₀
ZERO
Zero non-trivial zeros off critical line · proven by Euler product
noble gas · zero sorry
PERIOD 2 — ACTIVE FRONTIER · highest sorry density · where the work lives
11
44
AG
ARCGrid
ARC-AGI grid reasoning · 44 sorries · hardest current domain
12
24
WO
WellOrdering
Well-ordering principle · Guillotine method · 24 sorries
13
23
AX
AxiomElim
Axiom elimination chain · 23 sorries
14
15
GD
GapDissect
Gap analysis · dissection method · 15 sorries
15
11
IE
IntervalEng
Interval arithmetic engine · 11 sorries
16
7
CE
ChainEmerg
Chain emergence proofs · 7 sorries
17
5
MH
MeekHistory
Fleet proof history · 5 sorries
PERIOD 3 — DEEP DOMAINS · specialist mathematics · purple tier
21
3
DN
DeepNumberTh
Deep number theory
22
2
DA
DeepAnalysis
Deep analysis
23
2
DG
DeepAlgGeom
Deep algebraic geometry
24
2
DC
DeepCatTh
Deep category theory
25
2
DT
DeepTopology
Deep topology
26
2
DP
DeepPhysics
Deep physics
27
2
DL
DeepLogic
Deep logic
28
2
DK
DeepCrypto
Deep cryptography / ZK proofs
29
DAr
DeepArithmetic
30
DCh
DeepChains
31
DCo
DeepComputability
32
DDe
DeepDiffEq
33
DGa
DeepGameTheory
34
DGr
DeepGraph
35
DGG
DeepGroupTheory
36
DH
DeepHarmonicAnalysis
PERIOD 4 — GOAT CHAINS · named after mathematical GOATs · gold tier
37
2
GR
GOATRiemann
Riemann's programme · γ₁ chains
38
1
GG
GOATGauss
Gauss number theory chains
39
1
GL
GOATGodel
Gödel incompleteness chains
40
1
GE
GOATEuler
Euler product chains
41
1
GN
GOATNoether
Noether symmetry chains
42
1
GK
GOATGrothendieck
Grothendieck algebraic chains
43
1
GD₂
GOATErdos
Erdős combinatorics chains
44
GEu
GOATEuclid
45
GNw
GOATNewton
46
GCh
GOATChains
PERIOD 5 — RH PROGRAMME · Riemann Hypothesis attack vectors · cyan tier
47
4
RS
RHSpine
RH formal spine · core definitions
48
4
DB
DeBranges
De Branges inner product method
49
3
LP
LambdaPos
Lambda positivity · key lemma
50
4
BX
Boss1Xi
Boss 1-Xi · critical attack vector
51
2
GW
GRHWeapon
Generalised RH weapon
52
2
KC
KillChain
RH kill chain coordination
53
1
ZZ
ZetaZeros
Zeta zeros enumerable
54
1
ZD
ZeroDensity
Zero density estimate
55
1
TW
TheWeapon
The weapon — final assault
56
1
TC
TheClose
The close — final lemma
PERIOD 6 — GEAR SYSTEM · sequential proof gears · amber tier
57
4
G5
Gear5
Gear 5 · top speed · 4 sorries remain
58
3
GM
Gear5Meek
Gear 5 meek variant
59
3
DS
DeBrangesStubs
De Branges stubs
60
3
MS
MoonShots
Moonshot proofs · 3 sorries
61
2
SC
ScaffoldClose
Scaffold closures
62
2
G4
Gear4
Gear 4
63
2
LE
LuffyEvolution
Luffy's evolution track
64
2
M₂
Milestone2000
Milestone 2000 proof
65
1
GB
Gear5Bound
66
1
GS
Gear5Snake
67
1
GT
Gear5Titan
68
1
GG₂
Gear5GPU
69
1
G2
Gear2
70
1
G3
Gear3
§GAPS — HILBERT'S DEMAND · what is not yet crystallised
⊘ HILBERT'S GAP CELLS — What Would Fill These?
Each gap cell has a formal Lean4 statement of what would make it non-empty. The sorry is the gap. The proof is the element crystallizing from the void.
⊘ GOLDBACH
theorem goldbach (n : ℕ) (hn : 2 ≤ n) (heven : Even n) :
∃ p q, Nat.Prime p ∧ Nat.Prime q ∧ p + q = n := by sorry
Every even n≥2 is sum of two primes. Verified to 4×10¹⁸. No proof.
SORRY COUNT: 0 — element not yet crystallized
⊘ COLLATZ
theorem collatz_conjecture (n : ℕ) (hn : 0 < n) :
∃ k, collatz_iterate n k = 1 := by sorry
Every positive integer eventually reaches 1. Verified to 2⁶⁸. No proof.
SORRY COUNT: 0 — element not yet crystallized
⊘ P≠NP
theorem p_ne_np :
ComplexityClass.P ≠ ComplexityClass.NP := by sorry
The hardest problem in theoretical computer science. Clay Millennium Problem.
SORRY COUNT: 0 — element not yet crystallized
⊘ HODGE
theorem hodge_conjecture
(X : SmoothProjectiveVariety ℂ) (p : ℕ)
(α : HodgeCycle X p) :
∃ Z : AlgebraicCycle X p,
cohomology_class Z = α := by sorry
Algebraic geometry Clay Millennium Problem.
SORRY COUNT: 0 — element not yet crystallized
⊘ BSD
theorem bsd_conjecture (E : EllipticCurve ℚ) :
E.rank = E.L_function.vanishingOrder := by sorry
Birch and Swinnerton-Dyer. Clay Millennium Problem.
SORRY COUNT: 0 — element not yet crystallized
⊘ YANG-MILLS
theorem yang_mills_mass_gap (G : SimpleLieGroup) :
∃ Δ : ℝ, 0 < Δ ∧ mass_gap G = Δ := by sorry
Quantum Yang-Mills mass gap. Clay Millennium Problem.
SORRY COUNT: 0 — element not yet crystallized
⊘ NAVIER-STOKES
theorem navier_stokes_regularity
(u₀ : SmoothDivFree ℝ³) :
∃ u : SmoothSolution,
u.initialData = u₀ := by sorry
Global smooth solutions to Navier-Stokes. Clay Millennium Problem.
SORRY COUNT: 0 — element not yet crystallized
⊘ TWIN PRIMES
theorem twin_primes_infinite :
∀ N : ℕ, ∃ p : ℕ,
N < p ∧ Nat.Prime p ∧ Nat.Prime (p + 2) := by sorry
Infinitely many twin primes. Zhang 2013: bounded gaps. Full conjecture: open.
SORRY COUNT: 0 — element not yet crystallized