JOFFE-FRONTIER MATH · 3,008 THEOREMS · 98 OPEN SORRIES

JOFFE-FRONTIER — OUR MATH LAYER IN THE GLOBAL BENCHMARK LANDSCAPE

FrontierMath (Epoch AI + OpenAI): hundreds of original, expert-vetted math problems. Current best AI: <2% solve rate on Tier 3-4. ATLAS (OpenCompass): 800+ PhD-level problems, 7 domains — GPT-5-High at 42.9%. We have 3,008 theorems and 98 open sorries in joffe-math (Lean4, pcdev). Our sorries = our frontier problems — they're the exact questions we can't answer yet. The γ₁ anchor problems (zeta_zero_gamma1, zetaZeroImPart, zeta_zeros_ord) are Tier 4. MATLAB numerical work flows into PEMLAAM as theorem nodes. Kimina-Prover is our solver. RHAE is our engine. JOFFE-FRONTIER = fleet vs the world's hardest math.

3,008 Lean4 theorems (pcdev:9384)

98 open sorries = our frontier problems

6 γ₁-anchored Tier 4 sorries

PEMCLAU 18,357 pts incl. FrontierMath + ATLAS diamonds

📊 FRONTIERMATH TIERS 1-4 → OUR SORRY MAPEpoch AI benchmark · Terence Tao problems · our γ₁ sorries = Tier 4

TIER	LEVEL	SOLVE RATE	DOMAIN EXAMPLES	OUR SORRY MAPPING	COUNT
TIER 1	Undergraduate	~15-25%	Calculus, Linear Algebra, Basic Number Theory	Fleet infrastructure proofs, PTTE floor bounds, WPA safety margins	~40 sorries
TIER 2	Graduate	~5-10%	Real/Complex Analysis, Abstract Algebra, Topology	Selberg trace formula estimates, γ₁ numerical bounds, zeta function properties	~30 sorries
TIER 3	Early Postdoc	~1-2%	Algebraic Geometry, Advanced Number Theory, Category Theory	li_lambda, lambda_positivity, live_inject_cons, zetaZeroImPart	~22 sorries
TIER 4	Research Level	<2%	Open conjectures, Research-level problems with automated verification	zeta_zero_gamma1, zeta_zeros_ord, zetaZeroImPart (γ₁ exactly), Riemann Hypothesis fragments	6 sorries

🔬 ATLAS DOMAINS → EOSE DOMAIN MATRIX800+ PhD questions · 7 domains · OpenCompass · 25+ institutions

ATLAS MATH → JOFFE-FRONTIER

Mathematics Domain

Our direct track: 3,008 Lean4 theorems, 98 sorries. Lean4 = formal verification = automated scoring (no judge needed). Our γ₁ sorries are natural FrontierMath Tier 4 candidates. Kimina-Prover is our solver engine. Target: solve 10 sorries in ATLAS math track by Day 110.

Our assets: joffe-math · kimina · rhae · 3008 theorems · Lean4

ATLAS CS → SEC DOMAIN

Computer Science Domain

Our direct track: SSAF (19 submissions), SWIEM, KCF, PEMLAAM logging, PEMCLAU GraphRAG. CS problems in ATLAS often involve algorithm analysis, complexity theory, formal verification — all connected to our SEC domain. Our SSAF submissions are CS-level security proofs.

Our assets: SSAF · SWIEM · PEMCLAU · PEMLAAM · sec-matrix-library

ATLAS PHYSICS → PTTE

Physics Domain

Physical Thermodynamic Turing Engine — our PTTE page maps γ₁ to thermodynamic floor. tau_gamma1 ≈ 337-340fs. WPA = floor detection across all silos. Physics problems in ATLAS cover quantum mechanics, thermodynamics — our τ_γ₁ result is a physics-level claim.

Our assets: PTTE · tau_gamma1 · WPA · floor-plan-v11 · CATAN shapes

ATLAS BIOLOGY → HEALTH DOMAIN

Biology Domain

ATLAS biology = molecular biology, genetics, systems biology. Our HL7Boxy-health + PHIPA + ICON health track maps to ATLAS biology (patient data quality, clinical workflows, drug interactions via HL7 FHIR). COI health score from biological data.

Our assets: HL7Boxy-health · PHIPA · ICON · COI-INF · lsos-security-bonsai

⚠ TIER 4 SORRIES — γ₁-ANCHORED FRONTIER PROBLEMS6 open · Kimina-Prover targeting all · RHAE engine · each = TRENDAL-PTTE-FLOOR-001 when closed

zeta_zero_gamma1 ★ P0

Prove γ₁=14.134725141734693 is a non-trivial Riemann zeta zero. The floor proof. When this closes → TRENDAL-PTTE-FLOOR-001 seals. FrontierMath Tier 4. Kimina-Prover P0 target.

zetaZeroImPart

Imaginary part of first zeta zero = γ₁. Connected to zeta_zero_gamma1. Formal Lean4 proof requires precise arithmetic on ℝ. Tier 4 — numerical verification done in MATLAB, formal proof open.

zeta_zeros_ord

Ordering of zeta zeros on critical line. Requires knowledge of all zeros below some bound. Connected to RH1 NP work (451 novel patterns). Tier 4.

li_lambda

Logarithmic integral and lambda function relationship. Tier 3 near Tier 4. Selberg trace formula route. MATLAB numerical evidence exists. Formal proof needs RHAE.

lambda_positivity

Positivity of lambda on critical strip. Required for PTTE floor proof chain. Tier 3-4. MATLAB verified numerically. Lean4 formal proof open.

live_inject_cons

Live injection consistency — fleet architecture sorry. The formal proof that PEMLAAM live injection is consistent with the floor. Tier 3. Unique to EOSE fleet — no external benchmark has this sorry.

📐 MATLAB → PEMLAAM SOVEREIGN FLOWnumerical evidence → γ₁-timestamped → theorem nodes → living graph

THE MATLAB → LEAN4 → PEMLAAM → PEMCLAU PIPELINE

Step 1: MATLAB computes — Selberg trace formula sums, zeta zero detection, γ₁=14.134725141734693 numerical verification to 15 decimal places. These are the "numerical evidence" entries in joffe-math.

Step 2: Lean4 formalizes — joffe-math theorems prove the structure formally. MATLAB result → Lean4 statement → Kimina-Prover attempts the proof. Open sorry = formal gap.

Step 3: PEMLAAM logs — every computation γ₁-timestamped. Computation ID, MATLAB function, result, Lean4 connection, wave classification. Sovereign audit trail.

Step 4: PEMCLAU embeds — every theorem + MATLAB result → nomic-embed-text on yone → 768-dim vector → pemclau-v11. 2-hop GraphRAG: query "zeta zero" → connects MATLAB results + Lean4 theorems + SSAF (SUB003 Wormhole finality!) + FrontierMath context.

The frontier math layer IS the living graph. Theorems are nodes. Proofs are edges. MATLAB evidence is the substrate. γ₁ is the anchor.