Mathematical City · Core Atlas & Entry
The front door. Structure is discovered. Invariance is selected. Everything else is tested.
• The Mathematical City — Atlas Clone: 125 → K → 47 canonical object, Ωc = 47/125, E0 / E1 ceiling. Open Atlas ↗
• Rosetta Torus — Central Plaza: Entry through the torus, canonical formalism, roads = theorem dependencies, bridges = structure-preserving maps.
• E47 in Two Pages: K² · why dim V₂ = 5 · recursive selection · exact claim boundary.
• Foundations: Definitions and ambient types.
• Representation Theory: Decomposition and multiplicities, V₂⊗3 carrier dim 125.
• Spectral Theory: Selectors, null spaces, projectors, K = (C − 6I)(C − 30I)
• START HERE — First Visit: Five-stop route: 125 → K → 47 → certificate → correction.
• City Core — This Website: Sticky Atlas navigation, executable plate playback, laboratories, certificates, and source.
02 · Research · Executable Instruments / Kartekeya
Live surfaces around the object. Only current public routes are promoted.
• E47 Kartekeya — Instrument Portal: Repository-owned instrument router. Native GitHub Pages interface. No external artifact dependency. Open Portal ↗
• Live Work Catalog: 15 published Live Work entries — the executable catalog.
• E47 Applications Index: Most comprehensive public share page alongside Live Work.
• Monorail — 17 Doors: Verified transit, elevated. Reproducibility Monorail for dependency inspection, environment reconstruction, version locking, and certificate renewal.
• Python Subway — Numerical Validation: Subway = logical translation, executable Python and QuTiP validators.
• E47 LOCK — Seed 42 Plate: dim ker 47 of 125, Ωc 0.376, bound 15/17, recorded lock t = 55, residual < 1e−6.
• PIP Kid-Friendly Interactive Explainer · E47 → MANTA: 125 states → exact E47 sector → 125-node morph flight simulation. E0 / E1 / E2
• E47 Flight Deck: Watch what remains. One state, two perspectives. Follow 125 dimensions toward the 47 that survive. Open Flight Deck ↗
03 · Quantum Systems
• Quantum Information: Quantum models, error correction, QEC district.
• Quantum State Subspace Convergence: Analytic lower envelope from q⊥ ≤ 15/17 with Ωc = 47/125, Tr(Pρ) plate.
• Quantum Clock: Prime 47-cycle marks round the rim, one run population in E47. Open Quantum Clock ↗
• Q5 — Typed Neighbor, Not Identification: Separate 5×5×5 / 125-word packing ledger. Sharing 125 labels does not identify that representation with E47.
• Professor’s Cube / Rubik / C₅³ Carrier: Orbit-kernel equivalence and heat-projection theorem, Γcanⁿ → Pcan with rate (15/17)ⁿ.
• AQSFT & Spectral Cryptography: Finite AQSFT product-kernel, E47–AQSFT Spectral Cryptography — Multi-Silo Reconciliation Monograph.
• PQC Reconciliation: Exact finite layer dim V=125, dim ker = 47, P₄₇² = P₄₇ = P₄₇†, KP₄₇ = 0. Public operator yields projector in polynomial time — not a hardness assumption.
• Metamaterials & Defense & Engineering: Physics & field theory, engineering applications district. Validated math stays math in a new domain until domain correspondence is independently established
04 · Formal Verification and Research Memory
• Identity Laboratory: Formal E47 research and computational identity infrastructure.
• Mnemosyne: Research memory, kernel census and certificate archive.
• Lean 4 and Coq: Public explanation of machine-checked proof evidence.
• Formal Validation Archive: Compiler evidence and formal verification records.
• Kernel Census: Research evidence for kernel selection and related claims
• SPECTRA: Spectral research interface and related operator resources.
• Route Packets: Research navigation and machine-readable evidence packets.
• Machine Certificates: E47-JSSC-20260813 PASS 14/14, Acan = K² + 11664(I − Psym), ker Acan = im Pcan, ‖Γcanⁿ − Pcan‖₂ = (15/17)ⁿ.
05 · Simulation · Worlds & Computation
• Graph Theory: Graphs, topology, geometry, Rosetta Torus (T³) structural district.
• Molecular Applications: Molecular district — domain firewall applies.
• Babylonian Mathematics — Historical Computation: Sexagesimal computation, square roots, Newton–Heron lineage, L_IG and Babylonian computational formalism.
• L_IG Formal Language: Formal-language paper defining L_IG — tracked as open deliverable in Publication Program.
• Fibonacci–Lucas Family: L² − 5F² = −4 connects admissible spins. Spin 2 is first member with proper selected subspace.
• Simulation — E2 Models: Model-dependent computation. Assumptions and falsifiers must be stated.
• Worlds / Flight + Application Deck: Fly a world. Shape a field. Explore an invariant. 25 direct destinations, 5 areas to explore.
• Executable Validation Certificate — 2026-08-07: Exact Spectral Core and Continuum Evidence Boundary. 37 PASS · 10 FORMAL REVISIONS · 8 CONSTITUTIVE REQUIREMENTS · 0 FAIL.
06 · Archives · Provenance & Publication
• Notion Atlas — Canonical Narrative: Canonical long-form pages, provenance, corrections, and research lineage. Open Notion ↗
• AIMS Publication — Postable Atlas: Continuous-scroll public clone of the Atlas, readable as publication surface. Open AIMS ↗
• Visual Archive: Visual plates, city overviews, citadel broadcast, monorail overlay.
• Publications: Corpus Publication Release 2026-08-09 — Recursive Intelligence / Kouns–Killion Paradigm — Corpus Publication Monograph and Evidence Atlas.
• Correction Page — Correction Boundaries Preserved: Failed claims preserved, diagnosed, replaced, propagated. L_C₅³ rank-one vs L_twist rank-10, 14-qubit label superseded, Hodge repaired chain-complex form, Newton-Mean κ=0.376 stable.
• Linear — E47 Project: Open questions, next actions, discussions, development handoffs. Workspace access required. Open Linear ↗
• GitHub — Source · Reproduce · Applications: The machinery stays inspectable. Atlas is front door, repository remains full workshop. Open Source ↗
• SEE · Citadel Gateway — Shared Inspection Point: Residuals, hashes, environments, provenance. Open SEE · Citadel ↗
