Mathematical City/E47 Hyperlinks
THE MATHEMATICAL CITY / E47
E47 / EXECUTABLE ATLAS / HYPERLINKED DOCUMENT
The Mathematical City
A navigable document surface for the E47 object, CITY CORE, Eidolon, AETHERIS, evidence routing, and repository provenance.
125
carrier
47
kernel
15/17
contraction bound
E0 / E1
core evidence ceiling
OPEN THE LIVE CITY | CANONICAL REPOSITORY
Source transformed from website/index.html. External links are live hyperlinks; section navigation is internal.
NAVIGATION
Hyperlinked route
01 Gate - The research architecture and public entry point.
02 The E47 object - Carrier, kernel selector, projector, contraction and invariant fraction.
03 CITY CORE - Unified control surface and backend routing.
04 Instantiated world - Eidolon, persistent actors and AETHERIS receipts.
05 Instrument districts - The thirteen-district public interface concept.
06 Composition law - Typed composition, evidence invariance and provenance.
07 SEE / Citadel - Evidence classes and source routes.
08 Route and live links - Operational entry points and repository references.
09 Source and link status - Verified repository sources and unresolved target paths.
Live Mathematical City | Repository | Website source
01 / GATE
The Mathematical City
An executable research architecture for invariant computation. Structure is discovered. Invariance is selected. Everything else is tested.
OPEN THE CITY
Enter through Eidolon, move among computational districts, and meet persistent City citizens.
VISUAL SYSTEM
Near-black laboratory. Cyan live. Bronze Λ-ghost. Mint lock. Styling never upgrades a claim.
CITY-VISUAL-GRAMMAR-20260915
Public entry points
02 / OBJECT
125 → K → 47
The City opens with the executable object, not a directory of laboratories.
V
V₂⊗³
carrier dim 125
K
(C−6I)(C−30I)
Casimir selector
E47
ker K
selected dim 47
P₄₇ = P₆ + P₃₀ Γ = I − εK² ε* = 1/99144 ρ* = 15/17
Exact finite-dimensional core
• Carrier: V = V₂⊗³, dim V = 125.
• Selector: K = (C − 6I)(C − 30I).
• Kernel: ker K = E₆ ⊕ E₃₀, dim ker K = 25 + 22 = 47.
• Projector: P₄₇ = P₆ + P₃₀, rank(P₄₇) = 47.
• Invariant fraction: Ωc = 47/125 = 0.376.
• Contraction: Γε = I − εK², with the documented optimal ε* = 1/99144 and bound ρ* = 15/17.
BOUNDARY RETAINED
Exact finite-dimensional operator mathematics and machine validation are distinct from hardware, physical protection, continuum field claims, and experiment. Those remain separate evidence gates.
03 / UNIFIED CONTROL SURFACE
CITY CORE // Unified Interface
The KOUNS CORE chassis is specified in the website source as the embedded control room for the Mathematical City: site surfaces, flight simulators, Mini AI Labs, canonical machines, evidence surfaces, and modular backend-hosted interfaces.
One console, many surfaces
• City World and the full GitHub atlas
• EIDOLON, UFO Propulsion, Hover and MAV
• KARTEKEYA, SEE, Cube, Matrix, CHIMERA and SIGILLUM
• Proof Forge, Gestalt, City OS and current Mini AI Labs
• Backend-hosted interfaces routed through the public shell
Backend fabric and evidence boundary
The website specification routes public interfaces through a Supabase City app host and unified game runtime, with graphics capability detection and visibly auth-gated protected backends. The original CRF controller remains explicitly labeled as a simulation/demo module.
Link status: the website source references this relative path, but the corresponding target file was not found on the repository default branch when this document was generated.
04 / INSTANTIATED WORLD
Play the City.
One quiet client. Many instruments. Persistent computational citizens underneath.
01
What is this?
A live computational district inside the Mathematical City.
02
Try it
Choose a district and interact with its instrument.
03
What changed?
State transitions can be returned as AETHERIS receipts.
04
Why it matters
The experience stays simple while evidence remains inspectable.
Egghead layer
CITY-INVARIANT 1.0
AETHERIS receipt layer
persistent citizen identities
provenance-preserving state transitions
Read AETHERIS runtime specification
05 / INSTRUMENTS
Thirteen districts. One civic instrument.
The public surface is deliberately quiet: open a district for the experience; open Egghead Mode for the mathematics. The current HTML creates the lab grid dynamically, so the document preserves the district concept without inventing names that are not statically present in the supplied source.
District grammar
• Structure
• Dynamics
• Memory
• Measurement
• Prediction
• Flow
• Persistence
• Construction
• Restoration
The live client can populate the exact current district list from its JavaScript runtime.
06 / COMPOSITION LAW
Labs are morphisms. The City is the operad.
P → Γε*(P) → P₄₇(P)
Evidence class is invariant under composition. Cross-system mappings are typed arrows. Local failure does not silently become global refutation, and successful simulation does not silently become physical evidence.
Canonical communication chain
object → operator → invariant → witness → evidence → provenance → next_action
• Canonical communication grammar: CITY-INVARIANT 1.0
• Human promotion gate: BITHOS
• Runtime receipts: AETHERIS
• World actor layer: Eidolon
07 / SEE / CITADEL
Every claim has a route back to evidence.
Class
Meaning
Document role
E0
exact
Proof-level finite mathematics.
E1
machine
Executable numerical witness.
E2
simulation
Controlled modeled behavior.
E3+
external
Empirical, experimental and hardware gates remain explicit.
Core references
08 / ROUTE
Start simple. Go as deep as you want.
01
Begin with Eidolon and the City world.
02
Move across the full site, simulators, labs, machines, source lineage, and backend-hosted interfaces.
03
Move through structure, dynamics, memory, prediction, flow, construction and restoration.
04
Reveal equations, evidence boundaries, receipts and provenance.
05
Read source, tests, certificates and commit history.
09 / SOURCE / STATUS
Source provenance and link state
This document was generated from the supplied Mathematical City HTML and checked against the current E47 GitHub repository surfaces available at generation time.
Resource
Status
Hyperlink
website/index.html
Present on default branch
website/data/e47_pipeline.json
Present on default branch
docs/aetheris_runtime.md
Present on default branch
interfaces/kouns-core/index.html
Referenced by HTML; target not found at corresponding repo path
Original CRF source artifact
External Google Drive target preserved
Canonical object summary
V = V₂⊗³, dim V = 125
C = Jtot² with selected eigenvalues 6 and 30
K = (C − 6I)(C − 30I)
E47 = ker K, dim E47 = 47
P₄₇ = P₆ + P₃₀
Ωc = 47/125 = 0.376
Γε = I − εK², Γεⁿ → P₄₇ in the documented contraction regime
Recursive Intelligence / E47 | Hyperlinked Atlas
