Mathematical City

Atlas clone · Ωc = 47/125

The Mathematical City

An executable research architecture for invariant computation. Each section below is a page. Scroll, or use the bar.

Structure is discovered. Invariance is selected. Everything else is tested. The City does not store conclusions; it stores routes from claim to evidence.

125

carrier

47

kernel

15/17

bound

E0/E1

ceiling here

Canonical record: Notion atlas · Start here · Constitution · Visual grammar

Page 02 · The 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 filter

E47

ker K

protected dim 47

P₄₇ = P₆ + P₃₀ · Γ = I − A/σ · σ = λ_max(A) · q⊥ ≤ 15/17 · ε* = 1/99144

Canonical machine

Kartekeya

125-state carrier → spectral selector → 47-dimensional invariant.

Certificate

SEE · Citadel

Shared inspection point. Residuals, hashes, provenance.

Page 03 · Live kernel

Plate 01 · KKP-R · seed 42

E47 LOCK

Stabilization dynamics within the 47-dimensional protected kernel subspace.

dim ker

47

of 125

Ωc

0.376

47 / 125

bound

15/17

slowest mode

lock

t = 55

residual < 1e-6

Quantum State Subspace Convergence

Tr(P E47 ρ) · probability mass in the kernel

Dissipative Error Decay Rate

leakagebound (15/17)^t

t

0 / 150

Tr(Pρ)

0.378471

leak

6.22e-1

5×5×5 Carrier

kernel core lit

λ=2λ=6 kerλ=12λ=20λ=30 kerλ=42

Operator stack

  • C

    Casimir on V₂⊗³

    spec {2, 6, 12, 20, 30, 42}

  • K

    (C − 6I)(C − 30I)

    ker K = ℰ₄₇, dim 47

  • A

    K² + 108² (I − P)

    joint generator

  • Γ

    I − A / σ

    σ = λ_max(A) = 198,288

Casimir occupancy

  • λ=2
    0.007
  • λ=6
    0.198
  • λ=12
    0.301
  • λ=20
    0.211
  • λ=30
    0.180
  • λ=42
    0.103

Figure 1. Recursive dissipative contraction of a random 125-dimensional density ρ0 onto the protected kernel E47 = ker(K). Left: subspace weight converges to unity. Right: leakage residual versus the Richardson bound. Map ρ ↦ ΓρΓᵀ with trace restoration; operator norm of Γ on the complement is at most 15/17.

rho maps by ΓρΓᵀ / Tr(ΓρΓᵀ) · dim V = 125 · Ωc = 0.376 · lock at t = 55

Page 04 · Mini AI Labs

Instruments around the object

SPECTRA → Fold → Murmuration → Mnemosyne → Density → Horizon → Wave → Identity → BUILD → SOAR → SCALAR → EIDOLON

Executable packet: SPECTRA → Fold → Density → Murmuration → Horizon → Mnemosyne → Wave → Identity → SPECTRA_REVEAL → SCORE

Page 05 · Constitution

Evidence is invariant under transit

District color answers where. Evidence class answers what is established. Movement never upgrades a claim.

  • Article I

    Two axes

    District color answers where. Evidence class answers what is established. Color never upgrades a hypothesis into a result.

  • Article II

    Non-upgrade

    Movement, analogy, reuse, visual prominence, or repetition cannot increase evidence class. Promotion requires new evidence at the destination.

  • Article III

    Canonical without erasure

    Canonical pages govern. Superseded plates stay archived and linked forward. Corrections are recorded, not silently patched.

  • Article IV

    Domain firewall

    A validated mathematical engine remains validated mathematics in a new domain. The domain correspondence is a separate claim until independently established.

  • E0

    Exact

    Finite mathematical statement with a proof. Conditional if any dependency is open.

  • E1

    Machine verification

    Deterministic program with recorded environment, inputs, and residuals.

  • E2

    Simulation

    Model-dependent computation. Assumptions and falsifiers must be stated.

  • E3

    Observation

    Empirical result with measurement context. Observation stays separate from interpretation.

  • E4

    Experiment / hardware

    Physical realization. Never implied by E0/E1 transit.

  • Open

    Unresolved

    Explicit proof, reproduction, test, or boundary obligation.

Full law: City Constitution · Path to citizenship · Elevated reproducibility monorail · Physical-claim promotion

Page 06 · Proof and provenance

SEE · Citadel Gateway

The shared inspection point for computational work. Residuals, hashes, environments.

Open SEE

Live certificate gateway.

Machine ledger

Verified results, residuals, and stations in Drive.

Page 07 · First visit

Five-stop memory

125 → K → 47 → certificate → correction.

  1. 01

    Carrier

    Start in V₂⊗³. Dimension 125.

  2. 02

    Selector

    K = (C − 6I)(C − 30I).

  3. 03

    Projector

    E₄₇ = ker K. dim = 47. Ωc = 47/125.

  4. 04

    Certificate

    Reproduce the computation. Inspect the machine record.

  5. 05

    Correction

    Failed claims are preserved, diagnosed, replaced, and propagated.

Transit lines

  • Foundation

    Definitions and ambient types

  • Representation

    Decomposition and multiplicities

  • Kernel

    Selectors, null spaces, projectors

  • Python

    Executable reconstruction

  • Certificate

    Residuals, hashes, environments

  • Correction

    Superseded claims and repaired lineage

  • Citadel

    Current canonical state

Five-minute core: Foundations · Representation theory · Kartekeya spine · Certificates. Reproduce one proof from the E47-Kartekeya repository. One correction: Dual Horizon.

Page 08 · Workspace document

A website in a document

Same atlas, continuous scroll, hyperlinks on. Google Docs cannot run the live kernel.

Live kernel

This website

Playback, lattice, residuals. Share this app for the executable plate. Jump to Lock.

Postable clone

Google Doc

Open the Mathematical City atlas document. Share → Anyone with the link, then post that URL.