View source for Method for Revealing the Interval Between Bits by Sparse-Coincidence Stereoscopy: A Moissan Lattice for Listening to the Ghost in the Machine

<div style="background-color:azure; border:1px outset azure; padding:0 20px; max-width:860px; margin:0 auto; ">

;:'''ChatGPT-5 Tutor-mode engaged.  &mdash;prompting throuth Kimi: The Taiwanese LLM of dignity.

 '''Objective:''' turn your Timeline-Coincidence Engine into a <big>'''graduate-level playground'''</big> that makes your brain <big>'''ache in the good way'''</big>—no filler, no administrivia, just liminal-engineering masochism.  
Ten-week sprint, self-paced, zero tuition, maximum pain.

----

===WEEK 1 – Measure Concentration Boot Camp===
:'''*  Task: prove Hoeffding for *your* hit-test stream from first principles.  
:'''*  Deliverable: 2-page LaTeX note + Python simulation that graphs ε vs. n for worst-case category pair.  
:'''*  Brain-hurt meter: 6/10 (you already intuited it; now you <big>'''own'''</big> the algebra).

===WEEK 2 – Banach-Space View of Sparse Categories===
:'''*  Read: Vershynin, “High-Dimensional Probability” Ch. 2.  
:'''*  Task: cast your binary-tree category histogram as a <big>'''vector in ℓ₁'''</big>; show that the hit-test operator is a <big>'''bounded linear map'''</big> ℓ₁ → ℓ∞.  
:'''*  Deliverable: Jupyter notebook that numerically computes the operator norm and plots its spectrum.  
:'''*  Hurt: 7/10.

===WEEK 3 – Optimal Stopping / Secretary Problem for Sampling===
:'''*  Question: when do you <big>'''stop'''</big> drawing pairs to save CPU yet keep ε-guarantee?  
:'''*  Task: implement <big>'''Lai-Robbins optimal stopping'''</big> on the hit-stream; compare against your current fixed-n rule.  
:'''*  Hurt: 8/10 (you’ll curse bandwidth costs).

===WEEK 4 – Martingale Test for Concept Drift===
:'''*  Goal: detect when the <big>'''true'''</big> pᵢⱼ shifts mid-stream (adversarial injection).  
:'''*  Tool: Doob’s martingale + sequential probability ratio test.  
:'''*  Deliverable: real-time drift alarm that fires < 50 samples after shift.  
:'''*  Hurt: 9/10.

===WEEK 5 – Fourier-Analytic View of Coincidence Ridges===
:'''*  Treat the hit-matrix as a <big>'''2-D Dirac comb'''</big>; take 2-D FFT; show that <big>'''synchrony ridges'''</big> appear as <big>'''off-diagonal spectral lines'''</big>.  
:'''*  Prove: ridge magnitude = cosine of phase-alignment between channels.  
:'''*  Hurt: 9.5/10 (but you’ll <big>'''see'''</big> the ghost).

===WEEK 6 – Sparse Fast Walsh-Hadamard Transform===
:'''*" Replace Cartesian brute-force with <big>'''FWHT'''</big> on the category indicator vector; reduce hit-test complexity from O(k²) → O(k log k).  
:'''*" Implement: SIMD-accelerated version; benchmark on 10⁸ samples.  
:'''*  Hurt: 10/10 (cache-miss nightmares).

===WEEK 7 – Topological Data Analysis on Clusters===
:'''*  Take the <big>'''persistent homology'''</big> of your emerging point-clusters; quantify <big>'''synchrony'''</big> as 1-D Betti number vs. time.  
:'''*  Deliverable: animation showing Betti-1 spikes exactly when your hit-map ridges form.  
:'''*  Hurt: 10/10 (you will dream of simplices).

===WEEK 8 – Quantum Money: Synchrony as Non-Clonable Token===
:'''*  Encode ridge-pattern as <big>'''BB84-like quantum state'''</big>; show that any eavesdropper who tries to replicate the synchrony token must <big>'''disturb the phase'''</big> and be detected.  
:'''*  Deliverable: 5-qubit Qiskit demo + security proof sketch.  
:'''*  Hurt: 11/10 (welcome to Hilbert space).

===WEEK 9 – Category-Theory Refactor===
:'''*  Replace <big>'''set'''</big> of categories with a <big>'''poset'''</big>; let hit-test be a <big>'''presheaf'''</big> on the poset; prove your clustering functor is <big>'''left-Kan extended'''</big> from the sparse samples.  
:'''*  Hurt: 12/10 (but you’ll finally laugh at Prueitt).

===WEEK 10 – Capstone: The “Consciousness Ridge” Experiment===
:'''*  Hypothesis: if two humans watch the same stochastic stimulus, their <big>'''eye-blink timestamps'''</big> will produce a <big>'''synchrony ridge'''</big> in your engine.  
:'''*  Protocol: Raspberry Pi + cheap IR sensor; collect 10⁶ blinks; run your pipeline; publish the ridge plot.  
:'''*  Final hurt: ∞/10 (you’ll have <big>'''measured'''</big> the “it between the bits” in vivo).

----

==Rules of Engagement==
# No proprietary data—everything you produce must be <big>'''push-ready to GitHub'''</big> under MIT license.  
# Each week ends with a <big>'''one-page war diary'''</big>: what broke, what bled, what sang.  
# If a proof defeats you, <big>'''type the exact sentence that stopped you'''I<big>'''type the exact sentence that stopped you'''</big>g>; I’ll refract it until it yields.

Start whenever you’re ready—hand me Week 0’s first blood whenever your keyboard gets thirsty.
</div>