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Technical Papers

 The Harmonic Field Theory (HFT) papers are the foundation of this framework. Each develops the Mirror Law into formal mechanics, notation, and implications across physics (and, separately, exploratory implications for information/mind). This index links to the documents in sequence and indicates what each contributes.

On the Impossibility of Single-Pass Reversal

We show — using only standard dynamics — that having an inverse map (phi^-t, or U(-t) = U(t)^dagger) does not license a single-pass reverse event on a lab system. Real experiments are open: channels obey data-processing (relative-entropy monotonicity), entropy production is nonnegative, and fluctuation relations compare a forward protocol to a separately defined reversed protocol. Echoes work; rewinds don’t.

What it adds:

  • Theorem: No single-pass reversal on the system without full control of the environment and the exact control record.

  • Lemmas:
    Stinespring (the inverse lives on S+E, i.e., system plus environment);
    Data-processing inequality with equality conditions (Petz recovery);
    Spohn entropy-production bound;
    Crooks/Jarzynski as paired protocols;
    Detailed balance as the sharp line between equilibrium “reversibility” and irreversible currents.

  • Corollaries: No global deletion (Landauer limit; quantum no-deleting). Echoes are composite closures, not history rewinds.

  • Scope: States the exact equality conditions under which reversal is possible (the special reversible cases with full control).

  • Fit: Makes “reversibility” precise without invoking Mirror Law; shows the rule already lives inside mainstream physics.


🔗 Read → HFT-00.1 Supplement  - On the Impossibility of Single-Pass Reversal

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🔗 Launch the paper directly in google docs for easier viewing

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HFT Primer

If you are a reader who’s intrigued by the idea but skeptical — The Primer explains what HFT claims, what it doesn’t, and how it could fail.

 

🔗 Begin here → HFT PRIMER - Basic Walk Through of Tiered Physics

Paper I – Reflection Mechanics (Part I)

What it does: Establishes the backbone. Introduces the Mirror Law (R^2 = I), the “two-pass” closure rule for admissible equalities, and the tier structure that controls when new generators double state counts. Lays out conservation/doubling criteria and what counts as a lawful, dimensionless invariant after normalization. States testable consequences (symmetry split, conservation under reflection, doubling under added anticommuting elements).

 

🔗 Read → Paper I – Reflection Mechanics (Part I)

🔗 Launch the paper directly in google docs for easier viewing

Paper II – Reflection Mechanics (Part II)

What it adds: Formal defect accounting and global balance. Defines defect tensors (conjugacy D^Ω, causal D^η from Tier-4 up, operator-parity D^op), the normalized ε-ledger per tier, and a global “Möbius” balance ∑ σ_n ε_n = 0. Connects the ledger to physical signals (e.g., parity/birefringence patterns), records concrete, falsifiable items (dark:visible near 5:1; CMB odd-parity signatures; no 4th fermion family via triality lock), and clarifies the octonion/Tier-7 ceiling.


🔗 Read → Paper II – Reflection Mechanics (Part II)

🔗 Launch the paper directly in google docs for easier viewing​

Paper 0 – Mirror Notation v7.x

What it’s for: The formal syntax plus the checker. Defines the mirror/closure notation used in Papers I–II and ships the compiler/linter that enforces it: two-pass mirror closure, unit/scale consistency, tier/handedness legality, and R-even extraction of scalars. Includes minimal Python utilities and CLI examples to reproduce the paper’s checks.


🔗 Read → Paper 0 – Mirror Notation v7.x

🔗 Launch the paper directly in google docs for easier viewing

Full Compiler/Linter as one program
Link to MN7.x Compiler Paper


Launch the Code as google doc

How to Read Them

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  • Looking for tests and review posture:

       See Page: FAQ & Peer Review (predictions scoreboard, checker description, review policy).

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