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. If you want to get down to specifics and test it yourself - jump to Mirror Notation "Light" test protocol below. If you want model specifics and theory try the other documents.
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:
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Theorem: No single-pass reversal on the system without full control of the environment and the exact control record.
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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.
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Scope: States the exact equality conditions under which reversal is possible (the special reversible cases with full control).
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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. This paper gives the full ontology & use of Mirror Notation in both code form and logic form.
🔗 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
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Mirror Notation "Light" test protocol (Alternative to Long Form Notation Above)
Help me break this model!
This model is at the point where I am seeking unofficial peer review, the current and best path to testing the model is to run this test protocol - it's a scaled down simple version of the HFT model built for onboarding quickly to the models thinking, and pixel typing any equation as a test.
How to Read Them
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New to HFT, want the big picture first?
Start with Plain-Language Overview (No Equations), then jump to Paper I.
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Technical readers (physics/math):
Begin with Paper I – Reflection Mechanics (Part I) for the core rules, then Paper II for defect/ε-ledger machinery and predictions. Use Paper 0 as a reference and to run the linter/CLI when you want to audit an equality or reproduce examples.
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Looking for tests and review posture:
See Page: FAQ & Peer Review (predictions scoreboard, checker description, review policy).