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
(Launches google doc paper)
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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.
Full Compiler/Linter as one program
Link to MN7.x Compiler Paper
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