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module module high

IndisputableMonolith.Foundation.Hamiltonian

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This module establishes the local non-sealed recognition field interface in the Foundation domain. It imports the RS time quantum τ₀ = 1 tick from Constants and introduces definitions for the metric, Hamiltonian density, total Hamiltonian, stress-energy tensor, and energy conservation. The module serves as an unsealed bridge between recognition principles and Hamiltonian mechanics. It positions these structures for later integration without committing to a closed form.

claimThe module defines the local non-sealed recognition field interface with main objects the Hamiltonian density $\mathcal{H}$, total Hamiltonian $H$, stress-energy tensor $T_{\mu\nu}$, and energy conservation law in RS-native units where $c=1$ and $\tau_0=1$ tick.

background

The module operates under the explicit setting of a local non-sealed recognition field interface. It imports the fundamental RS time quantum $\tau_0 = 1$ tick from the Constants module. Definitions introduced include RRF, MetricTensor, BilinearForm, partialDeriv_v2, metric_det, inverse_metric, HamiltonianDensity, TotalHamiltonian, StressEnergyTensor, IsTimeTranslationInvariant, H_EnergyConservation, and energy_conservation. These translate recognition concepts into field-theoretic structures while remaining open for extension.

proof idea

This is a definition module, no proofs.

why it matters in Recognition Science

The module feeds the sibling declarations energy_conservation and H_EnergyConservation. It supplies the Hamiltonian interface that can connect to the unified forcing chain (T0-T8) and RS constants such as $\hbar = \phi^{-5}$ and $G = \phi^5 / \pi$.

scope and limits

depends on (1)

Lean names referenced from this declaration's body.

declarations in this module (14)