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module module moderate

IndisputableMonolith.Foundation.Hamiltonian

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This module supplies the Hamiltonian formalism as a local non-sealed recognition field interface in the Recognition Science foundation layer. It defines HamiltonianDensity, TotalHamiltonian, StressEnergyTensor, and supporting structures such as metric tensors and invariance conditions, all built on the imported RS time quantum τ₀. Field theorists or relativists working from the J-functional equation would reference these objects when expressing energy conservation or stress-energy relations. The module is purely definitional with no proofs or t

claimThe module defines the Hamiltonian density $H$, total Hamiltonian $H_{tot}$, stress-energy tensor $T_{μν}$, metric tensor $g_{μν}$, and time-translation invariance $IsTimeTranslationInvariant$ on the recognition field, with all quantities expressed in RS-native units where $τ_0=1$ tick.

background

The module opens the local non-sealed recognition field interface and imports the fundamental RS time quantum τ₀ = 1 tick from Constants. It introduces sibling definitions including RRF, MetricTensor, BilinearForm, partialDeriv_v2, metric_det, inverse_metric, HamiltonianDensity, TotalHamiltonian, StressEnergyTensor, IsTimeTranslationInvariant, H_EnergyConservation, and energy_conservation. These objects operate in the foundation domain where the J-cost and phi-ladder supply the underlying algebraic structure for field quantities.

proof idea

This is a definition module, no proofs.

why it matters in Recognition Science

The module supplies the Hamiltonian structures required for energy conservation statements and stress-energy relations that appear later in the Recognition Science forcing chain (T0–T8). It provides the interface that downstream results on time-translation invariance and conservation laws rely upon, consistent with the eight-tick octave and D = 3 spatial dimensions. It touches the open question of sealing the recognition field.

scope and limits

depends on (1)

Lean names referenced from this declaration's body.

declarations in this module (14)