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The Hamiltonian — the law of the flow
hamiltonian
The energy operator and the generator of time evolution: it governs how the many potentials develop between the one source and the one end. Four pillars rest on the floors already seeded - the generator (unitary, conserves the total, on the capstone), the eigenbasis (the change-of-domain door, on the solve path), the conserved invariant (Noether's energy), and the no-cut bridge (one generator classical to quantum, the reply to Copenhagen). Its one open end is the measurement gap: H never selects a single outcome. The seals and the four fits are on the stick (stick_the_hamiltonian_the_law_of_the_flow); this card places it on the map (tools/seed_the_hamiltonian.py).
- has part → The generator of time evolution — unitary, conserves the total — a pillar of the Hamiltonian (The generator of time evolution)
- has part → The energy eigenbasis — the stationary states — a pillar of the Hamiltonian (The energy eigenbasis)
- has part → The conserved invariant — energy, the same end through the flow — a pillar of the Hamiltonian (The conserved invariant)
- has part → The no-cut bridge — one generator, classical to quantum — a pillar of the Hamiltonian (The no-cut bridge)
- has open end → The measurement gap — what the Hamiltonian does not determine — the measurement gap - the one outcome H does not select
- part of → The Floor of Discovery — one floor, and by its design the fear of God — the law of the flow on the one map
- connects at → The Legendre dual of the Hamiltonian — H = p q' − L — the two faces of one dynamics: L is T - V, H is T + V, joined by the Legendre transform
- connects at → Time-translation symmetry gives energy — the Hamiltonian — time-translation symmetry -> conserved energy = the Hamiltonian; the seam between L and H
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