{"id": "card_ham_noether", "kind": "reference", "title": "The conserved invariant — energy, the same end through the flow", "body": "By Noether's theorem, time-translation symmetry gives one conserved quantity: the Hamiltonian, the energy. It is the invariant along every path the system can take. 'Many possibilities but the story ends the same way' has a precise echo - whatever path the potentials flow, H is conserved.", "source": {"label": "Narrow Highway — the Hamiltonian", "url": "", "authority_tier": "engine_derived"}, "shelf": "codex", "box": "hamiltonian", "bands": ["hamiltonian", "pillar", "noether", "one map"], "subject": "The conserved invariant — energy, the same end through the flow", "connections": [{"to_card_id": "card_floor_the_hamiltonian", "relationship": "part_of", "evidence": "a pillar of the Hamiltonian (The conserved invariant)"}], "author": "engine", "created_at": 0.0, "updated_at": 0.0, "visibility": "public", "lifecycle_stage": "public", "volatility": "permanent", "surface": "secular", "generated": false, "call": "codex.hamiltonian", "facets": {"subject": ["noether", "one map", "pillar"]}, "presentation": {"glyph": "•", "kind_label": "hamiltonian", "by": "Narrow Highway — the Hamiltonian", "authority": "engine_derived", "posted": "", "standing": ""}, "neighbors": [{"id": "card_floor_the_hamiltonian", "title": "The Hamiltonian — the law of the flow", "relationship": "part of", "why": "a pillar of the Hamiltonian (The conserved invariant)", "href": "/card/card_floor_the_hamiltonian", "resolved": true}], "house": {"door": "FIND", "kind": "card", "trail": "connections", "seal": "/card/card_ham_noether", "next_step": {"do": "follow a connection: what this card rests on, and what rests on it", "door": "FIND", "tool": "card_connections", "params": {"id": "card_ham_noether"}}, "ends": "a verdict or a card · the trail · a seal · one next step"}}