{"id": "card_instr_spectral", "kind": "reference", "title": "Change of domain - the eigenbasis flip", "body": "The Change of domain - the eigenbasis flip verifier (src/concordance/verifiers/spectral.py). On the one map it instruments: card_question_p_vs_np. Found from the code's own imports, never invented; the module keeps the logic, this card is a pointer.", "source": {"label": "verifier: spectral", "url": "", "ref": "src/concordance/verifiers/spectral.py", "domain": "mathematics", "authority_tier": "engine_derived"}, "shelf": "codex", "box": "instrument", "bands": ["instrument", "verifier", "one map", "spectral"], "subject": "Change of domain - the eigenbasis flip", "connections": [{"to_card_id": "card_floor_the_instruments", "relationship": "part_of", "evidence": "a root of the instrument trees (Change of domain - the eigenbasis flip)"}, {"to_card_id": "card_question_p_vs_np", "relationship": "connects_at", "evidence": "instruments the map: the change-of-domain door: put the problem in the eigenbasis where it diagonalizes, solve as independent scalars, map back - exact when the basis is cheap (Fourier, diagonalization), the structured sibling of get-close"}, {"to_card_id": "card_solve_change_domain", "relationship": "connects_at", "evidence": "Change of domain: uses card_instr_spectral"}], "author": "engine", "created_at": 0.0, "updated_at": 0.0, "visibility": "public", "lifecycle_stage": "public", "volatility": "permanent", "surface": "secular", "generated": false, "call": "codex.instrument", "facets": {"subject": ["one map", "spectral", "verifier"]}, "presentation": {"glyph": "•", "kind_label": "instrument", "by": "verifier: spectral", "authority": "engine_derived", "posted": "", "standing": ""}, "neighbors": [{"id": "card_floor_the_instruments", "title": "The instruments — every verifier and validator, and where they join", "relationship": "part of", "why": "a root of the instrument trees (Change of domain - the eigenbasis flip)", "href": "/card/card_floor_the_instruments", "resolved": true}, {"id": "card_question_p_vs_np", "title": "P versus NP", "relationship": "connects at", "why": "instruments the map: the change-of-domain door: put the problem in the eigenbasis where it diagonalizes, solve as independent scalars, map back - exact when the basis is cheap (Fourier, diagonalizatio", "href": "/card/card_question_p_vs_np", "resolved": true}, {"id": "card_solve_change_domain", "title": "Change of domain — solve in the eigenbasis, map back (the exact flip)", "relationship": "connects at", "why": "Change of domain: uses card_instr_spectral", "href": "/card/card_solve_change_domain", "resolved": true}], "house": {"door": "FIND", "kind": "card", "trail": "connections", "seal": "/card/card_instr_spectral", "next_step": {"do": "follow a connection: what this card rests on, and what rests on it", "door": "FIND", "tool": "card_connections", "params": {"id": "card_instr_spectral"}}, "ends": "a verdict or a card · the trail · a seal · one next step"}}