{
  "schema_version": "qft-overview-figure/v1",
  "artifact_id": "qft.artifact.many-body-quantum-matter.cold-atoms-synthetic-matter-structure-and-dictionary",
  "title": "Cold atoms and synthetic matter: structure and dictionary",
  "schematic": true,
  "not_to_scale": true,
  "evidence_cutoff": null,
  "description_url": "/many-body-quantum-matter/cold-atoms-synthetic-matter/platform-scales-traps/#nonvisual-description-of-the-synthetic-matter-structure-figure",
  "nodes": {
    "controls": {
      "role": "stage",
      "content_tex": "Laboratory controls $\\mathbf u$\\\\ fields, lasers, traps, ramps, gates, twist and strain"
    },
    "raw": {
      "role": "note",
      "content_tex": "A knob setting is not yet a Hamiltonian parameter"
    },
    "calibration": {
      "role": "stage",
      "content_tex": "Calibration with covariance\\\\ $p(\\boldsymbol\\theta,\\mathbf c,\\boldsymbol\\eta\\mid D_{\\rm cal})$"
    },
    "continuum": {
      "role": "branch",
      "content_tex": "Continuum and resonance\\\\ $n,T,a,r_e$, trap, loss"
    },
    "lattice": {
      "role": "branch",
      "content_tex": "Optical lattice and gauge\\\\ $t,U,\\Delta_{\\rm band}$, Berry connection"
    },
    "moire": {
      "role": "branch",
      "content_tex": "Molecules and moiré\\\\ dressing, screening, geometry, flavors"
    },
    "hamiltonian": {
      "role": "stage",
      "content_tex": "Platform Hamiltonian\\\\ $H_{\\rm plat}=H_{\\rm tar}(\\boldsymbol\\theta)+\\sum_\\alpha c_\\alpha\\mathcal O_\\alpha+H_{\\rm noise}(t)$"
    },
    "hierarchy": {
      "role": "note",
      "content_tex": "Check range, band, drive, confinement, and interaction hierarchies"
    },
    "state": {
      "role": "stage",
      "content_tex": "Prepared state $\\rho_{\\rm plat}$\\\\ entropy, equilibration, ramp history, lifetime"
    },
    "prep": {
      "role": "note",
      "content_tex": "Band adiabaticity need not imply spin or phase equilibration"
    },
    "measurement": {
      "role": "stage",
      "content_tex": "Observation map\\\\ $p(\\mathbf y\\mid\\rho_{\\rm plat},\\boldsymbol\\eta)$: resolution, fidelity, background"
    },
    "claim": {
      "role": "result",
      "content_tex": "Bounded conclusion: calibrated parameter, realized Hamiltonian, validated observable, or phase evidence"
    }
  },
  "edges": {
    "controls--construction--calibration": {
      "from": "controls",
      "to": "calibration",
      "relation": "construction",
      "label_tex": ""
    },
    "raw--condition--controls": {
      "from": "raw",
      "to": "controls",
      "relation": "condition",
      "label_tex": ""
    },
    "calibration--construction--continuum": {
      "from": "calibration",
      "to": "continuum",
      "relation": "construction",
      "label_tex": ""
    },
    "calibration--construction--lattice": {
      "from": "calibration",
      "to": "lattice",
      "relation": "construction",
      "label_tex": ""
    },
    "calibration--construction--moire": {
      "from": "calibration",
      "to": "moire",
      "relation": "construction",
      "label_tex": ""
    },
    "continuum--construction--hamiltonian": {
      "from": "continuum",
      "to": "hamiltonian",
      "relation": "construction",
      "label_tex": ""
    },
    "lattice--construction--hamiltonian": {
      "from": "lattice",
      "to": "hamiltonian",
      "relation": "construction",
      "label_tex": ""
    },
    "moire--construction--hamiltonian": {
      "from": "moire",
      "to": "hamiltonian",
      "relation": "construction",
      "label_tex": ""
    },
    "hierarchy--condition--hamiltonian": {
      "from": "hierarchy",
      "to": "hamiltonian",
      "relation": "condition",
      "label_tex": ""
    },
    "hamiltonian--construction--state": {
      "from": "hamiltonian",
      "to": "state",
      "relation": "construction",
      "label_tex": ""
    },
    "prep--condition--state": {
      "from": "prep",
      "to": "state",
      "relation": "condition",
      "label_tex": ""
    },
    "state--construction--measurement": {
      "from": "state",
      "to": "measurement",
      "relation": "construction",
      "label_tex": ""
    },
    "measurement--construction--claim": {
      "from": "measurement",
      "to": "claim",
      "relation": "construction",
      "label_tex": ""
    }
  },
  "context": [],
  "linear_equivalent": {
    "heading": "Nonvisual description of the synthetic-matter structure figure",
    "columns": [
      "Figure element or arrow",
      "Relation encoded",
      "Condition or resulting statement"
    ],
    "rows": {
      "row-93747bacb6739adc": {
        "key": "Laboratory controls",
        "cells": [
          "Laboratory controls",
          "Fields, lasers, traps, ramps, gates, twist, and strain form the control vector $\\mathbf u$.",
          "The dashed side note states that a knob setting is not yet a Hamiltonian parameter."
        ]
      },
      "row-192b2f6a34985414": {
        "key": "Controls → calibration",
        "cells": [
          "Controls → calibration",
          "Independent calibration produces a joint distribution $p(\\boldsymbol\\theta,\\mathbf c,\\boldsymbol\\eta\\mid D_{\\rm cal})$.",
          "Parameter, discrepancy, and nuisance covariances remain attached to later predictions."
        ]
      },
      "row-da3bdebe68a60b27": {
        "key": "Calibration → continuum and resonance branch",
        "cells": [
          "Calibration → continuum and resonance branch",
          "The continuum branch determines $n$, $T$, $a$, $r_e$, trap, and loss parameters.",
          "Resonant universality requires the range, confinement, gradient, and lifetime hierarchy appropriate to the claim."
        ]
      },
      "row-b3796a4ead430090": {
        "key": "Calibration → optical-lattice and gauge branch",
        "cells": [
          "Calibration → optical-lattice and gauge branch",
          "The lattice branch determines $t$, $U$, $\\Delta_{\\rm band}$, and the Berry connection.",
          "Higher bands, nonadiabatic dressing, scalar potentials, and heating remain possible corrections."
        ]
      },
      "row-6cf48f7e3e5c4fac": {
        "key": "Calibration → molecular and moiré branch",
        "cells": [
          "Calibration → molecular and moiré branch",
          "The molecular and moiré branch determines dressing, screening, geometry, and active flavors.",
          "Internal channels, relaxation, remote bands, strain, and inhomogeneity constrain the reduction."
        ]
      },
      "row-c500d572d5ca6282": {
        "key": "Three platform branches → platform Hamiltonian",
        "cells": [
          "Three platform branches → platform Hamiltonian",
          "Each branch feeds $H_{\\rm plat}=H_{\\rm tar}(\\boldsymbol\\theta)+\\sum_\\alpha c_\\alpha\\mathcal O_\\alpha+H_{\\rm noise}(t)$.",
          "The dashed hierarchy condition requires checks of interaction range, band isolation, drive, confinement, and correction scales."
        ]
      },
      "row-83e6aa3413d5de68": {
        "key": "Platform Hamiltonian → prepared state",
        "cells": [
          "Platform Hamiltonian → prepared state",
          "Hamiltonian realization is followed by preparation of $\\rho_{\\rm plat}$ with stated entropy, equilibration, ramp history, and lifetime.",
          "The dashed side note warns that band adiabaticity need not imply spin or phase equilibration."
        ]
      },
      "row-de71c184eed3153e": {
        "key": "Prepared state → observation map",
        "cells": [
          "Prepared state → observation map",
          "The state is mapped to $p(\\mathbf y\\mid\\rho_{\\rm plat},\\boldsymbol\\eta)$ with resolution, fidelity, and background.",
          "Measurement inversion and covariance are distinct from Hamiltonian calibration."
        ]
      },
      "row-938c75fe8f168e32": {
        "key": "Observation map → bounded conclusion",
        "cells": [
          "Observation map → bounded conclusion",
          "The completed chain supports only the strongest verified level: a calibrated parameter, realized Hamiltonian, validated observable, or phase evidence.",
          "No later level follows solely from success at an earlier level."
        ]
      }
    }
  }
}