{
  "id": "huxa-science-systems-03",
  "version": "0.1",
  "date": "2026-10-23",
  "language": "is",
  "title": "Eðlisfræði, kerfisfræði, rúmfræði, efnafræði og rafrásir",
  "kind": "source-based-study-and-design-proposal",
  "sources": [
    {
      "id": "energy",
      "author": "NASA Glenn",
      "url": "https://www1.grc.nasa.gov/beginners-guide-to-aeronautics/conservation-of-energy/",
      "read": "Introduction and first-law balance"
    },
    {
      "id": "feedback",
      "author": "James K. Roberge / MIT OCW",
      "url": "https://ocw.mit.edu/courses/res-6-010-electronic-feedback-systems-spring-2013/307cb9d5beb51f58cb44b699e0c9cac2_MITRES_6-010S13_chap02.pdf",
      "read": "Printed pages 21–25, 32; text only"
    },
    {
      "id": "geometry",
      "author": "Eric W. Weisstein / Wolfram MathWorld",
      "url": "https://mathworld.wolfram.com/SimilarityRatio.html",
      "read": "Definition"
    },
    {
      "id": "chemistry",
      "author": "IUPAC Gold Book",
      "url": "https://goldbook.iupac.org/terms/view/S06026",
      "read": "Search-indexed definition; direct page returned 403"
    },
    {
      "id": "rc",
      "author": "OpenStax",
      "url": "https://openstax.org/books/university-physics-volume-2/pages/10-5-rc-circuits",
      "read": "Charging a capacitor, equations 10.8–10.10"
    },
    {
      "id": "capacitor",
      "author": "OpenStax",
      "url": "https://openstax.org/books/university-physics-volume-2/pages/8-3-energy-stored-in-a-capacitor",
      "read": "Derivation through equation 8.10"
    }
  ],
  "connections": [
    {
      "domain": "physics",
      "topic": "energy balance and system boundary",
      "source": "energy"
    },
    {
      "domain": "systems",
      "topic": "feedback, measurement and stability",
      "source": "feedback"
    },
    {
      "domain": "geometry",
      "topic": "length k, area k², volume k³",
      "source": "geometry"
    },
    {
      "domain": "chemistry",
      "topic": "stoichiometric amounts and composition",
      "source": "chemistry"
    },
    {
      "domain": "electrical circuits",
      "topic": "time-dependent RC response",
      "source": "rc"
    }
  ],
  "examples": {
    "scaling": {
      "length_ratio": 2,
      "area_ratio": 4,
      "volume_ratio": 8
    },
    "water_balance": {
      "equation": "2 H2 + O2 -> 2 H2O",
      "left_atoms": {
        "H": 4,
        "O": 2
      },
      "right_atoms": {
        "H": 4,
        "O": 2
      },
      "scope": "Amount balance only; does not specify mechanism, conditions or rate"
    },
    "rc": {
      "supply_V": 5,
      "initial_capacitor_V": 0,
      "R_ohm": 1000,
      "C_F": 0.001,
      "tau_s": 1,
      "voltage_after_one_tau_V": 3.1606027941427883,
      "assumptions": [
        "constant ideal R and C",
        "ideal voltage step",
        "no leakage or additional load"
      ],
      "equations": [
        "tau=R*C",
        "Vc(t)=Vs*(1-exp(-t/tau))",
        "I(t)=(Vs/R)*exp(-t/tau)",
        "Ec=0.5*C*Vc^2"
      ],
      "data_kind": "calculated, not observed"
    }
  },
  "proposed_fields": [
    "domain",
    "system_boundary",
    "components",
    "typed_connections",
    "quantities_and_units",
    "initial_state",
    "rule",
    "validity_conditions",
    "invariants",
    "allowed_transformations",
    "prediction",
    "observation",
    "residual",
    "source"
  ],
  "synthesis": {
    "status": "our-design-proposal",
    "text": "Varpa tengslum milli orða, mynda og jafna þar sem skilgreind vörpun er til; skrá hvað varðveitist og hvað týnist."
  },
  "next_test": "Compare verbal, diagram and equation representations of a fixed RC example. Independent physical measurement not performed.",
  "limits": [
    "Scientific analogies do not establish a shared historical origin of writing systems.",
    "No general conservation law for word meaning is proposed.",
    "Symbol meaning under rotation/reflection requires separate evidence.",
    "Feedback can amplify errors or destabilize a system.",
    "Current site computes a teaching model; it is not an autonomous research engine."
  ]
}