Origin, observation scale and relational phase graphs

The proposition

A physical state is represented relative to a declared origin, observer, substrate scale, environment and time. Changing observation scale changes what is resolved. A valid scale transition must preserve the relations needed to predict the observables, or explicitly record the information lost and the extra closure terms required.

The retained source edition v2.9 defines U=1 as one admitted whole or origin identity. Coordinate components, payloads, active labels and measured quantities remain distinct. This test retains that identity contract; it does not substitute shifted arithmetic or claim that identity metadata supplies missing physical equations.

The author’s graphing description in Pasted text(20261011-004143).txt requires spatial extent across three directions and evolution over specified time, including wavelength and transverse diameter where relevant. The existing volumetric-wave reference is linked below. This thermal test reports resolved states and projection calculations; it does not claim to implement or validate the entire volumetric graphing standard.

Three separate relational graphs: liquid, ice and vapour

Represent the same declared H₂O inventory through three conditional physical configurations. Retain the shared material referent without treating the three scenarios as three origins. Each scenario has a distinct identity and its own constitutive model. Link scenarios for comparison; do not merge their physical states.

Declare total mass, external forcing, observation frame and comparison time. State whether geometry, initial energy, temperature or pressure is fixed. Those choices cannot all be imposed independently for every phase. Each all-phase configuration needs an admissibility check; an unstable configuration may immediately change phase.

A literal all-liquid scenario excludes its generated vapour until that restriction is released. A physically evolving liquid scenario must create and retain the vapour layer as an additional subsystem. “All vapour” is also a declared configuration, not a guarantee that self-gravity permits a stable vapour body at an arbitrary mass.

Use IAPWS fluid and ice equations within their stated validity domains; planetary extremes may require further equations of state. Wavelength-resolved optical data and transfer equations are needed for radiative graphs. No full three-phase or planetary solver was executed in this release.

Executed scale test: what a coarse observation loses

Two equal-area idealised thermal patches start at 260 K and 300 K. Their mean is 280 K, equal to their radiative surroundings. Each patch has heat capacity 500 J/K, area 0.005 m² and emissivity 0.95; mutual conductance is 0.02 W/K. The model excludes phase change and mass exchange, so these patches are not asserted to be liquid H₂O.

The resolved equations use radiative fourth powers and equal/opposite conductive exchange. Let m=(T₁+T₂)/2 and d=(T₁−T₂)/2. Exact projection gives

dm/dt = γ[T_env⁴ − m⁴ − 6m²d² − d⁴]
dd/dt = −γ[4m³d + 4md³] − (2K/C)d
γ = εσ_SB A/C

A mean-only model drops d and predicts no change from 280 K. The retained mean/contrast model preserves both patch temperatures through T₁=m+d and T₂=m−d.

Fourth-order Runge–Kutta, step 0.1 s. The retained model is an algebraic change of variables of the resolved model, so agreement is expected; the numerical result verifies this implementation. It does not prove universal closure for arbitrary coarse-graining. More complex distributions generally require further moments or other closure information.

Record round-trip checks preserve the singular U=1 origin field, body identity, observer, environment, units, time and two sample addresses. These are bounded software checks, not a native engine or hardware receipt.

What follows

The example establishes why one observed scalar may be insufficient and shows an exact retained representation for this two-patch case. The three H₂O graphs require separate physical calculations while sharing a declared identity and comparison contract. Their next executable stage requires specified mass, boundary conditions, initial preparation and constitutive/optical data.

IAPWS fluid water · IAPWS ice Ih · NASA energy exchange

Revision 0.1: formalises the author’s scale-aware proposition, retains the origin identity contract, executes a two-patch closure test and specifies three distinct phase scenario graphs. Independent assessment: not recorded.