Dual-Register Victorian Locomotive Home Products Grid

2x2 grid, 16:9, home products inspired by old locomotives: // ═══ THE DUAL-REGISTER MANIFOLD ═══ One design object 𝓞. Two observation registers: REG_GEN (Band A): orthographic projection, sepia ink, abstract material, dimensioned, annotated, time = design past REG_PHEN (Band B): perspective projection, full spectrum, real materials, lit by physical sources, time = present moment π_gen(𝓞) = sheet π_phen(𝓞) = hero The plate shows π_gen(𝓞) ⊕ π_phen(𝓞). The viewer's pleasure is RECOVERING 𝓞 FROM BOTH - matching panel III's barrel to the hero's barrel. // ═══ INVARIANT RECOVERY LAWS (what must survive both projections) ═══ For each component c of 𝓞, define invariants measurable in either register: INV-1 TOPOLOGY: genus & part-count of c identical in both (gauge = dial+needle+bezel in ink AND in steel) INV-2 PROPORTION: ratio(c) sheet == ratio(c) hero ± 5% (barrel L:D, gauge diameter : barrel diameter, lever sweep) INV-3 COUNT: |{c}| sheet == |{c}| hero (two gauges stay two gauges) INV-4 RHYTHM: rivet/seam pitch pattern congruent modulo scale INV-5 MATERIAL: callout(c) in panel II/IV == rendered material(c) in hero ("COPPER - BOILER" ⇒ the hero's boiler is copper, lit as copper) AUDIT: ∀c, ∀i∈{1..5}: recoverable(π_gen, c, i) ∧ recoverable(π_phen, c, i) ∧ equal(·) - else the plate depicts TWO machines. Reject. // ═══ REGISTER-LOCAL PHYSICS (why the split reads as truth) ═══ REG_GEN physics: light = flat scanner field (no shadows beyond drafted hatching) color = ink on aged paper; time encoded as foxing + plate wear truth criterion = INTERNAL CONSISTENCY of dimensions (leaders must agree) REG_PHEN physics: light = warm key 2700K + cool rim + filament practicals (inverse-square) material response per role: polished steel → anisotropic streaks along the brush direction brass/copper → warm bounce onto adjacent steel, colored GI spill walnut → pore-level grain, satin sheen at grazing angle truth criterion = PHYSICAL PLAUSIBILITY (steam rises, needles cast micro-shadows on dials, condensation beads on cold copper) THE BRIDGE CUE (the single element allowed in both registers): one dimension leader from panel IV may "continue" as a specular highlight edge on the hero - the drawing's line becoming light's line. // one poetic seam, exactly one. More than one breaks the registers. // ═══ TEMPORAL SEMIOTICS (the narrative the split performs) ═══ Band A = the machine's PAST: the source artifact and the reasoning. Band B = the machine's PRESENT: built, warm, operating. Reading order top→bottom = causality: idea → object. ⇒ the composite is not a collage; it is a PROOF with a conclusion. // ═══ COMPOSITION LAW ═══ split = 0.50 ± 0.05; gutters: plate border inside Band A, hard seam between bands hero focal point (barrel + gauges) sits on the vertical axis of panel III's principal primitive - the eye drops from drawing to object along one line. RENDER: {{SOURCE_ARTIFACT}} → {{TARGET_PRODUCT}}. One design, two registers, five invariants, one seam of light. The sheet argues. The hero exists. The plate proves they are the same thing.