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Blog: the golden ratio in this format is a scale factor, not information - #830
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Bilingual, and the first post to carry a diagram: adds a 'figure' block kind holding inline SVG, plus its renderer case. The SVG is authored in this repository's data files, never supplied by a reader, so no untrusted markup reaches that path. The post reports what was measured today: phi is not observable at all in the closed 2-bit format (1, 2, pi, 0.001 and 1e12 give identical tables), a GFTernary dot product is exactly phi^2 times the same codes read as balanced ternary, and the fp32 multiplier the board uses for that product costs 1654 cells against 13 for the exact unit -- 16/16 input pairs equivalent, on Yosys 0.65. The diagram is a difference diagram: the same constant in two placements, and the one edge that exists on the left and cannot exist on the right.
The body file was generated by concatenating two blocks that each carried the import line, so 'Block' was declared twice. My own check missed it: I ran tsc --noEmit -p tsconfig.json, and the project's typecheck is tsc -b, which is what the ratchet runs. Ratchet now: 179 errors across 26 files against a baseline of 184 across 27, and no file gained.
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Blog: the golden ratio in this format is a scale factor, not information (#830) * Blog: the golden ratio in this format is a scale factor, not information Bilingual, and the first post to carry a diagram: adds a 'figure' block kind holding inline SVG, plus its renderer case. The SVG is authored in this repository's data files, never supplied by a reader, so no untrusted markup reaches that path. The post reports what was measured today: phi is not observable at all in the closed 2-bit format (1, 2, pi, 0.001 and 1e12 give identical tables), a GFTernary dot product is exactly phi^2 times the same codes read as balanced ternary, and the fp32 multiplier the board uses for that product costs 1654 cells against 13 for the exact unit -- 16/16 input pairs equivalent, on Yosys 0.65. The diagram is a difference diagram: the same constant in two placements, and the one edge that exists on the left and cannot exist on the right. * Fix a duplicate type import the ratchet caught The body file was generated by concatenating two blocks that each carried the import line, so 'Block' was declared twice. My own check missed it: I ran tsc --noEmit -p tsconfig.json, and the project's typecheck is tsc -b, which is what the ratchet runs. Ratchet now: 179 errors across 26 files against a baseline of 184 across 27, and no file gained.
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Bilingual post (EN + RU) on what was measured today, and the first post to carry a diagram — adds a
figureblock kind holding inline SVG plus its renderer case.What it reports
And the theorem: ⟨x,y⟩ = phi²·⟨x̃,ỹ⟩ exactly, so phi is a per-tensor scale. The fp32 multiplier the board runs for that product costs 1654 cells against 13 for the exact unit, 16/16 input pairs equivalent, on Yosys 0.65.
The diagram
A difference diagram, not an illustration: the same constant in two placements, and the one edge that exists on the left (phi factors out) and cannot exist on the right (Stakhov's positional weights). Inline SVG in
currentColor, so it themes with the page.The SVG lives in this repository's own data files and is never supplied by a reader, so the
dangerouslySetInnerHTMLon that path sees no untrusted markup.Verification note, stated honestly
The post builds, and the figure is present in the DOM with all 30 labels and the right viewBox. I could not verify its rendered geometry: the browser pane in this session reports
window.innerWidth === 0, so every element measures 0×0 — includingbody. I nearly attributed that to my own SVG and started "fixing" it. The intrinsicwidth/heightattributes I added are a real improvement, but I am not claiming they fixed a bug I never demonstrated.Receipts in the post: trinity-fpga #582, #584, t27 #2177, and the two prior-art DOIs (Stakhov 2002, Bergman 1957), both verified through Crossref.