flagship · number theory
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Polar & radial plots
Reduced fractions, totient populations, primitive roots, equal-area annuli, and the exact TFG denominator-collapse map.
interactive plots · live data · 3D geometry · published research
Cerebral
Cerebral
Graphix
See the structure. Click the object. Check the rule.
Interactive visualizations spanning reduced-fraction shells, live market pressure, and inscribed 3D geometry. The site pairs inspectable objects with published papers, source artifacts, public receipts, and explicit fences around what is not claimed.
Three visual families.
The site now leads with what it has become: plots you can click, data that moves, and geometry you can rotate. The decoder tools remain public, but no longer define the front door.
live · descriptive, not signals
Φ
Live data & markets
A live 4×4 chamber grid that legibility-weights delayed public market data. Chamber-level public view only: no named constituents, no trade permission, no advice.
interactive · 3D
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Inscribed 3D geometry
Centered rational chambers, the 1:2:3 sphere frame, and the six-cardinal cone construction. Rotate the object; keep metric shells and arithmetic shells separate.
Featured objects.
Start with the plot, then follow its paper, method note, or verification trail.
The Finite-Observer Ledger
Interactive exact semidiscrete reflection symbol, odd reflected-power law, matched-pair falsifier, certification atlas, and six receipt-bound figures. Visualization exposes evidence without creating evidentiary status.
The Polar Shell Renderer
Place each reduced fraction k/n at radius √n and angle 2πk/n. Shell n carries φ(n) points, and each assigned denominator annulus has area π.
Triangular Addressing & Reciprocal-Metallic Locks
The publication HTML and interactive explorer for the scale-covariant plane geometry. It inherits the flattened TFG address but not the parent divisor-band theorem line.
Φ Finance Weather
The only object here that moves on its own. Read sixteen chamber-level pressure cells as weather, not trade instruction; freshness and boundary labels remain visible.
Chamber-Lift Atlas
Every node is a paper or tool. Every solid edge must be backed by a shared identity that can be written down. Shared shape alone does not earn an edge.
Rational Address Showpiece
A centered rational chamber inside the 1:2:3 sphere frame, with ray-snap address readout and live divisor-band accounting.
Centered Rational Chamber
GCD shell partition, Jordan-totient conservation, convention toggles, six-cardinal projection, and a null baseline.
Six Cardinal Picone
The six-cardinal geometry thread in one object. The √2/Pell cone-tip cascade and √3 sphere–cube–sphere recursion share a center but remain distinct mechanisms.
The research spine.
Paper ↔ plot links are explicit. Nearby shell language is fenced when the generator changes.
From Measure to Flux / The Finite-Observer Ledger
Two linked papers and one interactive evidence companion: exact boundary scattering, named energy channels, matched-pair falsification, claim manifests, receipt-bound figures, and a certification wall.
The Polar Shell Renderer
Equal-area denominator shells for reduced fractions and primitive roots of unity. The canonical interactive page is the live edition of the paper.
Divisor-Band Bijections and Totient Shells
The exact TFG parent: reduction supplies the denominator shell, the inverse address law recovers location, and the totient counts shell population.
Annular Shell Isolation Near Zeta Zeros
A different shell law: local zero-centered level sets contract as m increases. Same organizational metaphor, different generator, geometry, and theorem family.
Same object or same rule? The polar denominator shells, TFG totient shells, and primitive-root angles share exact identities. The zeta annular-shell diagnostic is a neighboring analytic construction, not the same shell law.
Utilities & origins.
Where Cerebral Graphix started: text → fraction → address tools, reconstruction challenges, and an experimental music instrument. Even the UTF-8 tool was already reaching for a plot.
ASCII Bridge
The theorem recovers an address; ASCII supplies a public readout convention.
UTF-8 Alpha
A wider byte-kernel bridge, including the early “Graphix — the data, drawn” mini-plot.
Maker's Mark
A public 337-fraction reconstruction challenge preserved as part of the site's origin story.
Forge OS v16.3
An offline just-intonation sequencer and synth built from rational harmonic ratios.
Receipts, fences, and public identity.
The bookkeeping remains. It is now the verification layer beneath the visual front door, not the first thing a visitor has to decode.
Claim fences
Coordinate first. Count second. Interpret last. A shared visual shape is not a shared mechanism unless the common identity can be written down.
Finance boundary
market_truth: NOT_PROVEN_BY_RECEIPTtrade_permission: NO
Research identity
Jeffery Huckstead · Cerebral Graphix · ORCID 0009-0007-0234-2177.