Informatico.ai

Contents

Engineering & Construction

  1. E.01 Stokes–Brinkman Porous Continuum, Helmholtz–Hodge Decomposition, and Percolation
  2. E.02 Herschel–Bulkley Yield-Stress Rheology: High-Performance Concrete Pumping & Tremie Placement
  3. E.03 Sub-Wavelength Acoustic Metamaterial Helmholtz Arrays and Viscothermal Boundary-Layer Damping
  4. E.04 Counter-Current Enthalpy Recovery Exchangers: Effectiveness–NTU, Membrane Sorption, and Frost Limits
  5. E.05 Terzaghi Soil Mechanics, CFA Augercast Deep Foundation Piling & Liquefaction Surcharge
  6. E.06 Nonlinear Structural Dynamics, ASCE 7-22 Inelastic Response Spectra & Seismic Base-Isolation Dampers
  7. E.07 Long-Span Suspension Bridge Aeroelastic Flutter, Scanlan Derivatives & Physics-Informed Neural Network (PINN) Digital Twins
  8. E.08 Earth-Pressure-Balance Tunnel Boring Machines (EPB-TBM), Peck–Mair Gaussian Settlement Troughs & GNN Subsurface Digital Twins
  9. E.09 Autogenous Bacterial & Crystalline Self-Healing Concrete: Lucas–Washburn Capillary Imbibition, Fickian–Michaelis–Menten Calcite Precipitation & Ultrasonic Coda-Wave Digital Twins
  10. E.10 3D Concrete Printing (3DCP) Extrusion Rheology & Buildability: Roussel Thixotropic Structuration, Elastic Buckling vs. Plastic Collapse & Robotic Toolpath Control
  11. E.11 Continuum Topology Optimization & Skyscraper Inerter Damping: SIMP Penalization, Michell Funicular Trusses & Trabecular Bone Mechanics
  12. E.12 Machine-Checked Silicon-to-Grid Safety: 180M-Line Rocq RISC-V Verification, Control Barrier Functions & Firefly-Synchronized Renewable Grids

Architecture

  1. A.01 Funicular Thrust Surfaces, Maxwell–Cremona Duals, and 1:5 Nodal Tectonics
  2. A.02 Reciprocal Timber Gridshells (Nexorades), Eccentric Lap Moments, and 1:5 Shear-Block Joinery
  3. A.03 Double-Skin Facade Buoyancy Stack Ventilation, Cavity Plumes, and 1:5 Acoustic Damper Louvers
  4. A.04 From Archigram's Plug-In Megastructures to British High-Tech Exoskeletons: Gerberette Cantilevers, Maxwell Space Frames & Shearing-Layer Pods
  5. A.05 Acoustic Sabin–Eyring Reverberation, Diffusive Coffered Vaults, and Speech Intelligibility (STI ≥ 0.68)
  6. A.06 Net-Zero Water & Greywater Constructed Wetlands: Subsurface Darcy Filtration, UV-C Photolysis, and Pathogen-Free Plumbing (CSI 22 13 00)
  7. A.07 Luis Barragán's Chromatic Tectonics, Kubelka–Munk Pigment Radiosity & Emotional Spatial Wavefields
  8. A.08 AI-Designed Daytime Radiative Sky-Cooling Photonic Roofs (8–13 μm Window) & Stefan Phase-Change Envelopes
  9. A.09 Bending-Active & Hygroscopic Programmable Timber Skins: Timoshenko Bilayer Curvature, Orthotropic Moisture Swelling & Zero-Energy Climate Facades
  10. A.10 Kinetic Origami & Miura-Ori Deployable Biomimetic Facades: Isometric Crease Kinematics, Auxetic Poisson Ratio Inversion & Solar Mashrabiya Envelopes
  11. A.11 3D Polyhedral Graphic Statics & Airy Stress Surfaces: Maxwell–Rankine Reciprocal Polyhedra, Guastavino Tile Vaulting & Zero-Rebar Floors
  12. A.12 Tensegrity Cable-Strut Domes & Radiative Sky-Cooling Envelopes: Pellegrino Equilibrium Nullspaces, Prestress Stiffening & Zero-Energy Cooling

Physics

  1. P.01 Non-Equilibrium Fluctuation-Dissipation Theorems and Allosteric Gating Energetics
  2. P.02 Active Matter Hydrodynamics and Ciliary Metachronal Wave Synchronization
  3. P.03 Soft Matter Rheology and Anomalous Subdiffusion in Entangled Mucin Hydrogels
  4. P.04 Electrokinetics, Donnan Equilibrium, and the Catastrophic Osmotic Collapse of the Periciliary Layer
  5. P.05 Quantum WKB Barrier Penetration, Proton-Coupled Electron Transfer, and Deaminase Base-Editing Catalysis
  6. P.06 de Gennes Polymer Reptation (D_rep ~ N⁻²), Doi–Edwards Tube Relaxation, and Kilobase Genetic Cargo Transport
  7. P.07 Formula 1 Ground-Effect Venturi Aerodynamics, 2026 Active X/Z-Mode Wings, Outwash Vortex Sealing & Porpoising Limit Cycles
  8. P.08 Electromagnetic Color Wave Physics: Bragg Thin-Film Interference, Gonioapparent Automotive Pearlescence & Barragán Stucco Optics
  9. P.09 Electrohydrodynamic Taylor Cones (49.3°), Rayleigh Fission Limits & Precision Monodisperse Aerosol Jet Physics
  10. P.10 Topological Photonics, Haldane–Raghu Photonic Chern Insulators, Berry Curvature & Backscatter-Free Chiral Edge Waveguides
  11. P.11 Fault-Tolerant Quantum Computing & Clean Nitrogen Fixation: Surface-Code Stabilizers, Non-Abelian Anyon Braiding & FeMoCo Catalysis
  12. P.12 Hilbert's Sixth Problem Resolved: Hard-Sphere Boltzmann Kinetics to Navier–Stokes Continuum & Neural Climate Operators

Series · Time & Gravity · 9 steps (T.00–T.10)

  1. T.00 Time & Gravity
  2. T.01 Gravity as a Slope in the Rate of Time
  3. T.02 Everyone Moves at One Rate
  4. T.03 What Sets the Slope
  5. T.04 A Clock in Two Places
  6. T.05 Does Gravity Entangle, and Would That Settle It?
  7. T.06 Does Gravity Collapse the Wave?
  8. T.07 The Equation with No Time
  9. T.10 Page's Counting Argument

Mathematics

  1. M.01 Modularity Lifting, Spectral Zero-Density Barriers, and #3-SAT Sparsification
  2. M.02 Riemann Zeta Zero-Density Estimates, Large Sieve Inequalities, and XiPrime Spectral Bounds
  3. M.03 Extremal Cap Sets in F_3^n, Polynomial Method Upper Bounds, and Rank-48 Matrix Tensors
  4. M.04 Polynomial Freiman–Ruzsa (PFR) Entropy Calculus and the 22-Million Equational Magma Graph
  5. M.05 Neuro-Symbolic Deductive Search (AlphaGeometry 2): Auxiliary Constructions and Allosteric Pocket Triangulation
  6. M.06 Sub-Cubic Fine-Grained Reductions (3SUM → APSP) and Step-Level Process Supervision (PRM800K)
  7. M.07 Formula 1 350 kW MGU-K Pontryagin Optimal Energy Control, Hamilton–Jacobi–Bellman Lap Time Minimization & Fourier Neural Operator Surrogates
  8. M.08 Riemannian Differential Geometry of Color Perception: Helmholtz–Schrödinger Geodesics, MacAdam Metric Tensors & Grassmann Spectral Hilbert Projections
  9. M.09 Monge–Kantorovich Optimal Transport, Benamou–Brenier Wasserstein-2 Geodesic Fluid Dynamics, Sinkhorn Entropic Regularization & Flow Matching
  10. M.10 Persistent Homology, Vietoris–Rips Simplicial Filtrations, Betti Barcodes & Topological Percolation Thresholds in Disordered Media
  11. M.11 Resolution of the 3D Kakeya Conjecture & Breaking Ingham's 1940 Riemann Barrier: Wang–Zahl Graininess, Guth–Maynard 30/13 & Lean 4
  12. M.12 Anthropic Lean 4 Complexity & Post-Quantum Crystal Locks: ETH Refutation (ETHIsFalse), Eight-Square Rank Compression & ML-KEM Lattices

Open-Bounty & Prize Crucible · 6 Dedicated Problem Folios (B.01–B.06)

  1. B.01 · BOUNTY-M1 Erdős Sidon B₂ Sets, Golomb Rulers & Anthropic Lean 4 Formalization Bounties
  2. B.02 · BOUNTY-P1 $5M XPRIZE Quantum Applications & Unitary Foundation: Surface-Code Thresholds & FeMoCo Catalysis
  3. B.03 · BOUNTY-E1 $100M XPRIZE Carbon Removal & IStructE Benchmark: Sub-45 kg CO₂e/m² SIMP Mineralized Slabs
  4. B.04 · BOUNTY-A1 $1M Holcim Awards & $3M Global Cooling Prize: Zero-Rebar 3D Graphic Statics Vaults & Sky-Cooling
  5. B.05 · BOUNTY-P2 Pareto Symbolic Regression (PySR) & Sparse PDE Discovery (PySINDy + Dedalus) from Noisy Sensor Fields
  6. B.06 · BOUNTY-M2 Machine-Checked Gauge Physics in PhysLean & Tensor-Network Quantum Criticality (ITensors.jl + NetKet)

Tech & Tools · The Toolbox · 6 Open 3D CAD & Studio Folios (X.01–X.06)

  1. X.01 · TOOL-CORE-1 Zero-Build WebGL2 GLB Inspector & Byte-Level 2-Manifold Geometry Verifier
  2. X.02 · TOOL-ENG-1 Code-First Parametric Solids & Measured STEP AP242, 3MF, and GLB Round-Trip Fidelity
  3. X.03 · TOOL-ARCH-1 The Small Architecture Studio's Vault, Timber & Reciprocal Frame Kit: Equilibrium to Open CAD
  4. X.04 · TOOL-ARCH-2 Miura-Ori Deployable Solar Screens: From 3D Folding Kinematics (GLB) to Flat-Pattern DXF
  5. X.05 · TOOL-FAB-1 Topology-Optimized Structural Struts to Watertight 3MF & Build-Plate Overhang Audit
  6. X.06 · TOOL-PHYS-MATH-1 Sub-Wavelength Acoustic & Topological Metamaterial Unit Cells: Genus g = 1 & Betti-Number Verification

Time & Gravity · A track where the open problem is the subject · Step 1 of 9 · 6 min read

Time & Gravity

A common intuition is that experience slides along a worldline and that gravity is a slope in the rate of time. Is any of that physics? Half of it is, and it is among the best-measured facts we have. The other half has no variable in any equation. These nine pages walk from the measured half to the open half without inventing a step.

Begin · Step 2 of 9 · 13 min readEveryone moves at one rate → See the nine steps ↓

Fixed boundary · printed on every T page · asserted by the lint Nothing on this page is a theory of everything, and this site proposes none. Every claim carries one of six labels, each tied to a ledger row: MEASURED, DERIVED, BOUND, PROPOSED, OPEN, or SINGLE RESULT. Preprints never rise above PROPOSED. Each page ends with one open question that the next page takes up.
Diagram for T.00: a worldline drawn across a shaded column that shows how fast a clock runs at each height, darker meaning slower, with one marker on the line. Drawn by a script from the page's own numbers; no text, no photograph.
Plate T.00-V · A worldline across a clock-rate gradient, with a marker for the 'now' the intuition imagines. General relativity has the line and the shading; it has no marker. Drawn by timegravity/make_plates.py from tools/timegravity_kernel.py.
About this illustration This plate is a deterministic drawing, not an AI-generated image and not a photograph. The curve is the kernel's own trajectory; the shading exaggerates a clock-rate difference of about one part in 10^16 per metre so that it can be seen at all.

The question, drawn once

A picture of the question, not a result. The horizontal axis is coordinate time, the vertical axis is height, and the shading is how fast a clock runs at each height, darker meaning slower. The marker is 'now' as the intuition imagines it, a point sliding along the worldline; move it with the slider or the arrow keys. General relativity has the worldline and the shading. It has no marker. Which pages carry that difference is what the map below is for.

A worldline across a clock-rate gradient with a movable marker Height against coordinate time. A shaded column shows clocks lower down running slower. One curve, the worldline, and one dot on it, the imagined now, which the slider moves. The physics has the curve and the shading; it has no dot. rate of a clock faster slower coordinate time height now?

The slider moves a picture, not a variable. No equation on the pages that follow has a term for it.

The nine steps, in reading order

  1. Step 1 of 9 T.00 The hub Ends with: Is any of this physics? Live
  2. Step 2 of 9 T.02 Everyone moves at one rate Ends with: Why can nothing opt out? Live
  3. Step 3 of 9 T.01 Gravity as a slope in the rate of time Ends with: What sets the slope? Live
  4. Step 4 of 9 T.03 What sets the slope Ends with: What if the mass is in two places? Live
  5. Step 5 of 9 T.04 A clock in two places Ends with: Which time does the clock read? Live
  6. Step 6 of 9 T.05 Does gravity entangle, and would that settle it? Ends with: If a classical slope can entangle, what would count as quantum gravity? Live
  7. Step 7 of 9 T.06 Does gravity collapse the wave? Ends with: If gravity neither collapses nor is shown to entangle, what is a superposition of slopes? Live
  8. Step 8 of 9 T.07 The equation with no time Ends with: Whose clock? Live
  9. Step 9 of 9 T.10 Page's counting argument Ends with: Where does the information go, in our universe? Live

How to read a T page

Every page in this track ships six things, and the build refuses a page that lacks one: a hand-written instrument whose knockout is the argument; a standard-library verifier that recomputes the page's central number and fails on a planted defect; a grounding ledger whose every DOI resolves in the site's offline Crossref cache; a label on every claim, derived from the ledger by a lint and decided by a person; a SKILL.md so any agent can rebuild the toy; and a Mexican Spanish twin in the same commit.

  • At least two collaborations, peer-reviewed DOIs, older than the replication window.
  • Follows by mathematics from a named MEASURED parent row.
  • An exclusion limit: what the data rule out, not what they show.
  • One collaboration, or anything inside the last twenty-four months.
  • A proposal or a preprint; a preprint can never be more.
  • A question the field has not closed.

The labels describe evidence, not confidence. MEASURED needs at least two collaborations with peer-reviewed results. BOUND is an exclusion limit. DERIVED follows by mathematics from a named MEASURED parent. SINGLE RESULT is one collaboration, or anything published inside the last twenty-four months. PROPOSED is a proposal, and a preprint can never be more. OPEN is a question the field has not closed. A lint checks the mechanics: rows, dates, collaborations, DOIs, the same label sequence in both languages. A human checklist decides the label itself.

This hub carries no claims at all, and the lint asserts that. It states the intuition once, above, as a question in the third person, and that sentence is banned on every other page of the track.

What would change this page

This page ends with one open question

Is any of this physics?

All Time & Gravity pages →