Making enterprise data and APIs agent-ready: the reliable, governable foundation that AI agents act on, after two decades in financial-services data and platforms.https://vamshij.com/en-GBhttps://vamshij.com/mathematics/orbits-and-eclipses/https://vamshij.com/mathematics/orbits-and-eclipses/Two browser pages that draw the Earth, the Moon and the inner planets with nothing exaggerated: true eccentricities, bodies and distances at one scale, and the umbra cone at its real proportions. The eclipse engine is checked against NASA's catalogue and finds all 24 eclipses between 2026 and 2030.Wed, 12 Aug 2026 00:00:00 GMTmathematicshttps://vamshij.com/writing/the-authority-surface/https://vamshij.com/writing/the-authority-surface/On your laptop you answer the question may-the-agent-do-this by being there to click yes. In production no one is, so what an agent may do alone, what needs a person, and what it must never do has to be decided in advance, action by action. Graded authority is a product decision, not a setting.Wed, 05 Aug 2026 00:00:00 GMTaiwritinghttps://vamshij.com/writing/the-record-nobody-agreed-to-keep/https://vamshij.com/writing/the-record-nobody-agreed-to-keep/Four days apart in July 2026, the EU postponed its record-keeping obligation for standalone high-risk AI by sixteen months and a widely adopted tool protocol deprecated its logging feature. Firms now have until December 2027 to produce a record nobody has agreed to keep. Each layer defers accountability to the layer next door, every deferral is locally correct, and the chain closes on nobody.Tue, 04 Aug 2026 00:00:00 GMTaiwritinghttps://vamshij.com/writing/encoding-judgement/https://vamshij.com/writing/encoding-judgement/Agents rarely lack judgement because the model is weak. They lack it because the judgement was never written down anywhere the agent can reach. From the expert systems that tried to state judgement as rules to the preference data and constitutions that now capture it by example, and why the hard part has moved from articulating judgement to seeing what we encoded.Wed, 24 Jun 2026 00:00:00 GMTaiwritinghttps://vamshij.com/writing/a-benchmark-is-not-a-control/https://vamshij.com/writing/a-benchmark-is-not-a-control/The most respected LLM benchmarks measure whether a model can do a task in a lab. None of them measure whether an agent's output is acceptable in a regulated workflow, and most cannot, by construction. A field guide to reading a leaderboard when you run agents on data you have to answer for.Mon, 15 Jun 2026 00:00:00 GMTaiwritinghttps://vamshij.com/writing/an-answer-that-runs/https://vamshij.com/writing/an-answer-that-runs/A generated query that runs is not one you can trust, and the gap widens as the data outgrows what a human can check by eye. What an agent harness for interactive data discovery has to do, told through a quant at a hedge fund: keep the analyst able to trust a result they can no longer inspect.Fri, 12 Jun 2026 00:00:00 GMTaiwritinghttps://vamshij.com/writing/the-cushions/https://vamshij.com/writing/the-cushions/An agent that works beautifully on your laptop is standing on cushions you stopped noticing: a human watching, a single user, your own credentials, a visible trace, your own judgment, and an undo key. Production removes them one by one. Engineering them back is what reliability actually means, and most of it is not a modeling problem.Wed, 03 Jun 2026 00:00:00 GMTaiwritinghttps://vamshij.com/writing/coase-vibe-coding/https://vamshij.com/writing/coase-vibe-coding/Vibe coding has not only moved the make-or-buy boundary; it has turned building into a cheap option that reprices the whole decision, even for the core systems the cloud era taught everyone to rent. What should decide it is no longer the falling cost of code but the costs that do not fall with it, amortisation, accountability, data, and optionality.Sat, 30 May 2026 00:00:00 GMTstrategywritinghttps://vamshij.com/mathematics/faulty_traffic_signal/https://vamshij.com/mathematics/faulty_traffic_signal/A 15-second pedestrian signal whose red/green split is itself uniformly random. Closed forms for the probability of red, the expected wait, and the expected total time to cross, each from a one-line integral, with a sample-space picture, an account of length-biasing, and a Monte Carlo check of every result.Fri, 29 May 2026 00:00:00 GMTmathematicshttps://vamshij.com/mathematics/charlottes_web/https://vamshij.com/mathematics/charlottes_web/A circular billiard puzzle by Xavier Durawa: Charlotte's strands reflect inside a circular frame; how many earlier strands does the n-th strand cross on average? A self-contained walk through the geometry, the modular-arithmetic reformulation, the piecewise integration, the antipode trick, and the telescoping sum that lands the exact closed form.Sat, 09 May 2026 00:00:00 GMTmathematicshttps://vamshij.com/writing/agent-ready-financial-data/https://vamshij.com/writing/agent-ready-financial-data/An architectural view of how a financial data provider can make its data ready for autonomous and semi-autonomous agents. Workflow archetypes, the three human-in-the-loop bands, the surfaces (REST, SDK, MCP, agents.md, skills, code-as-action), and why the semantic layer is the product.Sat, 02 May 2026 00:00:00 GMTaiwritinghttps://vamshij.com/mathematics/beautiful-problems/https://vamshij.com/mathematics/beautiful-problems/On the hunt for beautiful olympiad problems, the indignity of badly typeset mathematics on the web, and a small side project to surface AI training datasets back to the human readers the problems were originally written for.Sun, 26 Apr 2026 00:00:00 GMTmathematicshttps://vamshij.com/mathematics/cozy_circles/https://vamshij.com/mathematics/cozy_circles/A puzzle by Xavier Durawa: in a regular polygon, place a circle at the midpoint of each side, tangent to the side and as large as possible without overlap. What fraction of the polygon's area is covered by the n circles?Mon, 21 Apr 2025 00:00:00 GMTmathematicshttps://vamshij.com/notes/2025-04-cozy-circles/https://vamshij.com/notes/2025-04-cozy-circles/Closed form for the ratio of inscribed-circle area to polygon area when circles tangent to each side at its midpoint are maximal.Mon, 21 Apr 2025 00:00:00 GMTnotehttps://vamshij.com/mathematics/apollonian_gasket/https://vamshij.com/mathematics/apollonian_gasket/Constructing the Apollonian gasket fractal from Descartes' Circle Theorem and its complex extension. Includes an elementary algebraic proof, the Lagarias-Mallows-Wilks complex form, and a queue-based Python implementation.Sat, 12 Apr 2025 00:00:00 GMTmathematicshttps://vamshij.com/mathematics/cherry_blossom_puzzle/https://vamshij.com/mathematics/cherry_blossom_puzzle/A geometric-probability puzzle by Xavier Durawa: a random chord across a circle intersects a diameter; given that intersection, what is the expected ratio of the shorter segment of the diameter to the longer?Fri, 04 Apr 2025 00:00:00 GMTmathematicshttps://vamshij.com/mathematics/posidoku/https://vamshij.com/mathematics/posidoku/A Sudoku variant by Alf Smith with no number clues, only positional gold cells whose values must equal their row, column, or box position. Solved with Google's CP-SAT.Mon, 10 Feb 2025 00:00:00 GMTmathematicshttps://vamshij.com/writing/ironies-ai-automation/https://vamshij.com/writing/ironies-ai-automation/Lisanne Bainbridge showed in 1983 that automating a task makes the human who remains more important and less capable at the same time. Every one of her ironies survives the move to AI agents, and two of them get worse.Tue, 10 Dec 2024 00:00:00 GMTaiwritinghttps://vamshij.com/mathematics/jumping_julia/https://vamshij.com/mathematics/jumping_julia/A puzzle from the Julia Robinson Mathematics Festival: navigate from the top-left corner of a grid to the goal cell at the bottom-right, where each cell's number specifies the exact distance you may jump horizontally or vertically to the next cell.Sun, 01 Dec 2024 00:00:00 GMTmathematicshttps://vamshij.com/mathematics/linkedin_tango/https://vamshij.com/mathematics/linkedin_tango/A Z3 solver for LinkedIn's daily Tango puzzle: fill an n×n grid with suns and moons such that no three adjacent cells in any row or column share a symbol; row and column counts are balanced; and pairs of cells linked by = or × constraints match or oppose.Tue, 26 Nov 2024 00:00:00 GMTmathematicshttps://vamshij.com/mathematics/projectile_trajectory/https://vamshij.com/mathematics/projectile_trajectory/At what angle should a projectile be launched, under uniform gravity and no air resistance, so that the arc length of its trajectory is maximised? A standard integral and one implicit equation give the answer.Fri, 01 Nov 2024 00:00:00 GMTmathematicshttps://vamshij.com/mathematics/subsets_consecutive_pair/https://vamshij.com/mathematics/subsets_consecutive_pair/A generating-function argument in which the count is the convolution of Fibonacci numbers; partial fractions over the golden-ratio roots give a closed form involving Fibonacci and Lucas numbers, with f(10) = 235.Tue, 01 Oct 2024 00:00:00 GMTmathematicshttps://vamshij.com/mathematics/die_puzzle/https://vamshij.com/mathematics/die_puzzle/Roll a fair six-sided die until the running total first exceeds 12. What is the most likely final total?Wed, 07 Feb 2024 00:00:00 GMTmathematicshttps://vamshij.com/mathematics/linkedin_queens/https://vamshij.com/mathematics/linkedin_queens/LinkedIn's Queens puzzle: place one queen per row, column, and colour region of an n×n board, with the additional constraint that no two queens touch, not even diagonally.Mon, 01 Jan 2024 00:00:00 GMTmathematicshttps://vamshij.com/writing/catalog-as-query-interface/https://vamshij.com/writing/catalog-as-query-interface/An essay from 2023 arguing that natural-language queries would replace SQL as the primary interface to enterprise data, with the data catalog as the substrate that makes those queries trustworthy. Republished with a 2026 note.Fri, 15 Sep 2023 00:00:00 GMTdatawritinghttps://vamshij.com/writing/llm-apis-the-new-customer/https://vamshij.com/writing/llm-apis-the-new-customer/An essay from 2023 arguing that LLMs would become primary consumers of APIs, that API documentation would become in-demand training data, and that API product managers would soon be designing for a non-human customer. Republished with a 2026 note.Fri, 01 Sep 2023 00:00:00 GMTaiwritinghttps://vamshij.com/mathematics/geometric_expectation_polygon/https://vamshij.com/mathematics/geometric_expectation_polygon/Closed form for the expected distance from the centre of a regular n-gon of unit circumradius, via a Jacobian substitution on one fundamental triangle; three triangle-sampling methods for computational verification.Fri, 18 Dec 2020 00:00:00 GMTmathematicshttps://vamshij.com/mathematics/knights-on-a-chessboard/https://vamshij.com/mathematics/knights-on-a-chessboard/A white knight and a black knight on diagonally opposite corners of a 3×3 square. What is the expected number of moves until the black knight captures the white one? A clean Markov-chain problem with a closed form.Thu, 19 Nov 2020 00:00:00 GMTmathematicshttps://vamshij.com/mathematics/inversion/https://vamshij.com/mathematics/inversion/Inversion in a circle transforms two hard problems about tangent circles into routine ones: a Pappus chain (prove that the height of the n-th circle equals 2n times its radius) and the distance between the circumscribed and inscribed circles of three mutually tangent circles of radii 1, 2, 3.Mon, 08 Jun 2020 00:00:00 GMTmathematicshttps://vamshij.com/mathematics/islamic_geometric_patterns/https://vamshij.com/mathematics/islamic_geometric_patterns/A computational construction of star patterns from the Islamic tradition: translational units, motifs, rosettes, and the rosette dual, implemented in Python with NumPy.Tue, 28 Jan 2020 00:00:00 GMTmathematics