Writing
I write about how software behaves, how businesses decide, and how infrastructure gets paid for.
Featured
Checking Jane Street’s official route
The July 2026 answer is 33,609, and the route ends at 59,400. My Python checker recomputes both from the official route.
An AI megawatt is not a megawatt
The modeled facility fits 402,574 B300 GPUs. Its power date, workload, and customer contract decide what that equipment is worth.
Who owns Austin home services? 14 of 67 were sponsor-backed
Three ownership chains behind familiar Austin names, followed by the 67-brand census.
How airlines borrow against loyalty programs
Recurring partner receipts can support a loan before awards are redeemed. The analogy to GPU contracts stops at fulfillment, renewal and the assets a lender can recover.
Where do online returns go? The route has to earn its cost
In my model, a returned pair of $100 headphones is worth $22.56 after retrieval. The return still costs $77.44 of profit against a kept sale.
The shopkeeper in the machine
Luna’s July token bill left $6 before ordinary retail costs. The shops’ mistakes show what broader AI authority still has to earn.
Who owns Texas toll roads? Public owners, finite private rights
The public owns them, even where a private company collects your toll. On SH 130, a private concession runs the southern two segments.
Further reading
Which company stock can you actually buy?
As of October 26, Anthropic had filed for an IPO and xAI sat inside listed SpaceX. The “LEGO” ticker once belonged to a shell company that merged with a steel maker. The toy company is private.
Texas toll roads: the road can work while the investment fails
Texas agreed to pay $1.73 billion to end SH 288’s concession in 2024. Abertis, which paid about $1.53 billion for 56.76%, got $642.4 million back.
A double-binomial recurrence and its continued fraction
A formal-tail proof of the recurrence behind OEIS A302285, with exact computational checks.
CoreWeave debt: $7.513 billion due within twelve months
A financing commitment buys capacity to borrow. The filing shows the amount already owed and the cash needed to carry it.
GPU depreciation: debt can run past three-year contracts
A longer accounting life lowers annual expense. It does not reduce the lender’s scheduled payment.
Data-center financing: a contract can’t power the site
A signed customer contract can support a loan, but it can’t make an unfinished, unpowered site collect cash.
Data center lease vs. debt: rent adds another clock
Rent can preserve today’s cash while committing tomorrow’s collections. Recognized lease liabilities cover only leases that have started.
SH 130 bankruptcy: the road survived, and its owners changed
Debt paid for 84% of the $1.328 billion project. The company was in Chapter 11 from 2016 to 2017, and drivers kept paying tolls.
NTTA’s $96.2 million cash cushion after debt and capital
The headline 1.64-times coverage adds back maintenance the road still has to pay for. I’d judge NTTA by the cash left after debt and capital spending.
Toll-road bonds: debt coverage can hide the repair bill
Construction gets its money up front. The toll stream has to support the road, its creditors, and its next round of repairs.
Texas toll-road ownership: map, tables and source data
TxDOT runs SH 130’s first four segments, and a private concession runs the last two. Search a Texas toll road for its operator, its billing, and, where sourced, its owner.
When an AI tool call times out, did the action happen?
A lost response leaves an operation uncertain. Durable identity, atomic receipts and a current-state check give the application a defensible recovery path.
Who owns Buc-ee’s? Aplin and Wasek’s private company
Arch “Beaver” Aplin III founded it in 1982 and co-owns it with Don Wasek. The company is private, and so is their exact split.
Who owns Whataburger? BDT-affiliated funds bought the majority
Harmon Dobson opened the first one in Corpus Christi in 1950. After the 2019 sale, the chain kept its San Antonio headquarters.
Is Anthropic profitable? Its $80 billion loss was mostly paper
A $974 million June-quarter operating profit followed an implied $1.667 billion first-quarter operating loss. The first-half net loss tells a different story.
Who owns Chick-fil-A? The Cathy family
The Cathy family owns the private franchisor. Local Owner-Operators run restaurant businesses under its franchise model.
Who owns Texas Roadhouse? TXRH shareholders
The Texas brand began in Indiana and reports from Kentucky. Public shareholders own the parent, while 100 of its 832 restaurants were franchised in June 2026.
Who owns Dairy Queen? Berkshire owns the parent
Berkshire Hathaway bought International Dairy Queen in 1998. Most U.S. and Canadian restaurants are owned and run by independent franchisees.
Who owns ALDI? ALDI Süd runs the U.S. business
ALDI U.S. belongs to ALDI Süd. Trader Joe’s is owned by families that also own part of ALDI Nord, and it says it’s independent of both.
Austin ISD keeps 49 cents of each maintenance-tax dollar
Of the $1.511 billion in maintenance-and-operations taxes Austin ISD booked in FY2025, recapture sent $771.6 million away. Enrollment fell 9.5% over six years, and revenue per student lost ground to inflation.
Five Texas cities’ reserves coexist with long-term deficits
Dallas ended FY2025 with $399.6 million of unassigned General Fund balance and a $4.854 billion deficit once long-term obligations count. Four other big Texas cities show the same split.
Texas business maps: who owns, runs, and finances what
My study of 67 Austin home-service brands follows each to the company behind it. The toll map traces who runs each road, and the robotaxi map shows where you can book a ride.
Is your local contractor still locally owned? How to check
The legal name on the quote starts the trail. Texas filings and acquisition announcements help connect it to a platform and investor.
Divisibility patterns and the size of a witness
A superexponential lower bound for the maximum, an exact family rate, and a universal upper bound. The exact growth remains open.
Two recurrence proofs: a matrix inverse and a binomial transform
An alternating matrix inverse, a formal binomial transform, and two explicit proof requests.
Every ordering, from zeros and ones
One fixed set of inputs. Every possible ordering. A constructive proof with an exact, interactive example.
Anduril is building a prime. The price assumes a platform
I value the operations near $28 billion. The $61 billion price needs $99.5 billion of 2036 sales, about 37% growth a year.
Kalshi’s $40 billion question
Brokers and market makers take a cut of many trades. I value Kalshi’s equity at about $30 billion, below the $40 billion in recent talks.
Hyperliquid valuation: HYPE isn’t cheap at $80
A $30 central case can still assume an excellent business. The difference is what reaches the token, how long growth lasts, and how many claims share it.
Flock Safety: the renewal has to pay for the camera
In my hypothetical base case, 100 cameras collect $300,000 up front and still finish year one $90,000 behind. I’d finance them only if renewals pay that back quickly.
ElevenLabs: what a finished minute is worth
In my hypothetical workflow, a $168 monthly bill frees $1,800 of human time. If half of that becomes cash, the buyer nets $732 a month.
Expedia: the network beyond the booking
Expedia holds travelers’ money before the trip, which flatters its $4.46 billion of free cash flow. Strip out that float and stock pay and I count $2.65 billion. I forecast $360 a share by October 2028, from $268.47.
Crocs: a cash engine with a brand test
Q2 adjusted earnings fell while adjusted EPS rose: buybacks spread less profit over fewer shares. I forecast $165 a share by October 2028, from $116.90.
PayPal: a modest recovery worth buying at $56
Q2 revenue rose $394 million, but transaction-margin dollars rose only $56 million, about 14 cents per added dollar. I forecast $85 by October 2028.
Adobe: paid workflows at a price I like
At its October 12 price of $238.14, Adobe traded at about 10.9 times cash after stock compensation. I forecast $365 by October 2028, if paid renewals hold up.
Texas robotaxis, one trip at a time
In Austin, a Waymo costs the same as an Uber with a driver. I’d approve them in a travel policy, but I’d book committed cars before promising guests a ride to an event.
The Texas driverless truck has to finish the job
My $1,150 quote leaves $123 per accepted load for surprises. The return depends on the dock, the rejected freight, and the bill for recovery.
Vanta after the audit: compliance becomes recurring
The recurring job is maintaining evidence between audits. I model post-audit retention, new ARR and the investment return at the last disclosed financing benchmark.
Does Harvey justify its cost? Modeled break-even: 10.9%
In a hypothetical 100-lawyer firm paying $290,000 in year one, I calculate that about 10.9% of the hours Harvey frees must earn $200 each to break even.
Toast: I want the gross-profit engine near $24
I get $37 a share in three years, just 5.8% a year from $31.29. I’d want an entry near $24 for a 15% return.
Sell the review before you scale the app
The assisted offer wins at $399 and loses at $99. I would sell the first reviews to learn whether the higher price buys a recurring business.
Chegg has bought time
Debt retirement removes a maturity. The new business has replaced about 0.6% of the quarterly revenue lost.
Atlas: what two saved page captures reveal
A local audit console for deciding when to repair a page and when to take another measurement.
Who owns NTTA? A public authority, with nine appointed directors
It’s a public body run by nine directors: two each from Collin, Dallas, Denton, and Tarrant counties, and one from the governor.
Who owns U.S. toll roads? The agreement decides
Chicago leased its Skyway for 99 years and still holds the title. Virginia’s Dulles Greenway is privately owned.
Are Texas toll roads foreign-owned? Only concession stakes
Ferrovial holds a majority of all three Dallas–Fort Worth concession companies: NTE, LBJ, and NTE 35W. The contracts end in 2061, and Texas keeps the highway.
Why Search Console query totals do not match page totals
Anonymized queries, the 1,000-row UI limit, top-row API results and property-versus-page aggregation explain many mismatched totals.
Why Texas toll roads stay tolled after construction
Three years of audited accounts show how system debt, new borrowing, county transfers and concession rights keep tolls in place.
Where the 2020–2022 software buyouts stand
None of 25 selected software take-privates had a clean sponsor exit by August 17, 2026, though investors can still get cash back through continuation funds.
The U.S. magnet buildout is mostly still a project
Plants with disclosed commercial shipments account for 4,000 of 37,750 announced capacity units. I would finance the product and its customers before the national headline.
What happens when an index decides a company matters?
An index addition gives tracking funds a deadline to change their portfolios. Traders can buy ahead and sell into that demand; the fund’s investors carry the risk of any later fall in the share price.
Who keeps the risk in hardware financing?
Loans, leases, and customer prepayments let hardware companies deploy with less equity. When the machines earn less than planned, the contracts decide who takes the loss.
Who funds Waymo’s hardware? Alphabet buys the learning period
Waymo’s disclosed funding was all equity until October 8, when it closed a $5 billion term loan. Lenders now expect repayment, on terms that aren’t public.
A proposed Codex harness for ViralBench
A proposal to improve the marketing agent through saved traces, replay and independent evaluation.
