The person behind /teal-sea

Thomas
Lince.

Thomas Lince
Good to meet you.

I take products from first idea to launch, own the results, and build systems that take work off your hands.

Explore the workTalk through an idea
/teal-seaA study in waves
Forty-eight teal ribbons forming a sea of waves
Forty-eight waves.

From the workshop

Selected work.
Built to be used. Made to be explored.

An independent productMusic, theory & software

Modal Runs

Less thinking about playing.
More playing.

A guitar app that hears what you play, shows where you are, and gives you a musical world to explore. I built it from the theory and sound engine through the product around them.

Try Modal Runs
Modal Runs scale explorer showing all C Ionian notes and intervals across fifteen frets
Live pitch detectionGenerative audioGuided practice
Play a mode right hereSame notes, seven musical homes
One set of notes. Seven ways to hear them.Interactive study
modeD DoriannotesC D E F G A Bplayingthe mode

Tap a note to hear it, or use Tab and Enter. Play sound runs through the scale.

From music theory to a product you can play.

Talk through a product idea
Independent research Public research & proofs

Zeta Lab

An AI research lab.
With a theorem
to show for it.

I built a research environment where AI agents explore mathematics and proof kernels check the results. The work includes a formally checked extension of Anthropic's zeta result.

Explore the labSource & research
A landscape of the zeta function
Height shows sampled log magnitude, clipped for display. The orange curve follows the sampled column nearest σ = ½. Explore the function here; the proved result is reported separately.
Four-point certificate proved in Lean
67.28470%
At least this proportion of zeta zeros are simple and on the critical line, as an asymptotic lower bound.Lean × NanoDaIndependently rebuilt

Built on Furman & Alpöge's work at Anthropic: 67.25007% to 67.28470%, an extension of 0.03463 percentage points. The earlier advance from 41.6% to 67.25% is theirs.

What does this mean, in plain English?

Zeta Lab is where I build tools for AI agents to explore mathematics. The agents propose ideas; proof-checking software checks the formal results. The number above is one verified extension of earlier research, with the original work credited alongside it. It does not prove the Riemann Hypothesis.

  1. 01 / Explore

    Agents work in parallel.

    They propose mathematical ideas and test candidates.

  2. 02 / Formalize

    A claim becomes a proof.

    The formal statement and its proof are written in Lean.

  3. 03 / Check

    The kernels check it.

    Lean and NanoDa independently rebuild the registered result.

Explore the critical lineAn interactive numerical study
ζ(½ + it) / Hardy's ZComputed here
t10.0 to 70.0zeros in view0found0

Each dot is a sign change of Hardy's Z, computed in your browser. This numerical study is separate from the formal proof. The registered result is a verified asymptotic bound, not a proof of the Riemann Hypothesis; kernel checking is separate from peer review.

AI research tools. Agents exploring ideas. Results you can check.

Talk about the research

AI in production

AI answers the call.
Software follows through.

Since 2025, voice agents I built have answered the phone for a limo brokerage in two US markets. The agent quotes from live rate logic, places the card hold, and hands the booking to a person for review. Real customers, real money, three in the morning included.

In production, not a demo. I ran that operation from 2019 before I wrote the software that runs it.

Read the case study
01

AI handles the conversationCalls and customer questions

02

Software prepares the next stepQuotes, bookings, payment state

03

People make the final callReview, exceptions, fulfillment

SYSTEM / 01
The AI handles the call. Your team takes it from there.6 connected stages
Software prepares · 01–04 People decide · 05–06
Selected stage
quote

Pricing comes from business rate logic. The conversation does not invent the price.

The record at this stage
Request
Incoming question
Booking
Not yet prepared
Next owner
AI agent
Request
Trip details
Open fields
Still need an answer
Next step
Business pricing
Price source
Business rate rules
Availability
Must be established
Next step
Card authorization
Payment action
Authorize funds
Capture
A separate action
Next owner
Human reviewer
Decision
Made by a person
Exceptions
Available for review
Next owner
Fulfillment team
Owner
Human team
Context
Conversation + booking
Work
Coordinate fulfillment
Refuse before improvising.When the system cannot establish an answer, a person gets the question.
When certainty endsThe system has a stopping point.Six conditions. Six deliberate responses.
  1. G1
    Availability is unconfirmedKeep the booking unconfirmed. Ask a person to establish capacity.
    No invented availability
  2. G2
    A payment result is missingRead the payment provider’s state. A conversation cannot mark it paid.
    Provider is authoritative
  3. G3
    Business configuration is missingSurface what is missing. Stop the lookup instead of substituting a default.
    Unknown stays unknown
  4. G4
    The same action is retriedIdentify the original request before repeating an external action.
    Prevent duplicates
  5. G5
    An external service takes too longStop waiting at the deadline. Return the failure for the next decision.
    Explicit timeout
  6. G6
    The model claims something is trueCheck the business record before that claim can drive an action.
    Verify before acting
01 / Semantic · what is true
One shared record.

The same booking, read by people and agents.

CustomerBookingVehiclePayment
02 / Kinetic · who may act
One permission check.
PersonAI agentSame access rules

Neither gets a private copy of reality or a shortcut around permissions.

03 / Rulebooks · business policy
Change the rule in one place.

Client-specific policy lives outside the prompt and workflow.

DepositsOperating hoursBusiness exceptions

Architecture illustration. A card hold is not a payment capture. Review and fulfillment stay with people.

Explore any stage

01 / The operation

The AI takes the call.
The system prepares the booking.

The caller speaks to an AI agent. Software looks up rates, prepares a quote, and records the booking and card hold for the team to review.

Each step has a job, a record, and a clear next owner.

Scroll to explore the system

02 / The constraints

A confident wrong answer
is an expensive answer.

The agent needs a way to stop. It cannot invent availability or treat a spoken promise as a successful payment.

Six constraints keep business decisions tied to what the system can establish.

03 / The foundation

One shared truth.
For people and agents.

The booking, the permissions, and the business rules live outside the conversation. People and agents work from the same record.

Business policy changes in one place. It does not have to be rewritten into every prompt.

From the workWhy your AI startup dies at customer six

Put an AI agent to work in your business.

Plan my AI assistant

When I close the laptop

Good. Bad. Meh. Magic.

Bruno, a tricolor Sheltie, sitting in sunlit grass
BrunoBrutus Maximus Aurelius

At some point I sorted 168 GarageBand and Logic projects into four folders: Good, Bad, Meh, and Magic. It turns out 65% of the files with a key attached are in A minor or C major. Yep. I feel seen.

I've played guitar for more than 25 years. I improvise blues and space rock, mess with electronic music, study because I enjoy it, and generally follow whatever gives me dopamine at the moment.

Bruno is my one-year-old tricolor Sheltie. His full imperial name is Brutus Maximus Aurelius. He is used to long walks. I love him.

Ask me anything

The next thing starts with a conversation

Let's make
something happen.

A new product. A shared venture. An ambitious idea.
Or just a conversation we should have.

What's on your mind?

Build togetherWork togetherBack the workJust say hello

I'm looking for good people and ambitious work. Tell me what you have in mind.

LinkedInGitHub

Elsewhere in the work

Smaller tools, proofs, and things I've written.

Into the FlowA vortex opens up. A thirty-second film with music. Hardy's Z in mathlibA proposed formal definition in Lean 4 grounded-checkCheck a voice agent's claims against its tool results Why your AI startup dies at customer sixThe essay behind the three-layer architecture convai-webhook-guardAuthenticate incoming post-call webhooks omission-checkFind what an agent was supposed to do and never did