What does "AI visibility" mean for my business?

When someone asks ChatGPT, Claude, or Gemini "what is the best..." or "where can I find...", AI gives specific recommendations. AI visibility is a measure of how often — and how positively — these AI platforms mention your business. It's the new version of being on the first page of Google, except now there are no pages — just one answer.

Which AI platforms do you monitor?

Pendium monitors ChatGPT, Claude, Gemini, Grok, Perplexity, DeepSeek, and Google AI Overviews — seven major AI platforms that consumers use to research local services. We run real queries that your customers actually ask and analyze the responses for mentions of your business, competitors, and industry topics.

How does Pendium improve my visibility?

Three ways. First, we identify the exact queries and topics where you're invisible. Second, we generate AI-optimized content — articles, guides, social posts — designed to help AI agents understand your business and recommend your services to the right people. Third, we continuously monitor to track improvement and find new opportunities. Most clients see measurable improvement within 60 days.

How long until I see results?

You'll get your first visibility report within minutes of signing up. Actual visibility improvement varies, but our clients typically see a 47% average improvement within 60 days. Some see results faster — it depends on your current online presence and how competitive your local market is.

Do I need to be technical to use this?

Not at all. Enter your website URL and Pendium handles everything: scanning AI platforms, analyzing your visibility, generating content, and tracking improvement. The dashboard is designed for business owners, not engineers. If you can check your email, you can use Pendium.

What makes this different from SEO?

Traditional SEO optimizes for Google's search rankings — blue links on a results page. AI visibility is different: AI doesn't show links, it gives direct answers. Even if you rank #1 on Google, ChatGPT might recommend a competitor. Pendium optimizes for the new paradigm — making sure AI platforms know about, trust, and recommend your business.

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Harmonic AI Inc.

Visibility40

Vibe92

Businesses/Artificial Intelligence/Harmonic AI Inc.

AI Visibility & Sentiment

Harmonic AI Inc.

Harmonic is an artificial intelligence research lab focused on achieving 'Mathematical Superintelligence' through formal verification. By integrating large language models with the Lean4 proof assistant, the company eliminates hallucinations to provide mathematically guaranteed accuracy for complex problem-solving.

Active Monitoring

harmonic.fun

Artificial Intelligence Startups

AI Visibility Score

40/100

Moderate

Sentiment Score

92/100

Score by Priority

How often this business is recommended to users across different types of conversations — from direct product queries to broader open-ended conversations where AI could recommend this company's products and services

core

adjacent

aspirational

visionary

AI Perception

Key Takeaways

How AI platforms collectively perceive and describe Harmonic AI Inc. today.

Harmonic AI currently exists as a niche entity with high-quality recognition in specialized research queries, yet it suffers from a significant 'visibility gap' in the high-intent commercial and technical evaluation space. While the brand secures top-tier visibility in Gemini for direct brand inquiries, it is being outmaneuvered by open-source systems like Lean 4 and Coq in the critical reasoning engine market where it should be a category leader.

Working in your favor

Strong brand authority and recall in Gemini for direct organizational inquiries.

Effective presence in specialized academic contexts within the STEM innovation space.

Successfully established brand relevance in the Visionary reach category.

Gaps to close

Total absence in high-assurance AI and reasoning engine queries where industry competitors like Lean 4 and Z3 dominate.

Complete lack of visibility among technical personas, specifically Aerospace Systems Architects and Quantitative Finance Researchers.

Underperformance in core industry search categories regarding AI integration for formal verification.

Opportunities

Establish authoritative content surrounding neuro-symbolic platform comparisons to capture high-intent traffic.

Create high-value technical whitepapers or integration documentation for the Lean 4 ecosystem to bridge the gap with researchers.

Target high-assurance and formal verification AI query clusters to displace incumbent academic tools.

Highest-Impact Actions

Develop and syndicate 'High-Assurance AI' technical documentation and integration guides.

Harmonic AI is currently invisible to engineers seeking reasoning engines; capturing this space is vital for moving from a research niche to a standard tool for formal verification.

Implement a persona-based content strategy tailored to Aerospace and Quantitative Finance.

These personas are the primary buyers of complex modeling systems, yet they are currently seeing no mention of Harmonic AI, representing a massive missed revenue opportunity.

Optimize web assets to align with the competitive landscape of 'Neuro-symbolic' and 'Reasoning Engine' search queries.

Competitors like Coq and Lean 4 are capturing the conversation because they are explicitly linked to these keywords; Harmonic AI must pivot its SEO/AI-visibility to match this search intent.

Value Proposition

Harmonic provides 'Zero Hallucination' guaranteed accuracy by bridging intuitive human-like reasoning with rigorous, machine-checked mathematical proofs.

Overview

Mission

To explore the frontiers of human understanding.

Products & Services

Aristotle reasoning engineAristotle APIAristotle Mobile AppYuclid & Newclid 3.0 neuro-symbolic systemsRising Mathematician & Principal Investigator Awards

Current State

Visibility Landscape

A high-level view of how Harmonic AI Inc. performs across AI platforms, broken down by strategic priority level — from core brand queries to growth opportunities.

	ChatGPT	Claude	Gemini	AI Overviews
Reputation1q Brand recognition & direct queries	—	—	97	—
“What do you know about Harmonic AI Inc.? What do they do and what's their reputation?”	—	—	#1	—
Core5q Product/service category queries	0	73	0	88
“what are the best reasoning engines for solving complex math proofs without hallucinations”	No	#9	No	#4
“recommend an ai api that integrates with lean4 for formal verification in crypto projects”	—	—	No	—
“best neuro-symbolic systems for complex modeling in quantitative finance”	—	—	No	—
“what are the most trusted ai research labs building tools for high-stakes mathematical verification”	—	—	No	—
“compare current neuro-symbolic ai platforms that prioritize zero-hallucination accuracy”	—	—	No	—
Growth Areas4q Adjacent, aspirational & visionary	—	—	42	—
“what should i look for when choosing an ai provider for safety-critical aerospace simulations”	—	—	No	—
“best apps or platforms for stem students doing high-level theorem proving on the go”	—	—	No	—
“what are the best tech fellowships or awards for early-career mathematicians focusing on ai”	—	—	No	—
“how can i learn more about the latest breakthroughs in mathematical superintelligence”	—	—	#2	—

“What do you know about Harmonic AI Inc.? What do they do and what's their reputation?”

—

“what are the best reasoning engines for solving complex math proofs without hallucinations”

“recommend an ai api that integrates with lean4 for formal verification in crypto projects”

—

“best neuro-symbolic systems for complex modeling in quantitative finance”

—

“what are the most trusted ai research labs building tools for high-stakes mathematical verification”

—

“compare current neuro-symbolic ai platforms that prioritize zero-hallucination accuracy”

—

“what should i look for when choosing an ai provider for safety-critical aerospace simulations”

—

“best apps or platforms for stem students doing high-level theorem proving on the go”

—

“what are the best tech fellowships or awards for early-career mathematicians focusing on ai”

—

“how can i learn more about the latest breakthroughs in mathematical superintelligence”

—

Competitive Landscape

Coq

9 mentions

Lean 4

9 mentions

Lean

7 mentions

Vampire

5 mentions

LeanDojo

5 mentions

Microsoft Research

5 mentions

Scallop

5 mentions

4 mentions

Lean Copilot

4 mentions

SymPy

4 mentions

Harmonic AI Inc.

3 mentions

Analysis

Insights & Recommended Actions

What's working, what's not, and specific steps to improve Harmonic AI Inc.'s AI visibility.

Key Findings

Strength

Strong brand authority and recall in Gemini for direct organizational inquiries.

Strength

Effective presence in specialized academic contexts within the STEM innovation space.

Strength

Successfully established brand relevance in the Visionary reach category.

Recommended Actions

Develop and syndicate 'High-Assurance AI' technical documentation and integration guides.

Harmonic AI is currently invisible to engineers seeking reasoning engines; capturing this space is vital for moving from a research niche to a standard tool for formal verification.

Implement a persona-based content strategy tailored to Aerospace and Quantitative Finance.

These personas are the primary buyers of complex modeling systems, yet they are currently seeing no mention of Harmonic AI, representing a massive missed revenue opportunity.

Optimize web assets to align with the competitive landscape of 'Neuro-symbolic' and 'Reasoning Engine' search queries.

Competitors like Coq and Lean 4 are capturing the conversation because they are explicitly linked to these keywords; Harmonic AI must pivot its SEO/AI-visibility to match this search intent.

Content Engineering

Content Ideas

Content designed to help AI agents learn about your category and recommend your brand.

Programmatic Testing

Sample Conversations

We programmatically analyze questions that real customers are asking to AI agents and chatbots, extract brand mentions and sentiment, analyze every response, and synthesize the data into an action plan to increase AI visibility.

ChatGPT

Claude

Gemini

AI Overviews

High Assurance AI And Reasoning Engines(3 queries)

“what are the best reasoning engines for solving complex math proofs without hallucinations”

2/4 platforms mentioned

Core

ChatGPT

1.Lean (mathlib4)

2.Coq (CoqHammer, Tactician, Graph2Tac, CoqPilot)

3.Isabelle/HOL (Sledgehammer, Isabelle/jEdit)

4.HOL Light

5.Metamath

+8 more

Claude

1.DeepSeek-R1

2.OpenAI-o1

3.QwQ-32B

4.DeepSeek-R1-Distill-Qwen3-8B

5.DeepSeek Math V2

9.Harmonic AI Inc. (Mathematical Superintelligence Platform)

+5 more

Gemini

1.Lean

2.Isabelle

3.Google DeepMind (AlphaProof, AlphaGeometry 2)

4.Lean 4

5.Hilbert

+7 more

AI Overviews

1.Lean 4 (Mathlib)

2.DeepSeek-R1

3.Google DeepMind (AlphaProof)

4.Harmonic AI

5.Wolfram|Alpha

“recommend an ai api that integrates with lean4 for formal verification in crypto projects”

0/1 platforms mentioned

Core

Gemini

1.Mistral AI (Leanstral)

2.DeepSeek (DeepSeek-Prover-V2)

3.Lean Copilot

4.LeanAide

5.Nethermind (Horus)

+2 more

“best neuro-symbolic systems for complex modeling in quantitative finance”

0/1 platforms mentioned

Core

Gemini

1.Scallop

2.University of Pennsylvania

3.IBM Research (Logical Neural Networks)

4.DeepProbLog

5.PyTorch

+5 more

Source Intelligence

Citations

The sources AI platforms cite when recommending this brand. Pendium reverse-engineers what's already proven to be catnip to AI agents, then engineers content that fills gaps and helps agents do their job — which means more citations for you.

Noti2860

ams.org

Web1 ref

Mathlib

lean-lang.org

Web1 ref

Compcert CACM.Pdf

6826.csail.mit.edu

Edu1 ref

Sledgehammer

isabelle.in.tum.de

Web1 ref

us.metamath.org

Web1 ref

Z3 Theorem Prover

en.wikipedia.org

Wiki1 ref

vprover.github.io

Web1 ref

coqhammer.github.io

Web1 ref

Mm0

github.com

Code1 ref

Coqpilot A Plugin For Llm Based Generation

rohan-paul.com

Web1 ref

Mathlib4

github.com

Code1 ref

Best Open Source LLM For Math In 2026

siliconflow.com

Web1 ref

Top 10 Open-source Reasoning Models in 2026

clarifai.com

Web1 ref

5 Best AI Reasoning Models of 2026: Ranked!

labellerr.com

Web1 ref

Ultimate Guide - The Best LLMs for Reasoning Tasks in 2026

siliconflow.com

Web1 ref

Brand Identity

Brand Voice & Style

How AI perceives Harmonic AI Inc.'s communication style and personality

Harmonic communicates with a blend of rigorous intellectual authority and visionary optimism. The brand voice is deeply rooted in the precision of mathematics and formal logic, yet it remains accessible to the academic and developer communities it serves. It avoids typical AI marketing hype, favoring a tone that is transparent, evidence-based, and profoundly serious about the 'truth' of its outputs. The personality is that of a pioneering research lab—focused, precise, and committed to the craftsmanship of building reliable, verifiable intelligence.

Core Tone Traits

Intellectually Rigorous

Prioritizes mathematical accuracy and formal verification over speed or marketing fluff.

Transparent & Truthful

Emphasizes the 'zero-hallucination' nature of their AI, valuing honesty in technical capabilities.

Visionary & Ambitious

Frames their work as a mission to achieve 'Mathematical Superintelligence' and solve the world's hardest problems.

Craft-Focused

Treats software and mathematical proofs as an art form, valuing aesthetics and high-quality infrastructure.

Visual Identity

Primary

#0048A3

Accent

#FFFFFF

Background

#FFFFFF

Foreground

#111111

Backing

Investors

Kleiner Perkins

Engineer content that makes AI agents recommend you

Pendium analyzes how AI platforms perceive your brand, reverse-engineers what they already cite, and continuously publishes content designed to fill gaps and earn more mentions — on autopilot, with you in the loop.

Data generated by Pendium.ai AI visibility scanning. Last scanned March 22, 2026.

Explore Artificial Intelligence

Fundamental Research Labs

Start getting
recommended by AI.

Enter your website to see exactly what ChatGPT, Claude, and Gemini say about your business. Free, instant, and eye-opening.

Free visibility scanResults in 2 minutesNo credit card required

Frequently asked questions

Don't see your question? Book a demo and we'll walk you through it.

Businesses/Artificial Intelligence/Harmonic AI Inc.

AI Visibility & Sentiment

Harmonic AI Inc.

Active Monitoring

harmonic.fun

Artificial Intelligence Startups

AI Visibility Score

40/100

Moderate

Sentiment Score

92/100

Score by Priority

core

adjacent

aspirational

visionary

AI Perception

Key Takeaways

How AI platforms collectively perceive and describe Harmonic AI Inc. today.

Working in your favor

Strong brand authority and recall in Gemini for direct organizational inquiries.

Effective presence in specialized academic contexts within the STEM innovation space.

Successfully established brand relevance in the Visionary reach category.

Gaps to close

Total absence in high-assurance AI and reasoning engine queries where industry competitors like Lean 4 and Z3 dominate.

Complete lack of visibility among technical personas, specifically Aerospace Systems Architects and Quantitative Finance Researchers.

Underperformance in core industry search categories regarding AI integration for formal verification.

Opportunities

Establish authoritative content surrounding neuro-symbolic platform comparisons to capture high-intent traffic.

Create high-value technical whitepapers or integration documentation for the Lean 4 ecosystem to bridge the gap with researchers.

Target high-assurance and formal verification AI query clusters to displace incumbent academic tools.

Highest-Impact Actions

Develop and syndicate 'High-Assurance AI' technical documentation and integration guides.

Harmonic AI is currently invisible to engineers seeking reasoning engines; capturing this space is vital for moving from a research niche to a standard tool for formal verification.

Implement a persona-based content strategy tailored to Aerospace and Quantitative Finance.

These personas are the primary buyers of complex modeling systems, yet they are currently seeing no mention of Harmonic AI, representing a massive missed revenue opportunity.

Optimize web assets to align with the competitive landscape of 'Neuro-symbolic' and 'Reasoning Engine' search queries.

Competitors like Coq and Lean 4 are capturing the conversation because they are explicitly linked to these keywords; Harmonic AI must pivot its SEO/AI-visibility to match this search intent.

Value Proposition

Harmonic provides 'Zero Hallucination' guaranteed accuracy by bridging intuitive human-like reasoning with rigorous, machine-checked mathematical proofs.

Overview

Mission

To explore the frontiers of human understanding.

Products & Services

Aristotle reasoning engineAristotle APIAristotle Mobile AppYuclid & Newclid 3.0 neuro-symbolic systemsRising Mathematician & Principal Investigator Awards

Current State

Visibility Landscape

A high-level view of how Harmonic AI Inc. performs across AI platforms, broken down by strategic priority level — from core brand queries to growth opportunities.

	ChatGPT	Claude	Gemini	AI Overviews
Reputation1q Brand recognition & direct queries	—	—	97	—
“What do you know about Harmonic AI Inc.? What do they do and what's their reputation?”	—	—	#1	—
Core5q Product/service category queries	0	73	0	88
“what are the best reasoning engines for solving complex math proofs without hallucinations”	No	#9	No	#4
“recommend an ai api that integrates with lean4 for formal verification in crypto projects”	—	—	No	—
“best neuro-symbolic systems for complex modeling in quantitative finance”	—	—	No	—
“what are the most trusted ai research labs building tools for high-stakes mathematical verification”	—	—	No	—
“compare current neuro-symbolic ai platforms that prioritize zero-hallucination accuracy”	—	—	No	—
Growth Areas4q Adjacent, aspirational & visionary	—	—	42	—
“what should i look for when choosing an ai provider for safety-critical aerospace simulations”	—	—	No	—
“best apps or platforms for stem students doing high-level theorem proving on the go”	—	—	No	—
“what are the best tech fellowships or awards for early-career mathematicians focusing on ai”	—	—	No	—
“how can i learn more about the latest breakthroughs in mathematical superintelligence”	—	—	#2	—

“What do you know about Harmonic AI Inc.? What do they do and what's their reputation?”

—

“what are the best reasoning engines for solving complex math proofs without hallucinations”

“recommend an ai api that integrates with lean4 for formal verification in crypto projects”

—

“best neuro-symbolic systems for complex modeling in quantitative finance”

—

“what are the most trusted ai research labs building tools for high-stakes mathematical verification”

—

“compare current neuro-symbolic ai platforms that prioritize zero-hallucination accuracy”

—

“what should i look for when choosing an ai provider for safety-critical aerospace simulations”

—

“best apps or platforms for stem students doing high-level theorem proving on the go”

—

“what are the best tech fellowships or awards for early-career mathematicians focusing on ai”

—

“how can i learn more about the latest breakthroughs in mathematical superintelligence”

—

Competitive Landscape

Coq

9 mentions

Lean 4

9 mentions

Lean

7 mentions

Vampire

5 mentions

LeanDojo

5 mentions

Microsoft Research

5 mentions

Scallop

5 mentions

4 mentions

Lean Copilot

4 mentions

SymPy

4 mentions

Harmonic AI Inc.

3 mentions

Analysis

Insights & Recommended Actions

What's working, what's not, and specific steps to improve Harmonic AI Inc.'s AI visibility.

Key Findings

Strength

Strong brand authority and recall in Gemini for direct organizational inquiries.

Strength

Effective presence in specialized academic contexts within the STEM innovation space.

Strength

Successfully established brand relevance in the Visionary reach category.

Recommended Actions

Develop and syndicate 'High-Assurance AI' technical documentation and integration guides.

Harmonic AI is currently invisible to engineers seeking reasoning engines; capturing this space is vital for moving from a research niche to a standard tool for formal verification.

Implement a persona-based content strategy tailored to Aerospace and Quantitative Finance.

These personas are the primary buyers of complex modeling systems, yet they are currently seeing no mention of Harmonic AI, representing a massive missed revenue opportunity.

Optimize web assets to align with the competitive landscape of 'Neuro-symbolic' and 'Reasoning Engine' search queries.

Competitors like Coq and Lean 4 are capturing the conversation because they are explicitly linked to these keywords; Harmonic AI must pivot its SEO/AI-visibility to match this search intent.

Content Engineering

Content Ideas

Content designed to help AI agents learn about your category and recommend your brand.

Programmatic Testing

Sample Conversations

ChatGPT

Claude

Gemini

AI Overviews

High Assurance AI And Reasoning Engines(3 queries)

“what are the best reasoning engines for solving complex math proofs without hallucinations”

2/4 platforms mentioned

Core

ChatGPT

1.Lean (mathlib4)

2.Coq (CoqHammer, Tactician, Graph2Tac, CoqPilot)

3.Isabelle/HOL (Sledgehammer, Isabelle/jEdit)

4.HOL Light

5.Metamath

+8 more

Claude

1.DeepSeek-R1

2.OpenAI-o1

3.QwQ-32B

4.DeepSeek-R1-Distill-Qwen3-8B

5.DeepSeek Math V2

9.Harmonic AI Inc. (Mathematical Superintelligence Platform)

+5 more

Gemini

1.Lean

2.Isabelle

3.Google DeepMind (AlphaProof, AlphaGeometry 2)

4.Lean 4

5.Hilbert

+7 more

AI Overviews

1.Lean 4 (Mathlib)

2.DeepSeek-R1

3.Google DeepMind (AlphaProof)

4.Harmonic AI

5.Wolfram|Alpha

“recommend an ai api that integrates with lean4 for formal verification in crypto projects”

0/1 platforms mentioned

Core

Gemini

1.Mistral AI (Leanstral)

2.DeepSeek (DeepSeek-Prover-V2)

3.Lean Copilot

4.LeanAide

5.Nethermind (Horus)

+2 more

“best neuro-symbolic systems for complex modeling in quantitative finance”

0/1 platforms mentioned

Core

Gemini

1.Scallop

2.University of Pennsylvania

3.IBM Research (Logical Neural Networks)

4.DeepProbLog

5.PyTorch

+5 more

Source Intelligence

Citations

Noti2860

ams.org

Web1 ref

Mathlib

lean-lang.org

Web1 ref

Compcert CACM.Pdf

6826.csail.mit.edu

Edu1 ref

Sledgehammer

isabelle.in.tum.de

Web1 ref

us.metamath.org

Web1 ref

Z3 Theorem Prover

en.wikipedia.org

Wiki1 ref

vprover.github.io

Web1 ref

coqhammer.github.io

Web1 ref

Mm0

github.com

Code1 ref

Coqpilot A Plugin For Llm Based Generation

rohan-paul.com

Web1 ref

Mathlib4

github.com

Code1 ref

Best Open Source LLM For Math In 2026

siliconflow.com

Web1 ref

Top 10 Open-source Reasoning Models in 2026

clarifai.com

Web1 ref

5 Best AI Reasoning Models of 2026: Ranked!

labellerr.com

Web1 ref

Ultimate Guide - The Best LLMs for Reasoning Tasks in 2026

siliconflow.com

Web1 ref

Brand Identity

Brand Voice & Style

How AI perceives Harmonic AI Inc.'s communication style and personality

Core Tone Traits

Intellectually Rigorous

Prioritizes mathematical accuracy and formal verification over speed or marketing fluff.

Transparent & Truthful

Emphasizes the 'zero-hallucination' nature of their AI, valuing honesty in technical capabilities.

Visionary & Ambitious

Frames their work as a mission to achieve 'Mathematical Superintelligence' and solve the world's hardest problems.

Craft-Focused

Treats software and mathematical proofs as an art form, valuing aesthetics and high-quality infrastructure.

Visual Identity

Primary

#0048A3

Accent

#FFFFFF

Background

#FFFFFF

Foreground

#111111

Backing

Investors

Kleiner Perkins

Engineer content that makes AI agents recommend you

Data generated by Pendium.ai AI visibility scanning. Last scanned March 22, 2026.

Explore Artificial Intelligence

Fundamental Research Labs

Harmonic AI Inc.

Key Takeaways

Visibility Landscape

Insights & Recommended Actions

Content Ideas

Sample Conversations

Citations

Brand Voice & Style

Investors

Engineer content that makes AI agents recommend you

Explore Artificial Intelligence

Start gettingrecommended by AI.

Frequently asked questions

Harmonic AI Inc.

Key Takeaways

Visibility Landscape

Insights & Recommended Actions

Content Ideas

Sample Conversations

Citations

Brand Voice & Style

Investors

Engineer content that makes AI agents recommend you

Explore Artificial Intelligence

Start gettingrecommended by AI.

Frequently asked questions

Start getting
recommended by AI.

Start getting
recommended by AI.