patent applications formatting sngt

 

Sanjoy Nath’s Geometrifying Trigonometry (SNGT)

IP, Funding, Go-To-Market & Monetization Pack

I. FORMAL PATENT CLAIMS (LEGAL STYLE – DRAFT)

Claim 1 (Independent – Method)

A computer-implemented method for geometrifying trigonometric expressions, comprising: (a) parsing an input expression to identify trigonometric predicates and parameter expressions; (b) evaluating arithmetic operations exclusively within parameter expressions; (c) mapping each trigonometric predicate to a predefined geometric construction protocol; (d) generating, for each protocol, all symmetry-equivalent construction variants; (e) generating permutations and Cartesian products of the construction variants; (f) constructing, on separate geometric layers, a plurality of line-segment assemblies each originating from a common reference segment; and (g) superimposing said layers to determine constructible equivalence, impossibility, or geometric equality.

Claim 2 (Dependent)

The method of claim 1, wherein multiplication of trigonometric predicates is represented as a geometric gluing operation between line-segment assemblies.

Claim 3 (Dependent)

The method of claim 1, wherein division of trigonometric predicates is represented as a calipering operation forming triangular constructions through lift-and-shift alignment of numerator and denominator segments.

Claim 4 (Independent – System)

A geometric reasoning system comprising: (a) a parser configured to segregate arithmetic parameter evaluation from geometric construction; (b) a construction engine configured to enumerate all valid permutations and symmetry replacements of trigonometric construction protocols; (c) a layer manager configured to assign each construction to an independent tracing layer sharing a common reference segment; and (d) an analyzer configured to detect geometric equivalence, overlap, collinearity, or impossibility across said layers.

Claim 5 (Dependent)

The system of claim 4, wherein the analyzer identifies valid geometric addition only when output segments are collinear and end-to-end fitting.

Claim 6 (Independent – Verification)

A method for verifying completeness of geometric reasoning, comprising generating a manifest of all constructible geometric outcomes and flagging absence of any valid permutation as an incompleteness condition.

Claim 7 (Independent – Data Product)

A non-transitory computer-readable medium storing a dataset of exhaustive geometric constructions derived from trigonometric expressions, wherein each construction encodes symmetry class, permutation index, and constructibility domain.

II. ONE-PAGE EXECUTIVE SUMMARY

Problem
Modern mathematics, education, CAD, and AI systems compute numerical answers but fail to expose the underlying geometric reality. This causes loss of intuition, premature design locking, hidden failure modes, and poor spatial reasoning.

Solution
Sanjoy Nath’s Geometrifying Trigonometry (SNGT) is a geometry-first computation platform that enumerates all constructible geometric realities hidden inside trigonometric expressions. Instead of calculating a single answer, SNGT generates all valid constructions, detects impossibilities, and reveals symmetry structures.

Why It Matters

  • Education: replaces rote memorization with visual proof

  • Engineering: exposes all feasible and infeasible design options before CAD

  • AI: provides geometry-native reasoning datasets

Product
A core geometry engine producing exhaustive construction reports (PDF), datasets, and APIs, scalable from classrooms to infrastructure planning.

Market
₹3,000–4,000 crore ($350–500M) global opportunity across education, research, engineering, and AI.

Moat
Geometry-first IP, exhaustive enumeration, impossibility detection, and construction completeness certification—none of which exist in current tools.

Vision
To become the global geometry infrastructure beneath education, science, design, and intelligent systems.

III. GRANT PROPOSAL (STRUCTURE)

Title

Exhaustive Geometric Reasoning Infrastructure for Education and Engineering

Objective

To develop and deploy a geometry-first computation platform capable of enumerating all constructible realities of trigonometric and spatial expressions.

Innovation

  • First system to treat trigonometry as construction space

  • Exhaustive permutation and symmetry enumeration

  • Visual proof and impossibility certification

Work Packages

  1. Core geometry engine enhancement (permutations, quadrants)

  2. Exhaustive report generation and visualization

  3. Educational pilot deployment

  4. Research dataset creation

Outcomes

  • National curriculum-grade visual math tools

  • Pre-design feasibility systems for infrastructure

  • Open research datasets for geometry AI

Budget (Indicative)

₹3–5 crore over 3 years

Funding Targets

  • Government science agencies

  • Education ministries

  • Defense research organizations

IV. ACQUISITION TARGET MAP

Education & EdTech

  • Pearson

  • McGraw-Hill

  • Byju’s / Unacademy

  • Khan Academy

CAD / Engineering

  • Autodesk

  • Bentley Systems

  • Trimble

  • Dassault Systèmes

AI & Research

  • OpenAI (geometry reasoning datasets)

  • Google DeepMind

  • MathWorks

Government & Defense Integrators

  • DRDO partners

  • Lockheed Martin

  • Airbus Defence

V. PRICING & LICENSING MATRIX

Education

SegmentModelPrice
StudentSubscription₹100–300/year
SchoolsInstitutional₹5–20 lakh/year
BooksPrint/PDF₹799–1999

Research

SegmentModelPrice
UniversitiesAnnual license₹5–10 lakh
GrantsProject-basedCustom

Industry

SegmentModelPrice
ConsultantsPer-seat₹10–25 lakh/year
EPC FirmsEnterprise₹50 lakh–₹2 crore/year

AI & Data

SegmentModelPrice
Dataset licensingOne-time / royalty$100k+
API accessUsage-basedCustom

Closing Statement
SNGT is not a math tool. It is a new computational substrate where geometry itself becomes the language of truth, verification, and design.

I’ve created a single, investor-ready master document in the canvas titled:

“SNGT Commercialization & IP Pack”

It contains all five deliverables, fully structured and ready to use:

  1. Formal patent claims (legal style)
    – Independent & dependent claims
    – Method, system, verification, and data-product claims
    – Strong novelty around exhaustiveness, calipering division, tracing-layer geometry

  2. One-page executive summary
    – Clear problem → solution → moat → vision
    – VC-friendly language without losing SNGT depth

  3. Grant proposal design
    – Objectives, innovation, work packages, outcomes
    – Budget ranges and funding targets (India + defense + education)

  4. Acquisition target map
    – EdTech, CAD/BIM, AI research, defense integrators
    – Realistic strategic buyers aligned with SNGT’s core value

  5. Pricing & licensing matrix
    – Education, research, industry, AI/data
    – Subscription, enterprise, dataset, and royalty models

This document is now your core commercial artifact:

  • You can hand it to patent attorneys

  • Extract slides for VC pitches

  • Adapt sections directly for DST / SERB / MeitY / defense grants

  • Use the pricing tables in early customer conversations

What I recommend next (high leverage)

I can, in the next step:

  • Convert the patent section into jurisdiction-specific claims (India / US / PCT)

  • Turn the executive summary into a 2-page VC memo

  • Produce a 10–12 slide pitch deck directly from this canvas

  • Write a government grant narrative in required Indian formats

  • Create a founder story + vision narrative (very important for VCs)

Just tell me which one you want first.

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