> ## Documentation Index > Fetch the complete documentation index at: https://hotchilianalyticsllc.mintlify.site/llms.txt > Use this file to discover all available pages before exploring further. # Methodology > The science behind multimodal verification and probabilistic scoring # VerityNgn Methodology Documentation **Version 1.0** | **Last Updated:** October 23, 2025 *** ## Executive Summary VerityNgn is a multimodal AI-powered video verification system that analyzes YouTube videos to assess the truthfulness of claims made within them. The system combines cutting-edge multimodal LLM analysis, counter-intelligence techniques, and probabilistic reasoning to generate comprehensive truthfulness reports. **Core Innovation:** VerityNgn is the first system to combine: 1. Frame-by-frame multimodal video analysis (1 FPS sampling) 2. YouTube counter-intelligence (analyzing review videos for contradictory evidence) 3. Press release bias detection and penalty system 4. Probabilistic truthfulness assessment with evidence weighting *** ## Table of Contents 1. [System Architecture](#system-architecture) 2. [Multimodal Analysis Pipeline](#multimodal-analysis-pipeline) 3. [Claims Extraction Methodology](#claims-extraction-methodology) 4. [Counter-Intelligence System](#counter-intelligence-system) 5. [Probability Distribution Model](#probability-distribution-model) 6. [Evidence Classification & Weighting](#evidence-classification--weighting) 7. [Verification Algorithm](#verification-algorithm) 8. [Report Generation](#report-generation) 9. [Limitations & Future Work](#limitations--future-work) *** ## 1. System Architecture ### Overview VerityNgn follows a pipeline architecture with six main stages: ``` ┌─────────────────────────────────────────────────────┐ │ Stage 1: Video Download & Preprocessing │ │ - YouTube URL validation │ │ - Video metadata extraction │ │ - Transcript extraction │ └────────────┬────────────────────────────────────────┘ │ ▼ ┌─────────────────────────────────────────────────────┐ │ Stage 2: Multimodal Analysis │ │ - Frame-by-frame video analysis (1 FPS) │ │ - Audio transcription with timestamps │ │ - OCR for visual text extraction │ │ - Claims extraction (5-15 claims per video) │ └────────────┬────────────────────────────────────────┘ │ ▼ ┌─────────────────────────────────────────────────────┐ │ Stage 3: Counter-Intelligence Gathering │ │ - YouTube review search │ │ - Contradictory evidence detection │ │ - Press release identification │ └────────────┬────────────────────────────────────────┘ │ ▼ ┌─────────────────────────────────────────────────────┐ │ Stage 4: Claims Verification │ │ - Web search for supporting evidence │ │ - Evidence classification & weighting │ │ - Source credibility assessment │ └────────────┬────────────────────────────────────────┘ │ ▼ ┌─────────────────────────────────────────────────────┐ │ Stage 5: Probability Calculation │ │ - Multi-factor probability distribution │ │ - Counter-intelligence adjustments │ │ - Evidence quality boosts │ │ - Normalization & mapping to verdicts │ └────────────┬────────────────────────────────────────┘ │ ▼ ┌─────────────────────────────────────────────────────┐ │ Stage 6: Report Generation │ │ - HTML, Markdown, and JSON formats │ │ - Evidence compilation │ │ - Detailed explanations │ │ - Source attribution │ └─────────────────────────────────────────────────────┘ ``` ### Technology Stack * **Multimodal LLM:** Google Gemini 2.5 Flash (via Vertex AI) * **Context Window:** 64K tokens for comprehensive analysis * **Video Processing:** yt-dlp for video download and metadata * **Web Search:** Google Custom Search API * **Framework:** LangGraph for workflow orchestration * **Storage:** Local filesystem or Google Cloud Storage *** ## 2. Multimodal Analysis Pipeline ### Video Processing Strategy VerityNgn uses an **aggressive frame-sampling approach**: ```python theme={null} SAMPLING_RATE = 1 FPS # 1 frame per second TARGET_CLAIMS = 3 per minute of video CONTEXT_WINDOW = 64K tokens (Gemini 2.5 Flash) ``` ### Frame-by-Frame Analysis For each frame, the system analyzes: 1. **Visual Content:** * On-screen text and graphics * Demonstrations and visual evidence * Charts, graphs, and data visualizations * Product displays or examples 2. **Audio Track:** * Spoken statements with timestamps * Speaker identification * Tone and delivery analysis 3. **Metadata:** * Video title and description * Channel information * Upload date and view count * Comments and engagement metrics ### CRAAP Criteria Integration All claims are evaluated using the CRAAP framework: * **Currency:** When was the information published? * **Relevance:** Is it relevant to the video's main message? * **Authority:** What credentials or expertise is claimed? * **Accuracy:** Can it be verified with external sources? * **Purpose:** Is it promotional, educational, or persuasive? ### Prompt Engineering The system uses carefully crafted prompts to ensure high-quality claim extraction: ``` CRITICAL INSTRUCTIONS FOR MULTIMODAL VIDEO ANALYSIS: - Analyze this video with MAXIMUM detail at 1 FRAME PER SECOND sampling rate - Extract ALL factual claims, statements, assertions from ACTUAL VIDEO CONTENT - Focus on SPOKEN WORDS, VISUAL TEXT, ON-SCREEN GRAPHICS, and DEMONSTRATIONS - Ignore background music, decorative elements, or irrelevant visuals - Extract EXACTLY 5-15 specific, verifiable claims ``` **Claim Mix Requirements:** * 70% Scientific & Verifiable Claims (studies, statistics, product effectiveness) * 10% Speaker Credibility Claims (credentials, affiliations, experience) * 20% Other Verifiable Claims (dates, locations, specific statements) ### Output Format Claims are extracted in structured JSON: ```json theme={null} { "claim_text": "Dr. X has 20 years of experience in endocrinology", "timestamp": "02:15", "speaker": "Dr. X (Narrator)", "source_type": "spoken", "initial_assessment": "Verifiable credential claim requiring external verification" } ``` *** ## 3. Claims Extraction Methodology ### Claim Quality Criteria Each extracted claim must meet these requirements: 1. **Specificity:** Concrete, not vague or general 2. **Verifiability:** Can be checked against external sources 3. **Relevance:** Central to the video's message 4. **Factuality:** Stated as fact, not opinion 5. **Significance:** Meaningful for truthfulness assessment ### Claim Types **Primary Claims (70%):** * Study results: "Study X found Y outcome" * Statistics: "75% of patients experienced Z" * Product effectiveness: "Product causes W in N days" * Scientific findings: "Research shows..." **Secondary Claims (10%):** * Educational credentials: "Dr. X studied at Y" * Professional experience: "X years in field" * Institutional affiliations: "Works at Hospital Y" * Awards and recognitions **Other Claims (20%):** * Historical facts * Geographic information * Temporal data * Specific events or occurrences ### Anti-Patterns (Avoided) The system explicitly avoids: * Vague motivational statements * General health advice without specifics * Obvious facts not requiring verification * Micro-claims too granular for meaningful assessment * Subjective opinions without factual basis *** ## 4. Counter-Intelligence System ### Overview VerityNgn's counter-intelligence system is designed to detect and weight **contradictory evidence** that challenges claims made in the analyzed video. This is one of the system's most innovative features. ### Two-Pronged Approach #### A. Press Release Detection **Purpose:** Identify self-promotional content that lacks independent validation. **Detection Method:** ```python theme={null} PRESS_RELEASE_INDICATORS = [ 'prnewswire.com', 'businesswire.com', 'globenewswire.com', 'prnewswire', 'marketwired', 'accesswire', 'prweb.com', 'press release', 'newswire', 'press statement' ] ``` **Bias Application:** * **Probability Adjustment:** -0.4 (significant negative bias) * **Rationale:** Press releases are promotional, not independent verification * **Distribution Impact:** * Reduce TRUE by 60% of adjustment * Increase FALSE by 40% of adjustment * Increase UNCERTAIN by 40% of adjustment **Example:** ``` Claim: "Product X causes 15 pounds of weight loss" Evidence: 5 press releases from product manufacturer Result: TRUE probability reduced by 24% (0.4 * 0.6) FALSE probability increased by 16% (0.4 * 0.4) UNCERTAIN increased by 16% (0.4 * 0.4) ``` #### B. YouTube Counter-Intelligence **Purpose:** Find and analyze review videos that contradict claims in the original video. **Search Strategy:** ```python theme={null} COUNTER_INTEL_QUERIES = [ "{video_title} scam review", "{video_title} fake exposed", "{video_title} debunk analysis", "{main_keywords} + warning review", "{product_name} doesn't work" ] ``` **Transcript Analysis:** The system analyzes transcripts of review videos for: 1. **Counter-Signals:** * 'scam', 'fake', 'fraud', 'lie', 'misleading' * 'doesn't work', 'waste of money', 'no results' * 'red flags', 'warning', 'beware', 'avoid' * 'overpriced', 'overhyped', 'disappointing' * 'fabricated', 'deceptive', 'predatory', 'exposed' 2. **Supporting Signals:** * 'works', 'effective', 'results', 'recommend' * 'good', 'helps', 'success', 'positive' * 'beneficial', 'worth it', 'legit' **Stance Determination:** ```python theme={null} counter_ratio = counter_signals / (counter_signals + supporting_signals) if counter_ratio > 0.7: stance = 'counter' confidence = min(0.95, 0.6 + (counter_ratio - 0.7) * 1.17) elif counter_ratio < 0.3: stance = 'supporting' confidence = min(0.95, 0.6 + (0.3 - counter_ratio) * 1.17) else: stance = 'neutral' confidence = 0.5 ``` **Credibility Weighting:** Counter-intelligence evidence is weighted by: * **View Count:** Videos with 100K+ views = stronger signal * **Channel Credibility:** Established channels weighted higher * **Video Age:** Recent videos weighted higher * **Engagement:** Like ratio and comment sentiment **Probability Impact:** YouTube counter-intelligence has **reduced** impact compared to earlier versions: ```python theme={null} # Enhanced (balanced) approach: youtube_impact = min(0.20, youtube_counter_power * 0.08) enhanced_dist["FALSE"] = min(0.85, base_false + youtube_impact) # Reduction rationale: Avoid over-aggressive FALSE bias # Previous: max 0.35 impact, max 0.9 FALSE # Current: max 0.20 impact, max 0.85 FALSE ``` ### Counter-Intelligence in Action **Example Case:** ``` Original Video: "Amazing weight loss supplement - lose 15 pounds!" Counter-Intelligence Found: 1. "Product X Scam Exposed" (450K views) - Counter stance (90% confidence) 2. "I Tried Product X - My Honest Review" (120K views) - Counter stance (85% confidence) 3. "Product X Doesn't Work - Warning" (75K views) - Counter stance (80% confidence) Impact: - Base FALSE probability: 30% - YouTube CI adjustment: +12% (0.12 based on reach and confidence) - Final FALSE probability: 42% ``` *** ## 5. Probability Distribution Model ### Three-State Model VerityNgn uses a probabilistic approach rather than binary true/false: ``` P(TRUE) + P(FALSE) + P(UNCERTAIN) = 1.0 ``` ### Base Probability Initialization ```python theme={null} base_dist = { "TRUE": 0.3, # Starting assumption: neutral "FALSE": 0.3, # Equal weight to false "UNCERTAIN": 0.4 # Highest initial uncertainty } ``` ### Enhancement Factors The base distribution is adjusted based on five key factors: #### Factor 1: Evidence Coverage (10-30% boost) ```python theme={null} coverage_score = evidence_count / (claim_word_count / 5) if coverage_score > 1.0: boost = min(0.3, coverage_score * 0.15) enhanced_dist["TRUE"] += boost ``` **Rationale:** More evidence per claim indicates stronger validation. #### Factor 2: Independent Source Ratio (10-25% boost) ```python theme={null} independent_ratio = independent_sources / total_sources if independent_ratio > 0.5: boost = min(0.25, (independent_ratio - 0.5) * 0.5) enhanced_dist["TRUE"] += boost ``` **Rationale:** Independent sources provide unbiased validation. #### Factor 3: Scientific Evidence (up to 40% boost) ```python theme={null} science_weight = min(0.4, scientific_power * 0.2) enhanced_dist["TRUE"] += science_weight ``` **Rationale:** Scientific sources (journals, academic institutions) carry highest weight. #### Factor 4: YouTube Counter-Intelligence (-20% impact) ```python theme={null} youtube_impact = min(0.20, youtube_counter_power * 0.08) enhanced_dist["FALSE"] += youtube_impact ``` **Rationale:** Contradictory reviews reduce claim trustworthiness. #### Factor 5: Press Release Penalty (-40% impact) ```python theme={null} self_ref_count = count_self_referential_sources() penalty = min(0.4, self_ref_count * 0.15) enhanced_dist["FALSE"] += penalty ``` **Rationale:** Self-promotional content is inherently biased. ### Normalization After all adjustments, probabilities are normalized: ```python theme={null} total = sum(enhanced_dist.values()) if total > 0: enhanced_dist = {k: v / total for k, v in enhanced_dist.items()} # Ensure minimum thresholds for key in ["TRUE", "FALSE", "UNCERTAIN"]: enhanced_dist[key] = max(0.001, enhanced_dist[key]) ``` ### Verdict Mapping The continuous probabilities are mapped to human-readable verdicts: ```python theme={null} TRUE% = P(TRUE) * 100 FALSE% = P(FALSE) * 100 UNCERTAIN% = P(UNCERTAIN) * 100 if TRUE \> 70 and FALSE \< 10: verdict = "HIGHLY_LIKELY_TRUE" elif (TRUE + UNCERTAIN) \> 65 and FALSE \< 35: verdict = "LIKELY_TRUE" elif TRUE \> 40 and FALSE \< 35: verdict = "LEANING_TRUE" elif abs(TRUE - FALSE) \< 10: verdict = "UNCERTAIN" elif FALSE \> 35 and TRUE \< 30: verdict = "LEANING_FALSE" elif (FALSE + UNCERTAIN) \> 65 and TRUE \< 35: verdict = "LIKELY_FALSE" elif FALSE \> 75: verdict = "HIGHLY_LIKELY_FALSE" ``` **Rationale for Thresholds:** * 65% threshold for "likely" verdicts (relaxed from 70% to avoid over-conservatism) * 70% threshold for "highly likely" verdicts * Combination with UNCERTAIN allows for nuanced assessment *** ## 6. Evidence Classification & Weighting ### Source Categories Evidence is classified into six categories, each with distinct validation power: #### 1. Scientific Sources (Highest Weight: 2.5-4.0) **Characteristics:** * Peer-reviewed journals * Academic institutions (.edu domains) * Research papers and studies * Government research agencies **Examples:** * PubMed/NCBI publications * Journal articles (Nature, Science, NEJM) * University research papers * NIH/CDC reports **Validation Power:** 2.5 - 4.0 (highest) #### 2. Independent Sources (High Weight: 1.5-2.0) **Characteristics:** * Reputable news organizations * Fact-checking organizations * Independent analysis * No financial stake in outcome **Examples:** * Reuters, AP News, BBC * FactCheck.org, Snopes, PolitiFact * Independent medical websites (Mayo Clinic, WebMD) **Validation Power:** 1.5 - 2.0 #### 3. Government Sources (High Weight: 1.5-2.5) **Characteristics:** * .gov domains * Official government publications * Regulatory agency reports **Examples:** * FDA reports * CDC guidelines * NIH publications * FTC consumer alerts **Validation Power:** 1.5 - 2.5 #### 4. Press Releases (Negative Weight: -0.5 to -1.0) **Characteristics:** * Self-promotional content * Newswire services * Company press statements * Marketing materials **Examples:** * PR Newswire articles * Business Wire releases * Company blog posts * Marketing pages **Validation Power:** -0.5 to -1.0 (penalized) #### 5. YouTube Counter-Intelligence (Variable: 0.5-2.0) **Characteristics:** * Review videos * Debunking content * Investigation videos * Consumer experiences **Weight Determined By:** * View count (100K+ = higher weight) * Channel credibility * Stance confidence * Counter-signal strength **Validation Power:** 0.5 - 2.0 (variable) #### 6. Other Web Sources (Standard Weight: 1.0) **Characteristics:** * General web pages * Blogs * Forums * Social media **Validation Power:** 1.0 (baseline) ### Self-Referential Detection The system identifies "self-referential" sources that cite the original video or its creators: ```python theme={null} def is_self_referential(source_url, source_text, video_title, video_channel): # Check if source cites the original video if video_title.lower() in source_text.lower(): return True if video_channel.lower() in source_text.lower(): return True if source_url contains video_domain: return True return False ``` Self-referential sources are: * Separated into `press_releases` category * Given negative validation power * Excluded from supporting evidence counts *** ## 7. Verification Algorithm ### Claim Verification Process For each extracted claim, the system follows this process: ``` 1. Generate search queries ├─ Fact-check queries: "{claim} fact check" ├─ Scientific queries: "{claim} study research" ├─ General queries: exact claim text └─ Debunk queries: "{claim} debunk false" 2. Execute web searches ├─ Google Custom Search API ├─ Retrieve top 10 results per query └─ Extract URL, title, snippet 3. Classify evidence ├─ Identify source category ├─ Assign validation power ├─ Detect self-referential content └─ Determine supporting vs contradicting 4. Calculate probability distribution ├─ Start with base distribution ├─ Apply evidence boosts ├─ Apply counter-intelligence penalties ├─ Normalize to sum = 1.0 └─ Map to verdict category 5. Generate explanation ├─ Summarize evidence ├─ Explain probability factors ├─ Cite key sources └─ Provide confidence assessment ``` ### Multi-Factor Probability Calculation The complete algorithm: ```python theme={null} def calculate_enhanced_probability_distribution( base_dist: Dict[str, float], evidence_groups: Dict[str, List[Dict]] ) -> Tuple[Dict[str, float], List[str]]: enhanced_dist = base_dist.copy() modifications = [] # Extract evidence by category scientific_evidence = evidence_groups["scientific"] independent_evidence = evidence_groups["independent"] press_releases = evidence_groups["press_releases"] youtube_counter = evidence_groups["youtube_reviews"] # Calculate validation powers scientific_power = sum(e['validation_power'] for e in scientific_evidence) independent_power = sum(e['validation_power'] for e in independent_evidence) youtube_counter_power = sum(e['validation_power'] for e in youtube_counter) # Factor 1: Evidence coverage total_evidence = len(scientific_evidence) + len(independent_evidence) claim_length = len(claim_text.split()) coverage_score = total_evidence / (claim_length / 5) if coverage_score > 1.0: coverage_boost = min(0.3, coverage_score * 0.15) enhanced_dist["TRUE"] += coverage_boost modifications.append(f"Evidence coverage boost: +{coverage_boost:.2f}") # Factor 2: Independent source ratio if independent_power > 0: independent_ratio = independent_power / (independent_power + scientific_power + 0.01) if independent_ratio > 0.5: indie_boost = min(0.25, (independent_ratio - 0.5) * 0.5) enhanced_dist["TRUE"] += indie_boost modifications.append(f"Independent sources boost: +{indie_boost:.2f}") # Factor 3: Scientific evidence weighting if scientific_power > 0: science_weight = min(0.4, scientific_power * 0.2) enhanced_dist["TRUE"] += science_weight modifications.append(f"Scientific evidence boost: +{science_weight:.2f}") # Factor 4: YouTube counter-intelligence if youtube_counter_power > 0: youtube_impact = min(0.20, youtube_counter_power * 0.08) enhanced_dist["FALSE"] += youtube_impact modifications.append(f"YouTube CI penalty: +{youtube_impact:.2f} to FALSE") # Factor 5: Press release penalty self_ref_count = len([pr for pr in press_releases if pr.get('self_referential')]) if self_ref_count > 0: penalty = min(0.4, self_ref_count * 0.15) enhanced_dist["FALSE"] += penalty modifications.append(f"Press release penalty: +{penalty:.2f} to FALSE") # Normalize total = sum(enhanced_dist.values()) enhanced_dist = {k: v / total for k, v in enhanced_dist.items()} # Ensure minimums for key in ["TRUE", "FALSE", "UNCERTAIN"]: enhanced_dist[key] = max(0.001, enhanced_dist[key]) return enhanced_dist, modifications ``` *** ## 8. Report Generation ### Report Structure Each report contains: 1. **Executive Summary** * Total claims analyzed * Verdict distribution (Highly Likely True, Likely False, etc.) * Overall truthfulness assessment 2. **Video Information** * Title, channel, duration * Upload date and view count * Video embed/thumbnail 3. **Detailed Claims Analysis** * Claim text with timestamp * Speaker identification * Verification verdict * Probability distribution * Detailed explanation * Source links 4. **Evidence Summary** * Categorized by source type * Validation power indicators * Quality metrics 5. **Counter-Intelligence Section** * Press releases identified * YouTube review analysis * Impact on truthfulness scores ### Output Formats **HTML Report:** * Interactive source links (modal popups) * Video embed * Formatted tables * Visual probability bars **Markdown Report:** * Clean, readable format * Source citations with links * Table-formatted claims analysis * GitHub-compatible **JSON Report:** * Structured data format * All probabilities and evidence * Machine-readable * API-friendly ### Explanation Generation For each claim, the system generates a human-readable explanation: **Template:** ``` [VERDICT] based on [EVIDENCE_COUNT] sources ([SCIENTIFIC_COUNT] scientific, [INDEPENDENT_COUNT] independent). [COUNTER_INTEL_STATEMENT if applicable] Key supporting evidence: [TOP_SOURCES] Probability: TRUE: X%, FALSE: Y%, UNCERTAIN: Z% ``` **Example:** ``` LIKELY FALSE based on 8 sources (1 scientific, 3 independent). YOUTUBE COUNTER-INTELLIGENCE: Multiple review videos (450K+ views) contradict this claim, providing independent contradictory perspective. Press release sources have reduced validation power due to self-promotional nature. Key supporting evidence: [1] National Institutes of Health study shows no significant effect [2] Mayo Clinic states insufficient evidence. Probability: TRUE: 15%, FALSE: 70%, UNCERTAIN: 15% ``` *** ## 9. Limitations & Future Work ### Current Limitations #### 1. Language Support * **Current:** English-only * **Impact:** Cannot analyze non-English videos * **Mitigation:** Rely on auto-translated transcripts (degraded quality) #### 2. Visual Understanding * **Current:** Text-based analysis of visual content * **Impact:** May miss subtle visual cues or demonstrations * **Mitigation:** 1 FPS sampling captures most visual information #### 3. Context Understanding * **Current:** Individual claim verification * **Impact:** May miss broader narrative context * **Mitigation:** Video analysis summary provides context #### 4. Search API Limitations * **Current:** Dependent on Google Custom Search API * **Impact:** Results limited by search algorithm bias * **Mitigation:** Multiple query strategies, diverse sources #### 5. Real-Time Updates * **Current:** Analysis is point-in-time * **Impact:** New evidence published later not included * **Mitigation:** Reports include generation timestamp #### 6. Subjective Claims * **Current:** Best for factual, verifiable claims * **Impact:** Opinion-based claims harder to verify * **Mitigation:** Focus on CRAAP criteria, objective claims ### Future Enhancements 1. **Multi-Language Support** * Integrate translation APIs * Support major world languages * Cross-language evidence validation 2. **Enhanced Visual Analysis** * Deeper computer vision integration * Object detection and recognition * Facial recognition for speaker verification 3. **Real-Time Monitoring** * Continuous evidence updates * Alert system for new contradictory evidence * Live verification scores 4. **Community Validation** * Crowd-sourced evidence submission * Expert reviewer network * Public challenge system 5. **Automated Fact-Checking** * Integration with fact-checking databases * Automated source verification * Claim similarity detection 6. **Enhanced Counter-Intelligence** * Social media analysis (Twitter, Reddit) * Forum scanning (specialized communities) * Academic preprint servers 7. **Explainability Improvements** * Visual probability explanations * Interactive evidence exploration * Confidence intervals on scores *** ## Conclusion VerityNgn represents a significant advancement in automated video verification technology. By combining multimodal AI analysis, sophisticated counter-intelligence techniques, and probabilistic reasoning, the system provides transparent, evidence-based truthfulness assessments. **Key Strengths:** * Comprehensive multimodal analysis * Transparent probability calculations * Counter-intelligence innovation * Evidence-based reasoning * Detailed explanations **Ethical Commitment:** * Transparent methodology * Source attribution * Probabilistic rather than binary verdicts * Acknowledgment of uncertainty * Open documentation The system is designed to augment, not replace, human critical thinking. Users are encouraged to: * Review the evidence themselves * Consider the probability distributions * Understand the limitations * Make informed judgments *** **For Technical Implementation Details, see:** * `ARCHITECTURE.md` - System architecture * `API_DOCUMENTATION.md` - API reference * `DEPLOYMENT_GUIDE.md` - Deployment instructions **For Research Papers, see:** * `papers/verityngn_methodology.pdf` - Academic paper * `papers/counter_intelligence_techniques.pdf` - CI methods paper * `papers/probability_model.pdf` - Mathematical foundations *** *This methodology documentation is maintained as part of the VerityNgn open-source project. For updates and contributions, visit the GitHub repository.*