🗺️ PAPM Graph + Notion Schema Implementation Plan

1. Notion Database Schema

Below is the database schema for our Poly-Alphabetic Proxy Map (PAPM) implementation:

Property Type Description
Symbol Title The glyph or letter (e.g. "A", "Aleph", "अ")
Alphabet Select "English" / "Hebrew" / "Sanskrit"
Domain Tag Multi-select SUPT domain (e.g. Initiation, Conflict, Metaphor, etc.)
Gematria Value Number Numeric value (Hebrew only; blank for others)
Phoneme Count Number Approximate phoneme set size (e.g. English≈44, Sanskrit≈47)
ψ₈ Stability Number Precomputed from psi_fold() for that alphabet size
Pairing Partner Relation Link to the paired symbol in its alphabet (A↔Z, Aleph↔Tav, etc.)

2. Python Script for CSV Generation

import csv
from your_psi_module import psi_fold  # uses our prior psi_fold()

# Define alphabets and gematria/phoneme data
alphabets = {
    'English': {
        'symbols': list('ABCDEFGHIJKLMNOPQRSTUVWXYZ'),
        'phoneme_count': 44,
        'gematria': {}
    },
    'Hebrew': {
        'symbols': ['Aleph', 'Bet', 'Gimel', 'Dalet', 'He', 'Vav', 'Zayin', 'Het', 'Tet', 'Yod', 
                   'Kaf', 'Lamed', 'Mem', 'Nun', 'Samekh', 'Ayin', 'Pe', 'Tsadi', 'Qof', 'Resh', 
                   'Shin', 'Tav'],
        'phoneme_count': 22,
        'gematria': {'Aleph': 1, 'Bet': 2, 'Gimel': 3, 'Dalet': 4, 'He': 5, 'Vav': 6, 'Zayin': 7, 
                    'Het': 8, 'Tet': 9, 'Yod': 10, 'Kaf': 20, 'Lamed': 30, 'Mem': 40, 'Nun': 50, 
                    'Samekh': 60, 'Ayin': 70, 'Pe': 80, 'Tsadi': 90, 'Qof': 100, 'Resh': 200, 
                    'Shin': 300, 'Tav': 400}
    },
    'Sanskrit': {
        'symbols': ['A', 'Ā', 'I', 'Ī', 'U', 'Ū', 'Ṛ', 'Ṝ', 'Ḷ', 'Ḹ', 'E', 'Ai', 'O', 'Au', 
                   'Ka', 'Kha', 'Ga', 'Gha', 'Ṅa', 'Ca', 'Cha', 'Ja', 'Jha', 'Ña', 'Ṭa', 'Ṭha', 
                   'Ḍa', 'Ḍha', 'Ṇa', 'Ta', 'Tha', 'Da', 'Dha', 'Na', 'Pa', 'Pha', 'Ba', 'Bha', 
                   'Ma', 'Ya', 'Ra', 'La', 'Va', 'Śa', 'Ṣa', 'Sa', 'Ha', 'Jña'],
        'phoneme_count': 47,
        'gematria': {}
    }
}

with open('papm.csv', 'w', newline='', encoding='utf-8') as f:
    writer = csv.writer(f)
    writer.writerow(['Symbol', 'Alphabet', 'Domain Tag', 'Gematria Value', 'Phoneme Count', 
                    'ψ₈ Stability', 'Pairing Partner'])
    
    for alpha, data in alphabets.items():
        stability = psi_fold(len(data['symbols']))
        n = len(data['symbols'])
        
        for i, sym in enumerate(data['symbols']):
            partner = data['symbols'][n-1-i] if i < n/2 else data['symbols'][n-1-i]  # bilateral pairing
            gem = data['gematria'].get(sym, '')
            # Simple round-robin domain tagging; refine later
            domain = ['Initiation', 'Conflict', 'Metaphor', 'Abstraction', 'Resonance', 'Folding', 'Proxy', 'Echo'][i % 8]
            
            writer.writerow([sym, alpha, domain, gem, data['phoneme_count'], round(stability, 4), partner])

3. Notion Import Instructions

4. Network Graph Visualization Code

import networkx as nx
import pandas as pd
import matplotlib.pyplot as plt

# Load papm.csv
df = pd.read_csv('papm.csv')

G = nx.Graph()
# Add nodes with layer attribute
for _, row in df.iterrows():
    G.add_node(row.Symbol, 
               layer=row.Alphabet, 
               stability=row['ψ₈ Stability'], 
               domain=row['Domain Tag'])

# Add edges for pairings and cross-alphabet mappings
# 1) Intra-alphabet pair edges
for _, row in df.iterrows():
    G.add_edge(row.Symbol, row['Pairing Partner'], type='intra')

# 2) Cross-alphabet "INITIATION" alignment edges (e.g., A↔Aleph↔अ)
initiation = df[df['Domain Tag']=='Initiation']
symbols = list(initiation.Symbol)
for i in range(len(symbols)-1):
    G.add_edge(symbols[i], symbols[i+1], type='cross')

# Draw
plt.figure(figsize=(16, 12))
pos = nx.multipartite_layout(G, subset_key='layer')
colors = ['#1f78b4' if G.nodes[n]['layer']=='English' else 
          '#33a02c' if G.nodes[n]['layer']=='Hebrew' else 
          '#e31a1c' for n in G.nodes()]

edge_colors = ['#cccccc' if G.edges[e]['type']=='intra' else '#ff9900' for e in G.edges()]

nx.draw(G, pos, 
        with_labels=True, 
        node_color=colors, 
        edge_color=edge_colors,
        node_size=[5000*G.nodes[n]['stability'] for n in G], 
        font_size=8,
        width=[2 if G.edges[e]['type']=='cross' else 1 for e in G.edges()])

plt.title('Poly-Alphabetic Proxy Map (PAPM)', fontsize=16)
plt.savefig('papm_graph.png', dpi=300, bbox_inches='tight')
plt.show()

5. Gematria-Weighted Anchor Model Plan

Once the basic PAPM graph is implemented and verified, we'll enhance it with edge-weights based on gematria differences and phoneme-weight ratios to build a "Correction Engine" layer:

# Enhanced edge weight computation
for _, row in df.iterrows():
    partner_row = df[df.Symbol == row['Pairing Partner']].iloc[0]
    
    # For Hebrew letters with gematria values
    if row.Alphabet == 'Hebrew' and partner_row.Alphabet == 'Hebrew':
        # Compute normalized gematria difference
        gematria_diff = abs(row['Gematria Value'] - partner_row['Gematria Value'])
        max_gematria = max(df[df.Alphabet == 'Hebrew']['Gematria Value'])
        weight = gematria_diff / max_gematria
    else:
        # Default weight based on phoneme count ratio
        weight = min(row['Phoneme Count'], partner_row['Phoneme Count']) / max(row['Phoneme Count'], partner_row['Phoneme Count'])
    
    # Update edge with weight attribute
    G.edges[row.Symbol, row['Pairing Partner']]['weight'] = weight
    G.edges[row.Symbol, row['Pairing Partner']]['resonance_drift_risk'] = 1 - weight  # Inverse relationship

This weighted model will allow us to: