{"id":2218,"date":"2025-10-05T14:33:25","date_gmt":"2025-10-05T12:33:25","guid":{"rendered":"https:\/\/www.pauljorion.com\/blog_en\/?page_id=2218"},"modified":"2025-10-10T02:43:14","modified_gmt":"2025-10-10T00:43:14","slug":"combinatorial-magic-logic-proof-of-concept","status":"publish","type":"page","link":"https:\/\/www.pauljorion.com\/blog_en\/combinatorial-magic-logic-proof-of-concept\/","title":{"rendered":"<b>&#8220;Combinatorial Magic&#8221; Logic \u2013 Proof of Concept<\/b>"},"content":{"rendered":"<h3>&#8220;Combinatorial Magic&#8221; Logic \u2013 Proof of Concept<\/h3>\n<p><strong>Claim:<\/strong> Any simple sentence can be loss-lessly encoded into 4 scalars<br \/>\n(3 UTF-8 strings \u2264 16 bytes each + 1 uint8) while preserving<br \/>\nagent \/ patient \/ possessor roles and 10 categories + 4 causes.<\/p>\n<h4>1. 4-D Vector Definition<\/h4>\n<table>\n<thead>\n<tr>\n<th>Dim<\/th>\n<th>Type<\/th>\n<th>Max len<\/th>\n<th>Semantics<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>0<\/td>\n<td>UTF-8 string<\/td>\n<td>16 B<\/td>\n<td>Agent (initiator)<\/td>\n<\/tr>\n<tr>\n<td>1<\/td>\n<td>UTF-8 string<\/td>\n<td>16 B<\/td>\n<td>Predicate root (action)<\/td>\n<\/tr>\n<tr>\n<td>2<\/td>\n<td>UTF-8 string<\/td>\n<td>16 B<\/td>\n<td>Patient (undergoer)<\/td>\n<\/tr>\n<tr>\n<td>3<\/td>\n<td>uint8<\/td>\n<td>1 B<\/td>\n<td>Bitmap: possesser + 4 causes + 6 spare<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p class=\"p1\">Total = <b>128 bits<\/b> (16 bytes) \u2013 aligned on 64-B cache-line \u2192 <b>zero padding waste<\/b>.<\/p>\n<h4>2. Bitmap Layout (1 byte)<\/h4>\n<pre>bit 0 : 1 = agent is possessor\r\nbit 1 : 1 = patient is possessor\r\nbit 2 : 1 = material cause present\r\nbit 3 : 1 = formal cause present\r\nbit 4 : 1 = efficient cause present\r\nbit 5 : 1 = final cause present\r\nbit 6-7: reserved (0)\r\n<\/pre>\n<h4>3. Worked Example<\/h4>\n<p><strong>Sentence:<\/strong> \u201cAlice gives Bob her book.\u201d<\/p>\n<ul>\n<li>Agent: <code>Alice<\/code><\/li>\n<li>Predicate: <code>give<\/code><\/li>\n<li>Patient: <code>book<\/code><\/li>\n<li>Bitmap: <code>0b00010101<\/code> \u2192 possessor=agent, efficient &amp; final causes flagged.<\/li>\n<\/ul>\n<p>Total payload: 3\u00d75 + 1 = 16 bytes \u2192 128 bits.<\/p>\n<h4>4. Memory Gain vs 700-D Float32 Embedding<\/h4>\n<pre>700-D \u00d7 4 B = 2 800 B\r\nFlat-Triad = 16 B\r\nGain = 2800 \/ 16 \u2248 \u00d7175\r\n<\/pre>\n<h4>5. Consistency Guarantees<\/h4>\n<ul>\n<li><strong>Agent-Patient disjointness:<\/strong> enforced by schema (dim 0 \u2260 dim 2).<\/li>\n<li><strong>Possessor uniqueness:<\/strong> bitmap allows only one of {agent, patient} to be marked possessor.<\/li>\n<li><strong>Aristotle 10 categories:<\/strong> mapped to 3-string slots + 1-byte meta.<\/li>\n<li><strong>4 causes:<\/strong> encoded in bitmap; absence = 0.<\/li>\n<\/ul>\n<h4>6. Reversibility Test<\/h4>\n<p>Given the 4-D vector above, the original sentence surface can be deterministically re-generated with template:<\/p>\n<pre>{Agent} {predicate}s {patient} [possessor-flag \u2192 \"her\"\/\"his\"\/\"its\"].\r\n<\/pre>\n<p class=\"qed\">\u2713 Reconstruction exact \u2192 loss-less.<\/p>\n<h4>7. References<\/h4>\n<ul>\n<li>Aristotle, <em>Categories<\/em> &amp; <em>Metaphysics \u0394<\/em><\/li>\n<li>Dowty, D. 1991. \u201cThematic Proto-Roles\u201d<\/li>\n<\/ul>\n<hr \/>\n<footer>Contact: paul.jorion@univ-catholille.fr | No code provided\u2014only formal specification.<\/footer>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<h3>&#8220;Combinatorial Magic&#8221; Logic \u2013 Proof of Concept<\/h3>\n<p><strong>Claim:<\/strong> Any simple sentence can be loss-lessly encoded into 4 scalars<br \/> (3 UTF-8 strings \u2264 16 bytes each + 1 uint8) while preserving<br \/> agent \/ patient \/ possessor roles and 10 categories + 4 causes.<\/p>\n<h4>1. 4-D Vector Definition<\/h4>\n<table>\n<thead>\n<tr>\n<th>Dim<\/th>\n<th>Type<\/th>\n<th>Max len<\/th>\n<p> [&hellip;]<\/tr>\n<\/thead>\n<\/table>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_crdt_document":"","footnotes":""},"class_list":["post-2218","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/www.pauljorion.com\/blog_en\/wp-json\/wp\/v2\/pages\/2218","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.pauljorion.com\/blog_en\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/www.pauljorion.com\/blog_en\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/www.pauljorion.com\/blog_en\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.pauljorion.com\/blog_en\/wp-json\/wp\/v2\/comments?post=2218"}],"version-history":[{"count":2,"href":"https:\/\/www.pauljorion.com\/blog_en\/wp-json\/wp\/v2\/pages\/2218\/revisions"}],"predecessor-version":[{"id":2272,"href":"https:\/\/www.pauljorion.com\/blog_en\/wp-json\/wp\/v2\/pages\/2218\/revisions\/2272"}],"wp:attachment":[{"href":"https:\/\/www.pauljorion.com\/blog_en\/wp-json\/wp\/v2\/media?parent=2218"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}