========================================================================================== VALIDATION PROTOCOL V-BAUM Atlas Fracture Detection in Narrative Embedding Space ========================================================================================== ANALYSIS METADATA ------------------------------------------------------------------------------------------ Document: The Wonderful Wizard of Oz Author: L. Frank Baum Publication: 1900 Source: Project Gutenberg (epub/55) Analysis Date: 2025-12-01 00:22:47 Text Length: 212,653 characters Chapters Detected: 24 METHOD ------------------------------------------------------------------------------------------ Embedding Model: sentence-transformers/all-MiniLM-L6-v2 Window Size: 1000 characters Step Size: 200 characters Total Windows: 1059 Curvature Metric: Cosine distance between consecutive embeddings Peak Detection: Prominence ≥ 2.0σ Peaks Detected: 30 CURVATURE STATISTICS ------------------------------------------------------------------------------------------ Mean Curvature: 0.1088 Std Deviation: 0.0446 Maximum: 0.3691 Minimum: 0.0176 ========================================================================================== DETECTED ATLAS FRACTURES ========================================================================================== Peaks ranked by prominence (semantic discontinuity strength). Higher prominence indicates stronger atlas fracture. ────────────────────────────────────────────────────────────────────────────────────────── FRACTURE #1 ────────────────────────────────────────────────────────────────────────────────────────── Window Index: 909 Character Position: 181,800 Prominence: 0.1993 Curvature ||Ric||: 0.2472 Location: Chapter 19: "Attacked by the Fighting Trees" NARRATIVE CONTEXT: ────────────────────────────────────────────────────────────────────────────────────────── “So now let us all get ready, for it will be a long journey.” Chapter XIX Attacked by the Fighting Trees The next morning Dorothy kissed the pretty green girl good-bye, and they all shook hands with the soldier with the green whiskers, who had walked with them as far as the gate. When the Guardian of the Gate saw them again he wondered greatly that they could leave the beautiful City to get into new trouble. But he at once unlocked their spectacles, which he put back into the green box, and gave them many good wishes to carry with them. “You are now our ruler,” he said to the Scarecrow; “so you must come back to us as soon as possible.” “I certainly shall if I am able,” the Scarecrow replied; “but I must help Dorothy to get home, first.” As Dorothy bade ────────────────────────────────────────────────────────────────────────────────────────── ────────────────────────────────────────────────────────────────────────────────────────── FRACTURE #2 ────────────────────────────────────────────────────────────────────────────────────────── Window Index: 45 Character Position: 9,000 Prominence: 0.1340 Curvature ||Ric||: 0.2149 Location: Chapter 2: "The Council with the Munchkins" NARRATIVE CONTEXT: ────────────────────────────────────────────────────────────────────────────────────────── The Council with the Munchkins She was awakened by a shock, so sudden and severe that if Dorothy had not been lying on the soft bed she might have been hurt. As it was, the jar made her catch her breath and wonder what had happened; and Toto put his cold little nose into her face and whined dismally. Dorothy sat up and noticed that the house was not moving; nor was it dark, for the bright sunshine came in at the window, flooding the little room. She sprang from her bed and with Toto at her heels ran and opened the door. The little girl gave a cry of amazement and looked about her, her eyes growing bigger and bigger at the wonderful sights she saw. The cyclone had set the house down very gently—for a cyclone—in the midst of a country of marvelous beauty. ────────────────────────────────────────────────────────────────────────────────────────── ────────────────────────────────────────────────────────────────────────────────────────── FRACTURE #3 ────────────────────────────────────────────────────────────────────────────────────────── Window Index: 722 Character Position: 144,400 Prominence: 0.1253 Curvature ||Ric||: 0.2010 Location: Chapter 14: "The Winged Monkeys" NARRATIVE CONTEXT: ────────────────────────────────────────────────────────────────────────────────────────── s far below them. Dorothy found herself riding easily between two of the biggest Monkeys, one of them the King himself. They had made a chair of their hands and were careful not to hurt her. “Why do you have to obey the charm of the Golden Cap?” she asked. “That is a long story,” answered the King, with a winged laugh; “but as we have a long journey before us, I will pass the time by telling you about it, if you wish.” “I shall be glad to hear it,” she replied. “Once,” began the leader, “we were a free people, living happily in the great forest, flying from tree to tree, eating nuts and fruit, and doing just as we pleased without calling anybody master. Perhaps some of us were rather too full of mischief at times, flying down to pull the tails of the animals that had ────────────────────────────────────────────────────────────────────────────────────────── ────────────────────────────────────────────────────────────────────────────────────────── FRACTURE #4 ────────────────────────────────────────────────────────────────────────────────────────── Window Index: 286 Character Position: 57,200 Prominence: 0.1195 Curvature ||Ric||: 0.1717 Location: Chapter 7: "The Journey to the Great Oz" NARRATIVE CONTEXT: ────────────────────────────────────────────────────────────────────────────────────────── You can roast it by the fire, since your tastes are so peculiar that you prefer cooked food, and then you will have a very good breakfast.” “Don’t! Please don’t,” begged the Tin Woodman. “I should certainly weep if you killed a poor deer, and then my jaws would rust again.” But the Lion went away into the forest and found his own supper, and no one ever knew what it was, for he didn’t mention it. And the Scarecrow found a tree full of nuts and filled Dorothy’s basket with them, so that she would not be hungry for a long time. She thought this was very kind and thoughtful of the Scarecrow, but she laughed heartily at the awkward way in which the poor creature picked up the nuts. ────────────────────────────────────────────────────────────────────────────────────────── ────────────────────────────────────────────────────────────────────────────────────────── FRACTURE #5 ────────────────────────────────────────────────────────────────────────────────────────── Window Index: 468 Character Position: 93,600 Prominence: 0.1105 Curvature ||Ric||: 0.1644 Location: Chapter 10: "The Guardian of the Gate" NARRATIVE CONTEXT: ────────────────────────────────────────────────────────────────────────────────────────── There were two golden bands fastened to them that passed around the back of her head, where they were locked together by a little key that was at the end of a chain the Guardian of the Gates wore around his neck. When they were on, Dorothy could not take them off had she wished, but of course she did not wish to be blinded by the glare of the Emerald City, so she said nothing. Then the green man fitted spectacles for the Scarecrow and the Tin Woodman and the Lion, and even on little Toto; and all were locked fast with the key. Then the Guardian of the Gates put on his own glasses and told them he was ready to show them to the Palace. ────────────────────────────────────────────────────────────────────────────────────────── ────────────────────────────────────────────────────────────────────────────────────────── FRACTURE #6 ────────────────────────────────────────────────────────────────────────────────────────── Window Index: 698 Character Position: 139,600 Prominence: 0.1099 Curvature ||Ric||: 0.1671 Location: Chapter 14: "The Winged Monkeys" NARRATIVE CONTEXT: ────────────────────────────────────────────────────────────────────────────────────────── When the four travelers went in search of the Witch she had seen them coming, and so sent the Winged Monkeys to bring them to her. It was much harder to find their way back through the big fields of buttercups and yellow daisies than it was being carried. They knew, of course, they must go straight east, toward the rising sun; and they started off in the right way. But at noon, when the sun was over their heads, they did not know which was east and which was west, and that was the reason they were lost in the great fields. They kept on walking, however, and at night the moon came out and shone brightly. So they lay down among the sweet smelling yellow flowers and slept soundly until morning—all but the S ────────────────────────────────────────────────────────────────────────────────────────── ────────────────────────────────────────────────────────────────────────────────────────── FRACTURE #7 ────────────────────────────────────────────────────────────────────────────────────────── Window Index: 231 Character Position: 46,200 Prominence: 0.1012 Curvature ||Ric||: 0.1680 Location: Chapter 5: "The Rescue of the Tin Woodman" NARRATIVE CONTEXT: ────────────────────────────────────────────────────────────────────────────────────────── She thought of a new way to kill my love for the beautiful Munchkin maiden, and made my axe slip again, so that it cut right through my body, splitting me into two halves. Once more the tinsmith came to my help and made me a body of tin, fastening my tin arms and legs and head to it, by means of joints, so that I could move around as well as ever. But, alas! I had now no heart, so that I lost all my love for the Munchkin girl, and did not care whether I married her or not. I suppose she is still living with the old woman, waiting for me to come after her. “My body shone so brightly in the sun that I felt very proud of it and it did not matter now if my axe slipped, for it could not cut me. ────────────────────────────────────────────────────────────────────────────────────────── ────────────────────────────────────────────────────────────────────────────────────────── FRACTURE #8 ────────────────────────────────────────────────────────────────────────────────────────── Window Index: 847 Character Position: 169,400 Prominence: 0.1010 Curvature ||Ric||: 0.1812 Location: Chapter 17: "How the Balloon Was Launched" NARRATIVE CONTEXT: ────────────────────────────────────────────────────────────────────────────────────────── thy back to Kansas, and I’m sure I don’t know how it can be done.” Chapter XVII How the Balloon Was Launched For three days Dorothy heard nothing from Oz. These were sad days for the little girl, although her friends were all quite happy and contented. The Scarecrow told them there were wonderful thoughts in his head; but he would not say what they were because he knew no one could understand them but himself. When the Tin Woodman walked about he felt his heart rattling around in his breast; and he told Dorothy he had discovered it to be a kinder and more tender heart than the one he had owned when he was made of flesh. The Lion declared he was afraid of nothing on earth, and would gladly face an army or a dozen of the fierce Kalidahs. Thus each of the little pa ────────────────────────────────────────────────────────────────────────────────────────── ────────────────────────────────────────────────────────────────────────────────────────── FRACTURE #9 ────────────────────────────────────────────────────────────────────────────────────────── Window Index: 98 Character Position: 19,600 Prominence: 0.0985 Curvature ||Ric||: 0.1590 Location: Chapter 3: "How Dorothy Saved the Scarecrow" NARRATIVE CONTEXT: ────────────────────────────────────────────────────────────────────────────────────────── o barked after her loudly enough when she had gone, because he had been afraid even to growl while she stood by. But Dorothy, knowing her to be a witch, had expected her to disappear in just that way, and was not surprised in the least. Chapter III How Dorothy Saved the Scarecrow When Dorothy was left alone she began to feel hungry. So she went to the cupboard and cut herself some bread, which she spread with butter. She gave some to Toto, and taking a pail from the shelf she carried it down to the little brook and filled it with clear, sparkling water. Toto ran over to the trees and began to bark at the birds sitting there. Dorothy went to get him, and saw such delicious fruit hanging from the branches that she gathered some of it, finding it just what she want ────────────────────────────────────────────────────────────────────────────────────────── ────────────────────────────────────────────────────────────────────────────────────────── FRACTURE #10 ────────────────────────────────────────────────────────────────────────────────────────── Window Index: 967 Character Position: 193,400 Prominence: 0.0984 Curvature ||Ric||: 0.1504 Location: Chapter 20: "The Dainty China Country" NARRATIVE CONTEXT: ────────────────────────────────────────────────────────────────────────────────────────── The Clown put his hands in his pockets, and after puffing out his cheeks and nodding his head at them saucily, he said: “My lady fair, Why do you stare At poor old Mr. Joker? You’re quite as stiff And prim as if You’d eaten up a poker!” “Be quiet, sir!” said the Princess. “Can’t you see these are strangers, and should be treated with respect?” “Well, that’s respect, I expect,” declared the Clown, and immediately stood upon his head. “Don’t mind Mr. Joker,” said the Princess to Dorothy. “He is considerably cracked in his head, and that makes him foolish.” “Oh, I don’t mind him a bit,” said Dorothy. “But you are so beautiful,” she continued, “that I am sure I could love you dearly. ────────────────────────────────────────────────────────────────────────────────────────── ========================================================================================== END OF REPORT ========================================================================================== INTERPRETATION NOTES: Atlas fractures represent moments where the narrative's semantic geometry undergoes rapid transformation. These correspond to: • World-boundary crossings (entering/exiting bounded-observer spaces) • Identity transformations (character state transitions) • Institutional reconfigurations (authority/metric collapses) • Resolution changes (outer projection filter modifications) The dominant peak (#1) represents the most significant discontinuity in the text's embedding space, indicating the primary atlas fracture. For methodology details, see: Tiffany, P. (2025). The Wicked Prior as a Bounded-Observer Manifold: Atlas Fracture, Stackelberg Parentage, and Grace-Flow Repair.