VISUAL_TO_TRADITIONAL_CROSSWALK_v2.json

Paper VIII: Packet Operator Algorithms, Exact Compilation, and GPU Realization

VISUAL_TO_TRADITIONAL_CROSSWALK_v2.json

Download original file

This is the original source text. Reading it does not run or verify the program.

Read the typeset paper

Skip source text

1 {
2   "status": "PASS",
3   "traditional_map_sha256": "6a91b7c9093d217c98f3bf48a986dad41265893979f62f896e5b82668b9c9409",
4   "traditional_pdf_sha256": "3422b134597c097238d0ffd5646d5366c111c44df0b68147b47ba3449e0058ed",
5   "traditional_aux_sha256": "226a4ea670d91400914370bd7ca4e66542c5d38120a8e51ddac70bd39acc1e9e",
6   "traditional_source_sha256": "9f767602dfcc1145ba7d593d17dc2c95676bed88bd78a6a24a4fe553455bbaba",
7   "visual_pdf_sha256": "a78f1c18c7c36cecbaf9484bc6dc643300c3b5054df338f48be6390af5e520c7",
8   "scope": "32 exact declared reading rows. Targets verified against current map, named destinations, and actual printed and physical PDF page labels. The integrated atlas omits PDF locators. Reading references do not expand formal scope.",
9   "pages": [
10     {
11       "visual_page": 1,
12       "visual_physical_pdf_page": 3,
13       "visual_printed_page": "1",
14       "title": "Compute the representation first",
15       "source_line_original": "Traditional edition: Section 2, Section 3, Appendix F; PDF pp. 7, 10, 78.",
16       "source_line_current": "Traditional pp. 7, 10, 79 / Section 2, Section 3, Appendix F.",
17       "traditional_targets": [
18         {
19           "final_label": "sec:ir",
20           "number": "2",
21           "printed_page": "7",
22           "physical_pdf_page": 13,
23           "title_tex": "Packet operator representations",
24           "kind": "Section"
25         },
26         {
27           "final_label": "sec:cost",
28           "number": "3",
29           "printed_page": "10",
30           "physical_pdf_page": 16,
31           "title_tex": "Arithmetic, storage, and data movement",
32           "kind": "Section"
33         },
34         {
35           "final_label": "supp6:section:001",
36           "number": "F",
37           "printed_page": "79",
38           "physical_pdf_page": 85,
39           "title_tex": "Global small-core recompression from ordered thin SVD data",
40           "kind": "Appendix"
41         }
42       ]
43     },
44     {
45       "visual_page": 2,
46       "visual_physical_pdf_page": 4,
47       "visual_printed_page": "2",
48       "title": "The objects and their contracts",
49       "source_line_original": "Traditional edition: Definition 2.1, Definition 2.2, Definition 2.7, Section 8, Section 9, Section 11; PDF pp. 8, 10, 25, 29, 35.",
50       "source_line_current": "Traditional pp. 7, 9, 26, 30, 36 / Definition 2.1, Definition 2.2, Definition 2.7, Section 8, Section 9, Section 11.",
51       "traditional_targets": [
52         {
53           "final_label": "def:packet_layout",
54           "number": "2.1",
55           "printed_page": "7",
56           "physical_pdf_page": 13,
57           "title_tex": "Packet layout",
58           "kind": "Definition"
59         },
60         {
61           "final_label": "def:packet_ir",
62           "number": "2.2",
63           "printed_page": "7",
64           "physical_pdf_page": 13,
65           "title_tex": "Packet operator representation",
66           "kind": "Definition"
67         },
68         {
69           "final_label": "def:output_contract",
70           "number": "2.7",
71           "printed_page": "9",
72           "physical_pdf_page": 15,
73           "title_tex": "Output contract",
74           "kind": "Definition"
75         },
76         {
77           "final_label": "sec:precision",
78           "number": "8",
79           "printed_page": "26",
80           "physical_pdf_page": 32,
81           "title_tex": "Packetwise mixed precision",
82           "kind": "Section"
83         },
84         {
85           "final_label": "sec:compiler",
86           "number": "9",
87           "printed_page": "30",
88           "physical_pdf_page": 36,
89           "title_tex": "Discovery and exact packet compilation",
90           "kind": "Section"
91         },
92         {
93           "final_label": "sec:benchmark_protocol",
94           "number": "11",
95           "printed_page": "36",
96           "physical_pdf_page": 42,
97           "title_tex": "Benchmark contracts and measurement protocol",
98           "kind": "Section"
99         }
100       ]
101     },
102     {
103       "visual_page": 3,
104       "visual_physical_pdf_page": 5,
105       "visual_printed_page": "3",
106       "title": "A dense-looking matrix, one scalar coupling",
107       "source_line_original": "Traditional edition: Theorem 2.3, Theorem 3.4; PDF pp. 8, 11.",
108       "source_line_current": "Traditional pp. 7, 11 / Theorem 2.3, Theorem 3.4.",
109       "traditional_targets": [
110         {
111           "final_label": "thm:exact_evaluation",
112           "number": "2.3",
113           "printed_page": "7",
114           "physical_pdf_page": 13,
115           "title_tex": "Exact evaluation",
116           "kind": "Theorem"
117         },
118         {
119           "final_label": "thm:bdlr_counts",
120           "number": "3.4",
121           "printed_page": "11",
122           "physical_pdf_page": 17,
123           "title_tex": "BDLR application and storage",
124           "kind": "Theorem"
125         }
126       ]
127     },
128     {
129       "visual_page": 4,
130       "visual_physical_pdf_page": 6,
131       "visual_printed_page": "4",
132       "title": "Work removed is not time measured",
133       "source_line_original": "Traditional edition: Theorem 3.1, Corollary 3.2, Theorem 3.4, Corollary 3.9, Proposition 4.1; PDF pp. 11, 13, 14.",
134       "source_line_current": "Traditional pp. 10, 11, 12, 13 / Theorem 3.1, Corollary 3.2, Theorem 3.4, Corollary 3.9, Proposition 4.1.",
135       "traditional_targets": [
136         {
137           "final_label": "thm:packet_counts",
138           "number": "3.1",
139           "printed_page": "10",
140           "physical_pdf_page": 16,
141           "title_tex": "Dense and packet application counts",
142           "kind": "Theorem"
143         },
144         {
145           "final_label": "cor:equal_blocks",
146           "number": "3.2",
147           "printed_page": "10",
148           "physical_pdf_page": 16,
149           "title_tex": "Equal diagonal packets",
150           "kind": "Corollary"
151         },
152         {
153           "final_label": "thm:bdlr_counts",
154           "number": "3.4",
155           "printed_page": "11",
156           "physical_pdf_page": 17,
157           "title_tex": "BDLR application and storage",
158           "kind": "Theorem"
159         },
160         {
161           "final_label": "cor:capacity",
162           "number": "3.9",
163           "printed_page": "12",
164           "physical_pdf_page": 18,
165           "title_tex": "Capacity threshold",
166           "kind": "Corollary"
167         },
168         {
169           "final_label": "prop:block_banded_count",
170           "number": "4.1",
171           "printed_page": "13",
172           "physical_pdf_page": 19,
173           "title_tex": "Equal block banded count",
174           "kind": "Proposition"
175         }
176       ]
177     },
178     {
179       "visual_page": 5,
180       "visual_physical_pdf_page": 7,
181       "visual_printed_page": "5",
182       "title": "Four coefficients, four exact frequencies",
183       "source_line_original": "Traditional edition: Theorem 4.3; PDF p. 15.",
184       "source_line_current": "Traditional p. 14 / Theorem 4.3.",
185       "traditional_targets": [
186         {
187           "final_label": "thm:circulant",
188           "number": "4.3",
189           "printed_page": "14",
190           "physical_pdf_page": 20,
191           "title_tex": "Circulant spectral representation",
192           "kind": "Theorem"
193         }
194       ]
195     },
196     {
197       "visual_page": 6,
198       "visual_physical_pdf_page": 8,
199       "visual_printed_page": "6",
200       "title": "Padding is part of the theorem",
201       "source_line_original": "Traditional edition: Corollary 4.4; PDF p. 15.",
202       "source_line_current": "Traditional p. 15 / Corollary 4.4.",
203       "traditional_targets": [
204         {
205           "final_label": "cor:toeplitz_embedding",
206           "number": "4.4",
207           "printed_page": "15",
208           "physical_pdf_page": 21,
209           "title_tex": "Toeplitz circulant embedding",
210           "kind": "Corollary"
211         }
212       ]
213     },
214     {
215       "visual_page": 7,
216       "visual_physical_pdf_page": 9,
217       "visual_printed_page": "7",
218       "title": "A transpose, not an adjoint",
219       "source_line_original": "Traditional edition: Theorem 4.5, Corollary 4.6; PDF p. 16.",
220       "source_line_current": "Traditional p. 15 / Theorem 4.5, Corollary 4.6.",
221       "traditional_targets": [
222         {
223           "final_label": "thm:kronecker_apply",
224           "number": "4.5",
225           "printed_page": "15",
226           "physical_pdf_page": 21,
227           "title_tex": "Kronecker modewise application",
228           "kind": "Theorem"
229         },
230         {
231           "final_label": "cor:tensor_modewise",
232           "number": "4.6",
233           "printed_page": "15",
234           "physical_pdf_page": 21,
235           "title_tex": "Equal tensor factors",
236           "kind": "Corollary"
237         }
238       ]
239     },
240     {
241       "visual_page": 8,
242       "visual_physical_pdf_page": 10,
243       "visual_printed_page": "8",
244       "title": "See every butterfly value",
245       "source_line_original": "Traditional edition: Theorem 4.7; PDF p. 16.",
246       "source_line_current": "Traditional p. 16 / Theorem 4.7.",
247       "traditional_targets": [
248         {
249           "final_label": "thm:walsh_hadamard",
250           "number": "4.7",
251           "printed_page": "16",
252           "physical_pdf_page": 22,
253           "title_tex": "Walsh Hadamard recursion",
254           "kind": "Theorem"
255         }
256       ]
257     },
258     {
259       "visual_page": 9,
260       "visual_physical_pdf_page": 11,
261       "visual_printed_page": "9",
262       "title": "The cross term has somewhere to go",
263       "source_line_original": "Traditional edition: Theorem 5.1, Corollary 5.2; PDF pp. 17, 18.",
264       "source_line_current": "Traditional pp. 16, 17 / Theorem 5.1, Corollary 5.2.",
265       "traditional_targets": [
266         {
267           "final_label": "thm:bdlr_product",
268           "number": "5.1",
269           "printed_page": "16",
270           "physical_pdf_page": 22,
271           "title_tex": "Exact BDLR product",
272           "kind": "Theorem"
273         },
274         {
275           "final_label": "cor:rank_growth",
276           "number": "5.2",
277           "printed_page": "17",
278           "physical_pdf_page": 23,
279           "title_tex": "Rank growth in a product chain",
280           "kind": "Corollary"
281         }
282       ]
283     },
284     {
285       "visual_page": 10,
286       "visual_physical_pdf_page": 12,
287       "visual_printed_page": "10",
288       "title": "A large inverse, a small denominator",
289       "source_line_original": "Traditional edition: Theorem 5.3, Corollary 5.4; PDF p. 18.",
290       "source_line_current": "Traditional p. 18 / Theorem 5.3, Corollary 5.4.",
291       "traditional_targets": [
292         {
293           "final_label": "thm:woodbury",
294           "number": "5.3",
295           "printed_page": "18",
296           "physical_pdf_page": 24,
297           "title_tex": "Woodbury inversion",
298           "kind": "Theorem"
299         },
300         {
301           "final_label": "cor:inverse_norm",
302           "number": "5.4",
303           "printed_page": "18",
304           "physical_pdf_page": 24,
305           "title_tex": "Inverse norm bound",
306           "kind": "Corollary"
307         }
308       ]
309     },
310     {
311       "visual_page": 11,
312       "visual_physical_pdf_page": 13,
313       "visual_printed_page": "11",
314       "title": "Stored width is not intrinsic rank",
315       "source_line_original": "Traditional edition: Theorem 5.6, Section F.1; PDF pp. 19, 78.",
316       "source_line_current": "Traditional pp. 18, 79 / Theorem 5.6, Section F.1.",
317       "traditional_targets": [
318         {
319           "final_label": "thm:small_core_recompression",
320           "number": "5.6",
321           "printed_page": "18",
322           "physical_pdf_page": 24,
323           "title_tex": "Small core recompression",
324           "kind": "Theorem"
325         },
326         {
327           "final_label": "supp6:subsection:001",
328           "number": "F.1",
329           "printed_page": "79",
330           "physical_pdf_page": 85,
331           "title_tex": "Compact factors from actual column spaces",
332           "kind": "Section"
333         }
334       ]
335     },
336     {
337       "visual_page": 12,
338       "visual_physical_pdf_page": 14,
339       "visual_printed_page": "12",
340       "title": "Why a core optimum is global",
341       "source_line_original": "Traditional edition: Theorem 5.6, Section F.2, Section F.3, Section F.4; PDF pp. 19, 78, 79, 80.",
342       "source_line_current": "Traditional pp. 18, 80, 81 / Theorem 5.6, Section F.2, Section F.3, Section F.4.",
343       "traditional_targets": [
344         {
345           "final_label": "thm:small_core_recompression",
346           "number": "5.6",
347           "printed_page": "18",
348           "physical_pdf_page": 24,
349           "title_tex": "Small core recompression",
350           "kind": "Theorem"
351         },
352         {
353           "final_label": "supp6:subsection:002",
354           "number": "F.2",
355           "printed_page": "80",
356           "physical_pdf_page": 86,
357           "title_tex": "Why a small-core optimum is a global optimum",
358           "kind": "Section"
359         },
360         {
361           "final_label": "supp6:subsection:003",
362           "number": "F.3",
363           "printed_page": "80",
364           "physical_pdf_page": 86,
365           "title_tex": "Spectral optimality from a kernel witness",
366           "kind": "Section"
367         },
368         {
369           "final_label": "supp6:subsection:004",
370           "number": "F.4",
371           "printed_page": "81",
372           "physical_pdf_page": 87,
373           "title_tex": "Frobenius optimality from kernel weights",
374           "kind": "Section"
375         }
376       ]
377     },
378     {
379       "visual_page": 13,
380       "visual_physical_pdf_page": 15,
381       "visual_printed_page": "13",
382       "title": "Errors enter at different places",
383       "source_line_original": "Traditional edition: Theorem 5.8, Theorem 5.9; PDF p. 20.",
384       "source_line_current": "Traditional pp. 19, 20 / Theorem 5.8, Theorem 5.9.",
385       "traditional_targets": [
386         {
387           "final_label": "thm:product_chain_error",
388           "number": "5.8",
389           "printed_page": "19",
390           "physical_pdf_page": 25,
391           "title_tex": "Product chain perturbation",
392           "kind": "Theorem"
393         },
394         {
395           "final_label": "cor:recompression_chain",
396           "number": "5.9",
397           "printed_page": "20",
398           "physical_pdf_page": 26,
399           "title_tex": "Certified repeated recompression",
400           "kind": "Theorem"
401         }
402       ]
403     },
404     {
405       "visual_page": 14,
406       "visual_physical_pdf_page": 16,
407       "visual_printed_page": "14",
408       "title": "Two routes can cancel exactly",
409       "source_line_original": "Traditional edition: Theorem 2.5, Theorem 6.1, Corollary 6.3; PDF pp. 9, 21.",
410       "source_line_current": "Traditional pp. 8, 21 / Theorem 2.5, Theorem 6.1, Corollary 6.3.",
411       "traditional_targets": [
412         {
413           "final_label": "thm:block_composition",
414           "number": "2.5",
415           "printed_page": "8",
416           "physical_pdf_page": 14,
417           "title_tex": "Block composition",
418           "kind": "Theorem"
419         },
420         {
421           "final_label": "thm:path_support",
422           "number": "6.1",
423           "printed_page": "21",
424           "physical_pdf_page": 27,
425           "title_tex": "Path support of powers",
426           "kind": "Theorem"
427         },
428         {
429           "final_label": "cor:acyclic_nilpotence",
430           "number": "6.3",
431           "printed_page": "21",
432           "physical_pdf_page": 27,
433           "title_tex": "Acyclic transfer nilpotence",
434           "kind": "Corollary"
435         }
436       ]
437     },
438     {
439       "visual_page": 15,
440       "visual_physical_pdf_page": 17,
441       "visual_printed_page": "15",
442       "title": "A solve has a dependency clock",
443       "source_line_original": "Traditional edition: Theorem 6.5, Corollary 6.6, Theorem 10.3; PDF pp. 22, 34.",
444       "source_line_current": "Traditional pp. 22, 35 / Theorem 6.5, Corollary 6.6, Theorem 10.3.",
445       "traditional_targets": [
446         {
447           "final_label": "thm:level_schedule",
448           "number": "6.5",
449           "printed_page": "22",
450           "physical_pdf_page": 28,
451           "title_tex": "Level schedule for a triangular solve",
452           "kind": "Theorem"
453         },
454         {
455           "final_label": "cor:sequential_depth",
456           "number": "6.6",
457           "printed_page": "22",
458           "physical_pdf_page": 28,
459           "title_tex": "Sequential depth",
460           "kind": "Corollary"
461         },
462         {
463           "final_label": "thm:dag_depth",
464           "number": "10.3",
465           "printed_page": "35",
466           "physical_pdf_page": 41,
467           "title_tex": "Acyclic schedule depth",
468           "kind": "Theorem"
469         }
470       ]
471     },
472     {
473       "visual_page": 16,
474       "visual_physical_pdf_page": 18,
475       "visual_printed_page": "16",
476       "title": "Elimination creates new interactions",
477       "source_line_original": "Traditional edition: Theorem 6.7, Proposition 6.8; PDF p. 23.",
478       "source_line_current": "Traditional p. 23 / Theorem 6.7, Proposition 6.8.",
479       "traditional_targets": [
480         {
481           "final_label": "thm:inverse_support",
482           "number": "6.7",
483           "printed_page": "23",
484           "physical_pdf_page": 29,
485           "title_tex": "Inverse support lies in the transitive closure",
486           "kind": "Theorem"
487         },
488         {
489           "final_label": "prop:schur_fill",
490           "number": "6.8",
491           "printed_page": "23",
492           "physical_pdf_page": 29,
493           "title_tex": "Schur support inclusion",
494           "kind": "Proposition"
495         }
496       ]
497     },
498     {
499       "visual_page": 17,
500       "visual_physical_pdf_page": 19,
501       "visual_printed_page": "17",
502       "title": "Invariant does not mean independently addressable",
503       "source_line_original": "Traditional edition: Proposition 7.2, Theorem 7.3; PDF p. 24.",
504       "source_line_current": "Traditional p. 24 / Proposition 7.2, Theorem 7.3.",
505       "traditional_targets": [
506         {
507           "final_label": "prop:krylov_invariant",
508           "number": "7.2",
509           "printed_page": "24",
510           "physical_pdf_page": 30,
511           "title_tex": "Invariant packet Krylov decomposition",
512           "kind": "Proposition"
513         },
514         {
515           "final_label": "thm:approx_krylov",
516           "number": "7.3",
517           "printed_page": "24",
518           "physical_pdf_page": 30,
519           "title_tex": "Approximate packet Krylov bound",
520           "kind": "Theorem"
521         }
522       ]
523     },
524     {
525       "visual_page": 18,
526       "visual_physical_pdf_page": 20,
527       "visual_printed_page": "18",
528       "title": "Measure coupling after normalization",
529       "source_line_original": "Traditional edition: Theorem 7.4, Corollary 7.6, Classical input 7.5; PDF pp. 24, 25.",
530       "source_line_current": "Traditional p. 25 / Theorem 7.4, Corollary 7.6, Classical input 7.5.",
531       "traditional_targets": [
532         {
533           "final_label": "thm:block_jacobi",
534           "number": "7.4",
535           "printed_page": "25",
536           "physical_pdf_page": 31,
537           "title_tex": "Block Jacobi condition bound",
538           "kind": "Theorem"
539         },
540         {
541           "final_label": "cor:certified_pcg",
542           "number": "7.6",
543           "printed_page": "25",
544           "physical_pdf_page": 31,
545           "title_tex": "Certified packet preconditioning",
546           "kind": "Corollary"
547         },
548         {
549           "final_label": "fact:cg",
550           "number": "7.5",
551           "printed_page": "25",
552           "physical_pdf_page": 31,
553           "title_tex": "Preconditioned conjugate gradient convergence",
554           "kind": "Classical input"
555         }
556       ]
557     },
558     {
559       "visual_page": 19,
560       "visual_physical_pdf_page": 21,
561       "visual_printed_page": "19",
562       "title": "Twelve small blocks, one coherent error",
563       "source_line_original": "Traditional edition: Theorem 8.1, Proposition 9.2; PDF pp. 25, 29.",
564       "source_line_current": "Traditional pp. 26, 30 / Theorem 8.1, Proposition 9.2.",
565       "traditional_targets": [
566         {
567           "final_label": "thm:packet_error",
568           "number": "8.1",
569           "printed_page": "26",
570           "physical_pdf_page": 32,
571           "title_tex": "Packet perturbation certificate",
572           "kind": "Theorem"
573         },
574         {
575           "final_label": "prop:block_discovery_certificate",
576           "number": "9.2",
577           "printed_page": "30",
578           "physical_pdf_page": 36,
579           "title_tex": "Exact block discovery certificate",
580           "kind": "Proposition"
581         }
582       ]
583     },
584     {
585       "visual_page": 20,
586       "visual_physical_pdf_page": 22,
587       "visual_printed_page": "20",
588       "title": "Spend error where it is cheapest",
589       "source_line_original": "Traditional edition: Theorem 8.4, Theorem 8.5; PDF p. 27.",
590       "source_line_current": "Traditional pp. 27, 28 / Theorem 8.4, Theorem 8.5.",
591       "traditional_targets": [
592         {
593           "final_label": "thm:continuous_precision",
594           "number": "8.4",
595           "printed_page": "27",
596           "physical_pdf_page": 33,
597           "title_tex": "Continuous precision allocation",
598           "kind": "Theorem"
599         },
600         {
601           "final_label": "thm:clipped_precision",
602           "number": "8.5",
603           "printed_page": "28",
604           "physical_pdf_page": 34,
605           "title_tex": "Clipped precision allocation",
606           "kind": "Theorem"
607         }
608       ]
609     },
610     {
611       "visual_page": 21,
612       "visual_physical_pdf_page": 23,
613       "visual_printed_page": "21",
614       "title": "An exact budget is not a greedy choice",
615       "source_line_original": "Traditional edition: Theorem 8.7, Remark 8.8; PDF pp. 28, 29.",
616       "source_line_current": "Traditional p. 29 / Theorem 8.7, Remark 8.8.",
617       "traditional_targets": [
618         {
619           "final_label": "thm:discrete_precision",
620           "number": "8.7",
621           "printed_page": "29",
622           "physical_pdf_page": 35,
623           "title_tex": "Exact discrete precision program",
624           "kind": "Theorem"
625         },
626         {
627           "final_label": "rem:dtype_boundary",
628           "number": "8.8",
629           "printed_page": "29",
630           "physical_pdf_page": 35,
631           "title_tex": "",
632           "kind": "Remark"
633         }
634       ]
635     },
636     {
637       "visual_page": 22,
638       "visual_physical_pdf_page": 24,
639       "visual_printed_page": "22",
640       "title": "A penalty can miss the budget optimum",
641       "source_line_original": "Traditional edition: Theorem 9.4, Corollary 9.7, Theorem 9.8; PDF pp. 30, 32.",
642       "source_line_current": "Traditional pp. 31, 32, 33 / Theorem 9.4, Corollary 9.7, Theorem 9.8.",
643       "traditional_targets": [
644         {
645           "final_label": "thm:tree_compiler",
646           "number": "9.4",
647           "printed_page": "31",
648           "physical_pdf_page": 37,
649           "title_tex": "Exact Lagrangian packet compiler",
650           "kind": "Theorem"
651         },
652         {
653           "final_label": "cor:supported_pareto",
654           "number": "9.7",
655           "printed_page": "32",
656           "physical_pdf_page": 38,
657           "title_tex": "Supported Pareto points",
658           "kind": "Corollary"
659         },
660         {
661           "final_label": "thm:budget_compiler",
662           "number": "9.8",
663           "printed_page": "33",
664           "physical_pdf_page": 39,
665           "title_tex": "Quantized budget dynamic program",
666           "kind": "Theorem"
667         }
668       ]
669     },
670     {
671       "visual_page": 23,
672       "visual_physical_pdf_page": 25,
673       "visual_printed_page": "23",
674       "title": "Recompile the changed part, not everything",
675       "source_line_original": "Traditional edition: Theorem 9.11, Theorem 9.12; PDF p. 33.",
676       "source_line_current": "Traditional pp. 33, 34 / Theorem 9.11, Theorem 9.12.",
677       "traditional_targets": [
678         {
679           "final_label": "thm:compiler_stability",
680           "number": "9.11",
681           "printed_page": "33",
682           "physical_pdf_page": 39,
683           "title_tex": "Compiler stability",
684           "kind": "Theorem"
685         },
686         {
687           "final_label": "thm:local_recompilation",
688           "number": "9.12",
689           "printed_page": "34",
690           "physical_pdf_page": 40,
691           "title_tex": "Local recompilation",
692           "kind": "Theorem"
693         }
694       ]
695     },
696     {
697       "visual_page": 24,
698       "visual_physical_pdf_page": 26,
699       "visual_printed_page": "24",
700       "title": "Batch shapes, account for traffic",
701       "source_line_original": "Traditional edition: Proposition 3.6, Theorem 3.8, Proposition 10.2; PDF pp. 13, 34.",
702       "source_line_current": "Traditional pp. 11, 12, 35 / Proposition 3.6, Theorem 3.8, Proposition 10.2.",
703       "traditional_targets": [
704         {
705           "final_label": "prop:streaming_bytes",
706           "number": "3.6",
707           "printed_page": "11",
708           "physical_pdf_page": 17,
709           "title_tex": "Streaming byte count",
710           "kind": "Proposition"
711         },
712         {
713           "final_label": "thm:roofline",
714           "number": "3.8",
715           "printed_page": "12",
716           "physical_pdf_page": 18,
717           "title_tex": "Roofline lower bound",
718           "kind": "Theorem"
719         },
720         {
721           "final_label": "prop:shape_launch",
722           "number": "10.2",
723           "printed_page": "35",
724           "physical_pdf_page": 41,
725           "title_tex": "Launch reduction by shape",
726           "kind": "Proposition"
727         }
728       ]
729     },
730     {
731       "visual_page": 25,
732       "visual_physical_pdf_page": 27,
733       "visual_printed_page": "25",
734       "title": "The first win comes after the tie",
735       "source_line_original": "Traditional edition: Theorem 10.4, Corollary 10.5, Corollary 10.6; PDF pp. 34, 35.",
736       "source_line_current": "Traditional pp. 35, 36 / Theorem 10.4, Corollary 10.5, Corollary 10.6.",
737       "traditional_targets": [
738         {
739           "final_label": "thm:amortization",
740           "number": "10.4",
741           "printed_page": "35",
742           "physical_pdf_page": 41,
743           "title_tex": "Amortization threshold",
744           "kind": "Theorem"
745         },
746         {
747           "final_label": "cor:graph_threshold",
748           "number": "10.5",
749           "printed_page": "35",
750           "physical_pdf_page": 41,
751           "title_tex": "Graph replay threshold",
752           "kind": "Corollary"
753         },
754         {
755           "final_label": "cor:materialization_threshold",
756           "number": "10.6",
757           "printed_page": "36",
758           "physical_pdf_page": 42,
759           "title_tex": "Materialization threshold",
760           "kind": "Corollary"
761         }
762       ]
763     },
764     {
765       "visual_page": 26,
766       "visual_physical_pdf_page": 28,
767       "visual_printed_page": "26",
768       "title": "Same output before comparing times",
769       "source_line_original": "Traditional edition: Proposition 2.9, Section 11, Section 12; PDF pp. 10, 35, 36.",
770       "source_line_current": "Traditional pp. 9, 36, 37 / Proposition 2.9, Section 11, Section 12.",
771       "traditional_targets": [
772         {
773           "final_label": "prop:contract_conversion",
774           "number": "2.9",
775           "printed_page": "9",
776           "physical_pdf_page": 15,
777           "title_tex": "Contract conversion",
778           "kind": "Proposition"
779         },
780         {
781           "final_label": "sec:benchmark_protocol",
782           "number": "11",
783           "printed_page": "36",
784           "physical_pdf_page": 42,
785           "title_tex": "Benchmark contracts and measurement protocol",
786           "kind": "Section"
787         },
788         {
789           "final_label": "sec:measured",
790           "number": "12",
791           "printed_page": "37",
792           "physical_pdf_page": 43,
793           "title_tex": "Recorded CPU and GPU corpus",
794           "kind": "Section"
795         }
796       ]
797     },
798     {
799       "visual_page": 27,
800       "visual_physical_pdf_page": 29,
801       "visual_printed_page": "27",
802       "title": "Close the loop on the running example",
803       "source_line_original": "Traditional edition: Theorem 2.3, Theorem 3.4, Theorem 5.1; PDF pp. 8, 11, 17.",
804       "source_line_current": "Traditional pp. 7, 11, 16 / Theorem 2.3, Theorem 3.4, Theorem 5.1.",
805       "traditional_targets": [
806         {
807           "final_label": "thm:exact_evaluation",
808           "number": "2.3",
809           "printed_page": "7",
810           "physical_pdf_page": 13,
811           "title_tex": "Exact evaluation",
812           "kind": "Theorem"
813         },
814         {
815           "final_label": "thm:bdlr_counts",
816           "number": "3.4",
817           "printed_page": "11",
818           "physical_pdf_page": 17,
819           "title_tex": "BDLR application and storage",
820           "kind": "Theorem"
821         },
822         {
823           "final_label": "thm:bdlr_product",
824           "number": "5.1",
825           "printed_page": "16",
826           "physical_pdf_page": 22,
827           "title_tex": "Exact BDLR product",
828           "kind": "Theorem"
829         }
830       ]
831     },
832     {
833       "visual_page": 28,
834       "visual_physical_pdf_page": 30,
835       "visual_printed_page": "28",
836       "title": "What this edition certifies",
837       "source_line_original": "Traditional edition: Section 13, Section 14, Section F.6, Section F.7; PDF pp. 39, 40, 81, 82.",
838       "source_line_current": "Traditional pp. 41, 42, 83, 84 / Section 13, Section 14, Section F.6, Section F.7.",
839       "traditional_targets": [
840         {
841           "final_label": "sec:implementation",
842           "number": "13",
843           "printed_page": "41",
844           "physical_pdf_page": 47,
845           "title_tex": "Implementation and verification",
846           "kind": "Section"
847         },
848         {
849           "final_label": "sec:boundaries",
850           "number": "14",
851           "printed_page": "42",
852           "physical_pdf_page": 48,
853           "title_tex": "Hardware implications and exact boundaries",
854           "kind": "Section"
855         },
856         {
857           "final_label": "supp6:subsection:006",
858           "number": "F.6",
859           "printed_page": "83",
860           "physical_pdf_page": 89,
861           "title_tex": "Source map and verification",
862           "kind": "Section"
863         },
864         {
865           "final_label": "supp6:subsection:007",
866           "number": "F.7",
867           "printed_page": "84",
868           "physical_pdf_page": 90,
869           "title_tex": "Regressions, reproduction and claim boundary",
870           "kind": "Section"
871         }
872       ]
873     },
874     {
875       "visual_page": 29,
876       "visual_physical_pdf_page": 31,
877       "visual_printed_page": "29",
878       "title": "A complex range needs an adjoint",
879       "source_line_original": "Traditional edition: Theorem 5.6, Section F.1, Section F.2; PDF pp. 19, 78.",
880       "source_line_current": "Traditional pp. 18, 79, 80 / Theorem 5.6, Section F.1, Section F.2.",
881       "traditional_targets": [
882         {
883           "final_label": "thm:small_core_recompression",
884           "number": "5.6",
885           "printed_page": "18",
886           "physical_pdf_page": 24,
887           "title_tex": "Small core recompression",
888           "kind": "Theorem"
889         },
890         {
891           "final_label": "supp6:subsection:001",
892           "number": "F.1",
893           "printed_page": "79",
894           "physical_pdf_page": 85,
895           "title_tex": "Compact factors from actual column spaces",
896           "kind": "Section"
897         },
898         {
899           "final_label": "supp6:subsection:002",
900           "number": "F.2",
901           "printed_page": "80",
902           "physical_pdf_page": 86,
903           "title_tex": "Why a small-core optimum is a global optimum",
904           "kind": "Section"
905         }
906       ]
907     },
908     {
909       "visual_page": 30,
910       "visual_physical_pdf_page": 32,
911       "visual_printed_page": "30",
912       "title": "Inverse reachability is still an inclusion",
913       "source_line_original": "Traditional edition: Theorem 6.7, Theorem 6.1, Corollary 6.3; PDF pp. 21, 23.",
914       "source_line_current": "Traditional pp. 21, 23 / Theorem 6.7, Theorem 6.1, Corollary 6.3.",
915       "traditional_targets": [
916         {
917           "final_label": "thm:inverse_support",
918           "number": "6.7",
919           "printed_page": "23",
920           "physical_pdf_page": 29,
921           "title_tex": "Inverse support lies in the transitive closure",
922           "kind": "Theorem"
923         },
924         {
925           "final_label": "thm:path_support",
926           "number": "6.1",
927           "printed_page": "21",
928           "physical_pdf_page": 27,
929           "title_tex": "Path support of powers",
930           "kind": "Theorem"
931         },
932         {
933           "final_label": "cor:acyclic_nilpotence",
934           "number": "6.3",
935           "printed_page": "21",
936           "physical_pdf_page": 27,
937           "title_tex": "Acyclic transfer nilpotence",
938           "kind": "Corollary"
939         }
940       ]
941     },
942     {
943       "visual_page": 31,
944       "visual_physical_pdf_page": 33,
945       "visual_printed_page": "31",
946       "title": "One tree can serve a weighted family",
947       "source_line_original": "Traditional edition: Corollary 9.5, Theorem 9.4; PDF pp. 30, 31.",
948       "source_line_current": "Traditional p. 31 / Corollary 9.5, Theorem 9.4.",
949       "traditional_targets": [
950         {
951           "final_label": "cor:shared_compiler",
952           "number": "9.5",
953           "printed_page": "31",
954           "physical_pdf_page": 37,
955           "title_tex": "Shared compilation for an operator family",
956           "kind": "Corollary"
957         },
958         {
959           "final_label": "thm:tree_compiler",
960           "number": "9.4",
961           "printed_page": "31",
962           "physical_pdf_page": 37,
963           "title_tex": "Exact Lagrangian packet compiler",
964           "kind": "Theorem"
965         }
966       ]
967     },
968     {
969       "visual_page": 32,
970       "visual_physical_pdf_page": 34,
971       "visual_printed_page": "32",
972       "title": "Safe integers can still be conservative",
973       "source_line_original": "Traditional edition: Theorem 8.7, Theorem 9.8, Corollary 9.9; PDF pp. 28, 32.",
974       "source_line_current": "Traditional pp. 29, 33 / Theorem 8.7, Theorem 9.8, Corollary 9.9.",
975       "traditional_targets": [
976         {
977           "final_label": "thm:discrete_precision",
978           "number": "8.7",
979           "printed_page": "29",
980           "physical_pdf_page": 35,
981           "title_tex": "Exact discrete precision program",
982           "kind": "Theorem"
983         },
984         {
985           "final_label": "thm:budget_compiler",
986           "number": "9.8",
987           "printed_page": "33",
988           "physical_pdf_page": 39,
989           "title_tex": "Quantized budget dynamic program",
990           "kind": "Theorem"
991         },
992         {
993           "final_label": "cor:budget_complexity",
994           "number": "9.9",
995           "printed_page": "33",
996           "physical_pdf_page": 39,
997           "title_tex": "Pseudo polynomial complexity",
998           "kind": "Corollary"
999         }
1000       ]
1001     }
1002   ],
1003   "provenance_revision": {
1004     "id": "paper-viii-visual-crosswalk-2026-11-03",
1005     "supersedes": {
1006       "path": "papers/paper-viii/current/editable/visual_guide/VISUAL_TO_TRADITIONAL_CROSSWALK.json",
1007       "size": 34328,
1008       "sha256": "99d61945f6b8c322c650f254195e595297d65800ec51a558304e29d6cc142f9b",
1009       "git_blob_sha1": "46d9799bb2dfc348c5761320e897e8fbc76dbd25",
1010       "mode": "100644"
1011     },
1012     "change": "Rebind the visual PDF checksum to the retained 34-page PDF. All 32 page records and manuscript bindings are preserved.",
1013     "verification": "All 32 PDF plate titles, locators and footer labels rechecked; stable manuscript labels, numbers, kinds and titles rechecked by the HTML converter.",
1014     "scope": "Visual source/PDF/manuscript correspondence only; no new mathematical proof review or Lean execution."
1015   }
1016 }

Back to source controls

Other PDFs for this work

Original file and source record

This copy matches the recorded source file. Its publication here does not change the work’s review status.

SHA-256: 7227f8f643e430acb5cd66dfd16d3ca35c5d0d8757022ae026dc768b9ce8bfe6

Original source on GitHub

Back to Paper VIII: Packet Operator Algorithms, Exact Compilation, and GPU Realization