TFPT scientific source excerpt Original repository path: experiments/theory-contracts/elliptic-moebius-source-bridge-20261026/source_recursion_20261028/source_record_hodge.py Original file SHA-256: 5fb344b8ad49a6d85bf97228ba6d5b093576f69164fa3a3139e02eec19683119 Inclusive original lines: 201-334 Line numbers below refer to the original source. This bounded excerpt is source evidence; it is not a new proof/checker run. Conversation metadata and personal execution details are omitted where indicated. 000201 | require(V.rank() == 5, "five independent Hodge Kraus directions") 000202 | product_typing = plucker_typing(Cs) 000203 | 000204 | marked = [] 000205 | whole = [] 000206 | two_event = [] 000207 | for mark in range(6): 000208 | chart, _ = hodge.duad_chart(mark, mapping) 000209 | 000210 | W20 = exact_gaussian(vector_columns(marked_jump_kraus(old, mark, bell, six, mapping, chart))) 000211 | rank20 = W20.rank() 000212 | joint20 = W20.row_join(V).rank() 000213 | intersection20, plane20 = intersection_data(W20, V) 000214 | require(rank20 == 15, f"mark {mark}: exact marked jump Kraus rank 15") 000215 | require(joint20 == 18 and intersection20 == 2, 000216 | f"mark {mark}: marked source intersects Hodge span in dimension two") 000217 | require(not W20.row_join(V).rank() == W20.rank(), 000218 | f"mark {mark}: full Hodge support is not contained in marked source") 000219 | no_scalar_success(Cs, plane20) 000220 | marked.append({ 000221 | "mark": mark, 000222 | "source_kraus_count": 20, 000223 | "source_span_rank": rank20, 000224 | "hodge_span_rank": 5, 000225 | "joint_span_rank": joint20, 000226 | "intersection_dimension": intersection20, 000227 | "intersection_hodge_indices": plane20, 000228 | "full_hodge_support_contained": False, 000229 | "largest_exact_hodge_cp_subchannel_probability": "0", 000230 | "input_independent_success_from_intersection_plane": False, 000231 | }) 000232 | 000233 | # This is the one actual sixty-event source, represented in one of the 000234 | # six alternative source-derived duad charts. The six charts are not 000235 | # stacked into a new 360-event process. 000236 | W60 = exact_gaussian(vector_columns([chart.T @ U @ chart for U in bell])) 000237 | rank60 = W60.rank() 000238 | joint60 = W60.row_join(V).rank() 000239 | intersection60, plane60 = intersection_data(W60, V) 000240 | require(rank60 == 55, f"chart {mark}: actual sixty-event Kraus rank 55") 000241 | require(joint60 == 58 and intersection60 == 2, 000242 | f"chart {mark}: whole source intersects Hodge span in dimension two") 000243 | require(plane60 == plane20, f"chart {mark}: marked and whole-source Hodge planes agree") 000244 | require(not W60.row_join(V).rank() == W60.rank(), 000245 | f"chart {mark}: full Hodge support is not contained in whole source") 000246 | no_scalar_success(Cs, plane60) 000247 | whole.append({ 000248 | "duad_chart_mark": mark, 000249 | "same_actual_source_kraus_count": 60, 000250 | "source_span_rank": rank60, 000251 | "hodge_span_rank": 5, 000252 | "joint_span_rank": joint60, 000253 | "intersection_dimension": intersection60, 000254 | "intersection_hodge_indices": plane60, 000255 | "full_hodge_support_contained": False, 000256 | "largest_exact_hodge_cp_subchannel_probability": "0", 000257 | "input_independent_success_from_intersection_plane": False, 000258 | }) 000259 | two_event.append(two_event_record(Cs, V, bell, chart, plane60, mark)) 000260 | 000261 | require([x["intersection_hodge_indices"] for x in marked] == 000262 | [[3, 4], [1, 2], [1, 2], [1, 2], [0, 4], [0, 4]], 000263 | "six exact marked intersection planes") 000264 | require([x["intersection_hodge_indices"] for x in whole] == 000265 | [[3, 4], [1, 2], [1, 2], [1, 2], [0, 4], [0, 4]], 000266 | "six exact whole-source intersection planes") 000267 | 000268 | result = { 000269 | "verdict": [ 000270 | "NO_SINGLE_MARK_COHERENT_RECORD_EFFECT_REALIZES_A_NONZERO_EXACT_HODGE_CHANNEL", 000271 | "NO_ONE_EVENT_WHOLE60_RECORD_EFFECT_REALIZES_A_NONZERO_EXACT_HODGE_CHANNEL", 000272 | "EACH_SOURCE_CHART_SHARES_EXACTLY_TWO_OF_THE_FIVE_HODGE_KRAUS_DIRECTIONS", 000273 | "THE_ACCESSIBLE_TWO_PLANE_CANNOT_HAVE_NONZERO_INPUT_INDEPENDENT_SUCCESS", 000274 | "TWO_ACTUAL_WHOLE60_EVENTS_DO_SUPPORT_AN_EXACT_HODGE_SUBCHANNEL_WITH_OPTIMAL_SUCCESS_1_OVER_25", 000275 | "THE_REQUIRED_COHERENT_RECORD_FILTER_IS_TARGET_CONSTRUCTED_AND_NOT_SOURCE_SELECTED", 000276 | ], 000277 | "one_event_mathematical_reason": ( 000278 | "For a source Stinespring isometry sum_l |l> tensor K_l, every positive record effect E " 000279 | "has Choi range contained in span{vec K_l}. Positivity of J_source_effect-p J_Phi for p>0 " 000280 | "would require range(J_Phi) to lie in that source span. Exact ranks disprove this." 000281 | ), 000282 | "normalizations": { 000283 | "hodge": "Phi=(1/3) sum_m Ad(C_m)", 000284 | "marked": "normalized actual jump channel=(1/12) sum_{l in moving(mark)} Ad(U_l D_jump,l)", 000285 | "whole": "C60=(1/60) sum_l Ad(U_l)", 000286 | "note": "positive scalar normalizations do not alter Choi support", 000287 | }, 000288 | "marked_twenty_records": marked, 000289 | "actual_unmarked_sixty_record_in_each_alternative_chart": whole, 000290 | "two_event_actual_whole_sixty_record": two_event, 000291 | "chart_boundary": ( 000292 | "The six entries are coordinate tests of the same actual sixty matrices. They were not " 000293 | "combined into an artificial 360-event source. Without a fixed duad chart, the old Bell10 " 000294 | "and Lambda^2 C5 Hodge channel are not linearly identified." 000295 | ), 000296 | "source_boundary": ( 000297 | "The old coherent-record contracts establish only conditional record constructions and " 000298 | "explicitly leave physical record access and dynamics underived. This calculation grants " 000299 | "coherent record access as the changed premise. The exact obstruction applies at one event; " 000300 | "two events become sufficient only after a target-specific coherent record filter is chosen." 000301 | ), 000302 | "holomorphic_product_boundary": ( 000303 | "The same five epsilon tensors span the image of the wedge map Sym^2(Lambda^2 C5) to " 000304 | "Lambda^4 C5, but they are the five Plucker relations, hence the kernel of holomorphic " 000305 | "coordinate multiplication Sym^2(10) to the 50-dimensional degree-two coordinate ring. " 000306 | "The record subchannel is therefore not automatically an existing holomorphic product output." 000307 | ), 000308 | "plucker_wedge_typing": product_typing, 000309 | "one_event_extra_operation_needed": ( 000310 | "At one event, producing full Phi would require a system operation that adds the three " 000311 | "missing Hodge Kraus directions or a different source. A record-space projection alone " 000312 | "cannot add them." 000313 | ), 000314 | "two_event_selection_boundary": ( 000315 | "Two actual source events already span M10, so a coherent record contraction can realize " 000316 | "the exact subchannel (1/25)Phi. The minimum-norm contraction is fixed after a duad chart " 000317 | "and the Hodge target are supplied. Neither that target-specific record effect nor a physical " 000318 | "heralding apparatus is selected by the original source." 000319 | ), 000320 | "source_sha256": PINS, 000321 | "checks": len(checks), 000322 | } 000323 | if output is not None: 000324 | output.parent.mkdir(parents=True, exist_ok=True) 000325 | output.write_text(json.dumps(result, indent=2, sort_keys=True) + "\n") 000326 | return result 000327 | 000328 | 000329 | if __name__ == "__main__": 000330 | parser = argparse.ArgumentParser() 000331 | parser.add_argument("--out", type=Path) 000332 | args = parser.parse_args() 000333 | payload = main(args.out) 000334 | print(json.dumps(payload, indent=2, sort_keys=True))