{ "step": "C444", "completed_steps": [ 435, 436, 437, 438, 439, 440, 441, 442, 443, 444 ], "predecessor_summaries": [ { "step": "C435", "title": "Complete Input Census for the Six Source-Derived Pivot Pairs", "main_result": "All2238 six-map/input trials yield23 sourced first-leg outputs,10 integer final outputs,8 sourced final outputs and two complete coordinate paths: old2148→2020→1956 and additional3206→3170→3206, both withp3620/q2756. The loop has signed gaps414/−414 and changes36/−36, with SP/LXX-OFF Shem-birth endpoints and SP/LXX-OFF Flood-start intermediate. Its16 Cartesian label assignments are not yet16 same-record returns.", "calculation_checks": 2244, "authentication_checks": 18, "next_question": "Audit the source states and label identity of the3206→3170→3206 loop; derive its36-year offset from the existing100,60 and Gear4-year difference, and distinguish mixed-direction affine closure from chronological succession." }, { "step": "C436", "title": "Source Identity and Direction of the Shem–Flood Return Loop", "main_result": "The3206→3170→3206 loop has16 Cartesian labels:8 same-record returns and8 SP/LXX alias switches; one all-SP assignment and zero unchanged-context assignments. Source36=100−60−4. Signed gaps414→450 and−414→−450 establish a mixed-direction fixed-point return, not chronological repetition. Both pivot and station pairs share3188, already MT Noah birthG2/C1/T0/F1, with radii432 and18 (ratio24).", "calculation_checks": 17, "authentication_checks": 20, "next_question": "Census the six Gear/Terah local midpoint profiles already determined by C434: c=N−518, outer pivots c±432, inner stations c±18. Require every point to remain in the fixed source register and derive the role/context offsets without fitting a center." }, { "step": "C437", "title": "Finite Source Census of the 432 and 18 Midpoint Profile", "main_result": "Six derived c=N−518 profiles yield four sourced MT Noah centers3188,3190,3248,3250;3192/3252 require unavailableGear4. Onlyc3188 has all five points c±432,c±18,c. Source offsets are650−215−1−2=432;650−500−130−2=18;650−600−130+60+2=−18;650−950−130−2=−432. The ratio450/414=25/23 follows from432:18=24:1.", "calculation_checks": 28, "authentication_checks": 18, "next_question": "For the four already sourced centers3188,3190,3248,3250, census the local reflection R_c(x)=2c−x over the373 fixed regular coordinates. Identify the exact source domain and any role/context pairs, keeping these local comparisons distinct from the global Mirror." }, { "step": "C438", "title": "Complete Regular Source Domains of Four Local Reflections", "main_result": "All1492 local-reflection trials at3188/3190/3248/3250 yield maximal source domains61/67/19/61,106 coordinate orbits including4 fixed centers,258 unoriented labelled pairs and512 directed label pairings. Original432/18 pairs survive; additional Noah/Shem/Flood role exchanges occur. All four reflections remain partial on the373-coordinate domain; no global Mirror or full group action is inferred.", "calculation_checks": 1502, "authentication_checks": 18, "next_question": "Derive and verify the complete Noah-birth/Noah-death reflection subclass using the existing950 lifespan, complementary Cainan/sojourn states, SP companion choice and Gear/Terah sums; compare the rule with every C438 labelled hit." }, { "step": "C439", "title": "Source Complement Rule for Noah Birth–Death Reflections", "main_result": "All36864 Noah-birth/death reflection trials reduce exactly to one rule: SP/LXX endpoints, Cainan sum1, sojourn sum1, equal referenceTerah, Gear sum2g and exactly one SP companion. The unique bounded sum equation is6032+344=2×3188 with344=130+215−1. Counts bycenter are8/24/8/24 coordinate pairs and16/48/16/48 labels, totaling64/128. MT endpoints are excluded by maximum sum6200<6376.", "calculation_checks": 11, "authentication_checks": 18, "next_question": "Test whether the Noah-birth/Shem-death reflection class and the Shem-birth/Flood-boundary class are exactly related by opposed500-year source shifts. Preserve primary/companion and Flood-start/close distinctions, all aliases, and any change in pair ordering." }, { "step": "C440", "title": "Opposed 500-Year Transport of Two Reflection Classes", "main_result": "Opposed500 shifts Noah birth→Shem birth (−500) and Shem death→Flood start/close (+500) biject all16 coordinate pairs of the two reflection classes.40 source-label pairs yield40 tradition-preserving targets within48 target labels; the extra8 are LXX Flood-close aliases, not LXX companions. Four bounded context-sum templates classify the source class. One pair atc3250 reverses coordinate order:3705/2795→3205/3295.", "calculation_checks": 86, "authentication_checks": 19, "next_question": "Close the C438 reflection inventory by deriving the remaining Flood-start/close, MT Noah/Gear and Noah-birth/Flood-close alias classes, then verify that the resulting source grammar accounts for every labelled and coordinate pair without double-counting aliases." }, { "step": "C441", "title": "Complete Source Grammar of the Four Local Reflection Domains", "main_result": "Six source classes partition all258 labelled reflection pairs:Noah complement128;Noah/Shem40;Shem/Flood48;Flood boundaries32;Noah/Flood alias4;MT Noah Gears6. Their112 coordinate memberships reduce to106 orbits through six explicit role-alias overlaps. Residual Flood rule usesC1/T1, complementaryF and boundedGear sums; two600-year Noah-companion/Flood-close pairs overlap Noah-death labels via349=130+215+4; MT centerG2 exchangesG1/G3, whileG3 only fixes itself.", "calculation_checks": 18, "authentication_checks": 20, "next_question": "Test the reflection conjugacy R_c E_p R_c=E_q at the four sourced centers, census the reversed two-E order on the fixed373-coordinate domain, and determine whether the nonzero2K path and zero-net loop have fully sourced reflected counterparts." }, { "step": "C442", "title": "Source Bounds of Reflection Conjugacy and Reversed E Order", "main_result": "Reflection conjugacy R_cE_pR_c=E_q holds exactly, while forward/reverse two-E words fixc±18 and differ by−3456/529. All1492 reversed trials yield only3170→3206→3170 atc3188. Reflection of2148→2020→1956 is4228→4356→4420, all outside the fixed source range. Only five primitive reflected pairs survive:four zero-gap pivot arrows and one nonzero loop leg. Reversed integer outputs satisfyx≡c−18 mod529.", "calculation_checks": 2991, "authentication_checks": 20, "next_question": "Apply the two inherited fixed Mirror corner exchanges to the complete five-point3188 profile and the current local-reflection source domains. Test membership in the frozen cumulative register and preserve the original17K corner controls; do not fit a new exchange or cumulative source." }, { "step": "C443", "title": "Fixed Mirror Test of the Local Reflection Domains", "main_result": "Under inherited exchanges−2639−x/−2635−x, originali3/i5 positive controls retain17K. The four local reflection domains give416 slot trials with37 LXX cumulative source memberships, and212 orbit trials with5 complete images (4fixed). The only nonfixed image is MT Noah3246/3250→LXX-OFF Shem−5885/−5889 under−2639, a4-year pair. All16 images of the3188 core and two-E path stations are absent from the fixed48-record LXX cumulative menu. No new cumulative Gear or Mirror closure follows.", "calculation_checks": 428, "authentication_checks": 23, "next_question": "Consolidate C435–C443, verify the decisive source grammar and operator/Mirror boundaries with a separate implementation, audit all sealed packets, and publish C444 with the reading index and recovery packages. Leave C445 unexecuted." } ], "predecessor_main_checks": 7325, "predecessor_authentication_checks": 174, "predecessor_sealed_audit": { "status": "passed", "packets": [ { "step": 435, "payloads": 26, "bindings": 12, "sources": 13, "published_files": 3, "certificate_sha256": "e91dd6a9f0c2366141972ec6dc61191d5e615950ea9be0503c1b7a5bfbecec4e" }, { "step": 436, "payloads": 28, "bindings": 12, "sources": 15, "published_files": 3, "certificate_sha256": "d242df71dd3c679ffbe6e290654ab70cbd20bfc5feb2103684c78e675255ff83" }, { "step": 437, "payloads": 26, "bindings": 12, "sources": 13, "published_files": 3, "certificate_sha256": "50da87410bb2d6a2abd6e5b2dca34cf1ecfc46e31e2a46c6b7ab8a38eb857386" }, { "step": 438, "payloads": 26, "bindings": 12, "sources": 13, "published_files": 3, "certificate_sha256": "485fcf29349f1e27c0b9bc40beadd5f2c94f52f0fcc69b1b3d552c6b1c147272" }, { "step": 439, "payloads": 26, "bindings": 12, "sources": 13, "published_files": 3, "certificate_sha256": "b6710627206c3de35e18662154c390413d74b7da7f98a39db5b1729c58eb3b02" }, { "step": 440, "payloads": 27, "bindings": 12, "sources": 14, "published_files": 3, "certificate_sha256": "725beafca76ba87c678790512d5f01507e13861d05031f0feffcb5fee14f52e0" }, { "step": 441, "payloads": 28, "bindings": 12, "sources": 15, "published_files": 3, "certificate_sha256": "edfd3037f5d6c54aa6105d85ec29ef700549987e5de8c90400f48c859ab198d4" }, { "step": 442, "payloads": 28, "bindings": 12, "sources": 15, "published_files": 3, "certificate_sha256": "0f207fad873f96a568c93ec48c3544a0a58eb40bb4e0525b6cd124c2e4a75ae8" }, { "step": 443, "payloads": 31, "bindings": 12, "sources": 18, "published_files": 3, "certificate_sha256": "1fa632d4b98186f448f362033e696750b2d1a2fee22d9debac1ccf8a6874a7fa" } ], "totals": { "payloads": 246, "bindings": 108, "sources": 129, "published_files": 27 }, "standing_controls_unchanged": true, "C445_executed": false }, "alternate_method": { "step": "C444", "status": "passed", "check_count": 164, "checks": [ "direct source grid equals528 inherited records", "373 distinct coordinates", "source weighted midpoint identity 1/0", "source weighted midpoint identity 2/0", "source weighted midpoint identity 3/0", "source weighted midpoint identity 1/1", "source weighted midpoint identity 2/1", "source weighted midpoint identity 3/1", "forward census exact", "source loop36 and24-to1 geometry", "same-record loop returns versus Cartesian assignments", "four sourced centers", "all106 reflection orbits from pair sums", "all258 source label pairings", "source reflection domain 3188", "source reflection domain 3190", "source reflection domain 3248", "source reflection domain 3250", "Noah complement class128", "Noah source complement (3190, 300, 465)", "Noah source complement (3250, 447, 378)", "Noah source complement (3250, 394, 439)", "Noah source complement (3190, 204, 369)", "Noah source complement (3250, 298, 279)", "Noah source complement (3250, 510, 187)", "Noah source complement (3250, 299, 278)", "Noah source complement (3190, 204, 497)", "Noah source complement (3250, 298, 471)", "Noah source complement (3190, 385, 188)", "Noah source complement (3250, 299, 470)", "Noah source complement (3190, 289, 284)", "Noah source complement (3190, 445, 376)", "Noah source complement (3188, 204, 177)", "Noah source complement (3190, 201, 372)", "Noah source complement (3188, 204, 433)", "Noah source complement (3190, 201, 500)", "Noah source complement (3190, 288, 285)", "Noah source complement (3250, 474, 287)", "Noah source complement (3190, 192, 381)", "Noah source complement (3188, 201, 180)", "Noah source complement (3188, 444, 185)", "Noah source complement (3188, 201, 436)", "Noah source complement (3190, 396, 177)", "Noah source complement (3190, 397, 176)", "Noah source complement (3250, 198, 379)", "Noah source complement (3190, 396, 433)", "Noah source complement (3190, 397, 432)", "Noah source complement (3190, 301, 272)", "Noah source complement (3188, 192, 189)", "Noah source complement (3250, 395, 182)", "Noah source complement (3190, 301, 464)", "Noah source complement (3250, 395, 438)", "Noah source complement (3248, 194, 191)", "Noah source complement (3190, 393, 180)", "Noah source complement (3190, 477, 280)", "Noah source complement (3190, 393, 436)", "Noah source complement (3190, 297, 276)", "Noah source complement (3190, 509, 184)", "Noah source complement (3190, 297, 468)", "Noah source complement (3250, 507, 190)", "Noah source complement (3190, 444, 377)", "Noah source complement (3190, 476, 281)", "Noah source complement (3250, 391, 186)", "Noah source complement (3250, 475, 286)", "Noah source complement (3250, 443, 382)", "Noah source complement (3190, 200, 373)", "Noah source complement (3250, 295, 282)", "Noah source complement (3188, 445, 184)", "Noah source complement (3190, 200, 501)", "Noah source complement (3248, 206, 179)", "Noah source complement (3250, 199, 378)", "Noah source complement (3250, 206, 371)", "Noah source complement (3250, 442, 383)", "Noah source complement (3250, 207, 370)", "Noah source complement (3190, 473, 284)", "Noah source complement (3250, 206, 499)", "Noah source complement (3250, 294, 283)", "Noah source complement (3250, 207, 498)", "Noah source complement (3248, 206, 435)", "Noah source complement (3190, 293, 280)", "Noah source complement (3248, 447, 186)", "Noah source complement (3190, 197, 376)", "Noah source complement (3190, 440, 381)", "Noah source complement (3190, 205, 368)", "Noah source complement (3190, 205, 496)", "Noah source complement (3188, 200, 181)", "Noah source complement (3248, 203, 182)", "Noah source complement (3248, 446, 187)", "Noah source complement (3188, 200, 437)", "Noah source complement (3248, 203, 438)", "Noah source complement (3188, 197, 184)", "Noah source complement (3188, 440, 189)", "Noah source complement (3190, 508, 185)", "Noah source complement (3250, 194, 383)", "Noah source complement (3250, 195, 382)", "Noah source complement (3248, 202, 439)", "Noah source complement (3190, 384, 189)", "Noah source complement (3250, 399, 178)", "Noah source complement (3250, 399, 434)", "Noah source complement (3250, 303, 274)", "Noah source complement (3190, 296, 277)", "Noah source complement (3250, 390, 187)", "Noah source complement (3190, 389, 184)", "Noah source complement (3250, 303, 466)", "Noah source complement (3190, 296, 469)", "Noah source complement (3250, 506, 191)", "Noah source complement (3190, 505, 188)", "Noah source complement (3250, 302, 275)", "Noah source complement (3250, 302, 467)", "Noah source complement (3190, 441, 380)", "Noah source complement (3190, 504, 189)", "Noah source complement (3250, 387, 190)", "Noah source complement (3250, 479, 282)", "Noah source complement (3250, 291, 286)", "Noah source complement (3188, 441, 188)", "Noah source complement (3250, 203, 374)", "Noah source complement (3190, 196, 377)", "Noah source complement (3250, 446, 379)", "Noah source complement (3250, 290, 287)", "Noah source complement (3250, 203, 502)", "Noah source complement (3188, 205, 176)", "Noah source complement (3190, 392, 181)", "Noah source complement (3248, 202, 183)", "Noah source complement (3188, 205, 432)", "Noah source complement (3248, 443, 190)", "Noah source complement (3190, 193, 380)", "Noah source complement (3250, 202, 375)", "Noah source complement (3190, 392, 437)", "Noah source complement (3250, 202, 503)", "Noah source complement (3250, 398, 179)", "Noah source complement (3188, 196, 185)", "Noah source complement (3248, 199, 186)", "Noah source complement (3248, 442, 191)", "Noah source complement (3248, 207, 178)", "Noah source complement (3250, 398, 435)", "Noah source complement (3248, 207, 434)", "Noah source complement (3248, 198, 187)", "Noah source complement (3188, 193, 188)", "Noah source complement (3250, 511, 186)", "Noah source complement (3190, 388, 185)", "Noah source complement (3190, 472, 285)", "Noah source complement (3190, 292, 281)", "Noah source complement (3250, 386, 191)", "Noah source complement (3190, 300, 273)", "Noah source complement (3250, 394, 183)", "Noah source complement (3248, 195, 190)", "Noah source complement (3250, 478, 283)", "only LXX Flood-close has missing typed inverse (3188, 73, 411)", "only LXX Flood-close has missing typed inverse (3250, 91, 221)", "only LXX Flood-close has missing typed inverse (3250, 217, 95)", "only LXX Flood-close has missing typed inverse (3250, 89, 223)", "only LXX Flood-close has missing typed inverse (3188, 59, 313)", "only LXX Flood-close has missing typed inverse (3188, 75, 409)", "only LXX Flood-close has missing typed inverse (3188, 57, 315)", "only LXX Flood-close has missing typed inverse (3250, 93, 219)", "inverse opposed500 transport40 plus8 aliases", "seven role pairs form six source classes", "six coordinate aliases explain112 versus106", "reversed census only zero-net loop", "only five primitive conjugate pairs", "nonzero2K reflected path entirely outside range", "Mirror partial counts37 slots and5 orbits", "sole nonfixed Mirror orbit", "all16 core Mirror images absent" ], "source_records_generated": 528, "regular_coordinates": 373, "forward_complete_paths": [ [ 3206, 2148, 2020, 1956 ], [ 3206, 3206, 3170, 3206 ] ], "reflection_coordinate_orbits": 106, "reflection_labelled_pairs": 258, "typed_inverse_500": 40, "additional_aliases": 8, "reverse_complete_paths": [ [ 3188, 3170, 3206, 3170 ] ], "Mirror_sourced_slots": 37, "Mirror_complete_orbits": 5, "new_independent_agent_review": false, "method": "Source-table reconstruction, unordered pair sums, integer affine divisibility and inverse label transport; imports no main calculation modules.", "C445_executed": false }, "synthesis": { "new_loop": "3206→3170→3206 withp3620/q2756; opposite signed18×23→18×25 gaps.", "source_midpoint": "3188 MT NoahG2/C1/T0/F1; outer radius432, inner radius18;24:1.", "source_reflections": "Four sourced centers and six source classes account for106 coordinate orbits/258 labelled pairs.", "E_boundary": "Only the zero-net loop survives source reflection; reflected2K path4228/4356/4420 is absent.", "Mirror_boundary": "One four-year partial image survives; the core profile has no image in the retained48-record LXX cumulative menu." }, "regular_sources_unchanged": true, "canonical_or_graph_edits": false, "new_independent_agent_review": false, "C445_executed": false, "next_proposed_question": "Census all ordered compositions of the four fixed local reflections over373 source inputs, requiring sourced intermediate and output records, and reduce the resulting partial maps to source-qualified translations.5968 trials; no new centers or coordinates." }