{ "status": "PASS — new bounded preparation, no numbered root actions", "question_manifest_sha256": "d71176b923f00b784eb5a4755454f04822042cd63395257c8314505aa42409f8", "input_packet_sha256": "9ee64b0f8466b84294997ecfcf65d1effa1936734f5fe703d6e1110a2d59c462", "sequential_results": [ { "id": "RJ01", "result": "The ordinary domain contains MT19, LXX20 and SP16. The excluded three SP rows retain their inclusive tags and Lamech53/52 distinction.", "reassessment": "Which data are truly retained in the joint observation packet?" }, { "id": "RJ02", "result": "L,B,R are separate mathematical observations in the inverse call. All are generated from explored source inputs here; calculated r and Q(r) do not become independent textual premises.", "reassessment": "What is the complete integer fibre of exact L,B,R?" }, { "id": "RJ03", "result": "Fibre: b ranges through [max(0,B−2,L−R−2), min(L,B+2,L−R+2)]∩Z, r=L−b. Interior residuals u,v∈[−2,2] satisfy u+v=s=L−B−R; size5−|s| for |s|≤4.", "reassessment": "What does that same inverse return for every eligible source row?" }, { "id": "RJ04", "result": "All55 hidden source pairs belong to the complete reconstructed fibres. Every candidate is an algebraic alternative only. Singleton rows are listed explicitly with all unresolved rows alongside them.", "reassessment": "Does rounded total Q(L) add a new constraint when L is already exact?" }, { "id": "RJ05", "result": "Q(L) is a function of exact L and adds nothing after L is fixed. Without exact L, the three rounded values constrain residual sum by rounding, giving the inherited19-or3 class fibres; exact L selects one diagonal.", "reassessment": "What additional row measurement removes the remaining ambiguity?" }, { "id": "RJ06", "result": "A nonsingleton row needs a selector. One independently supplied exact b or residual u suffices. More generally M=αb+βr identifies b=(M−βL)/(α−β) iff α≠β; α=β repeats total L. No claim of global minimal bit encoding is made.", "reassessment": "What can the neighbouring Methuselah, Reu, Lamech and Cainan cases actually establish?" }, { "id": "RJ07", "result": "MT/LXX Methuselah and MT/LXX/SP Reu are singleton conditional fibres. Main LXX Lamech remains(181,572) or(182,571); native Cainan has five pairs. Existing source182 or130 resolves those roles, not the rounded packet alone.", "reassessment": "Can every admitted row shift act on rounded values alone?" }, { "id": "RJ08", "result": "Q(x+d) descends to a function of Q(x) for every integer x iff d is divisible by5. For other residue shifts, the five-element cell straddles two translated rounding cells; the hidden residual changes the answer.", "reassessment": "How do rounded values and residuals compose under source shifts?" }, { "id": "RJ09", "result": "Lift(y,rho)=(y+Q(rho+d),rho+d−Q(rho+d)). Transport through x=y+rho proves exact composition and the carry cocycle; keeping the residual is a lossless encoding, not compression.", "reassessment": "Does the carry lift preserve all observed ordinary inter-tradition row changes?" }, { "id": "RJ10", "result": "All35 named ordinary MT→LXX/SP comparisons, across all three streams, satisfy the same lift. The two scalar contribution orders in delta_r=delta_L−delta_b agree algebraically; no extra intermediate chronology route is claimed.", "reassessment": "Why does the LXX Lamech change move rounded remainder and rounded total differently?" }, { "id": "RJ11", "result": "Lamech original remainder595 has residual0; lifespan777 has residual2. The same−24 shift gives rounded changes−25 and−20 respectively. This is a controlled residual effect, not two different source displacements.", "reassessment": "What does rounding the cap retain and lose globally?" }, { "id": "RJ12", "result": "For T a multiple5, composite fibre is [max(0,T−2),T+2] if TQ(c). Saturation observation alone may include inputs below c.", "reassessment": "Does rounding commute with capping when both arguments use the same rounded representation?" }, { "id": "RJ13", "result": "Every monotone scalar Q preserves min: Q(min(L,c))=min(Q(L),Q(c)). Keeping c exact is a different mixed representation; the source Jared and Lamech rows then differ by−2 and+2.", "reassessment": "What are the complete nine source cap-plus-round fibres?" }, { "id": "RJ14", "result": "The complete cap-plus-round source field has six bounded rounding cells and three saturation rays. Exact births retain capacities but do not recover any hidden residual or ancestral cap excess by themselves.", "reassessment": "How do exact cap loss and rounding residual combine?" }, { "id": "RJ15", "result": "With y=min(L,c), z=L−y, rho_y=y−Q(y): L=Q(y)+rho_y+z and Q(L)−Q(y)=z+rho_y−rho_L. The complete exact reduction488 becomes rounded reduction485; cumulative responses are inherited consequences.", "reassessment": "Are cap loss and rounding residual two independent missing quantities on each known branch?" }, { "id": "RJ16", "result": "Complementarity y≤c,z≥0,z(c−y)=0 removes a false double count. On known active support y=c and rho_y=c−Q(c), so only z is missing; inactive support has z=0 and only rho_y missing. A declared tie determines L=c.", "reassessment": "What minimum source-supported observations would close the remaining whole-family losses?" }, { "id": "RJ17", "result": "Exact births plus exact capped lives have local rank15 on18 variables and three missing ancestral excesses. Replacing capped lives by rounded ones additionally loses finite residual choices on the six inactive rows. A separately supplied total excess adds one linear constraint; the inherited calculated488 is not an independent observation.", "reassessment": "What explanatory gain survives after source-input and inherited-result costs are counted?" }, { "id": "RJ18", "result": "New contribution: constructive observation fibres and branchwise composite information loss. Existing defect tables, source values, loss totals and full-residual inversion are reused. No historical generation follows from recovering values from derived observations.", "reassessment": "Adopt only the source-costed claims useful to the Strategy." } ], "joint_fibres_all55": [ { "key": "MT:Adam", "family": "MT", "name": "Adam", "L_exact": 930, "B": 130, "R": 800, "source_locator": { "source": "File18", "line": 1228 }, "s": 0, "b_interval": [ 128, 132 ], "candidates": [ [ 128, 802 ], [ 129, 801 ], [ 130, 800 ], [ 131, 799 ], [ 132, 798 ] ], "candidate_count": 5, "singleton": false, "hidden_source_pair_for_comparison": [ 130, 800 ], "source_pair_retained": true, "rounded_total": 930, "parts_minus_total_defect": 0, "three_rounded_candidates_without_exact_L": [ [ 128, 800 ], [ 128, 801 ], [ 128, 802 ], [ 129, 799 ], [ 129, 800 ], [ 129, 801 ], [ 129, 802 ], [ 130, 798 ], [ 130, 799 ], [ 130, 800 ], [ 130, 801 ], [ 130, 802 ], [ 131, 798 ], [ 131, 799 ], [ 131, 800 ], [ 131, 801 ], [ 132, 798 ], [ 132, 799 ], [ 132, 800 ] ], "Q_L_adds_information_after_exact_L": false }, { 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