A concise input register for the final synthesis
Use one role-keyed register. Each entry needs an ID, value or source-packet reference, subject, measure, source status, permitted scope and dependencies. A number reused by several constructions can share its source entry while retaining a separate role in each construction.
| Input bundle | Retain | Treat as generated |
|---|---|---|
| Ordered genealogy | Names, tradition, source-selected begetting ages and lifespans, native Cainan, and admitted insertion states | Calculated remainders, difference vectors, fitted amplitude summaries and accumulated coordinates |
| Counts and event bindings | SP counted-year convention, primary and companion bindings, Noah–Flood relation, inclusive capacity rule and cap domain | Completed Lamech interval 52, the 129 + 1 comparison, capacities and cap outputs |
| Finite variants | Terah harmonization, Cainan’s selected row, Sojourn allocations, source supports and permitted state choices | T = 60 when its source inputs are retained; S = 215 when both allocations are retained; offsets, widths and interval-response fields |
| Chronological placement and rounding | Mode, terminal, frame, node class, row measure being rounded and source-appointed subdivisions | Birth and cumulative fields, rounded values, residuals and carry patterns computed from the retained inputs |
| Covenant and Keys | Local named biographies and ages, phase choices, retained junctions, exact conversion ratios and their units | Clutch coordinates, generated landings, gains and allocation equivalences |
| NT and counted structures | Named order, slots or multiplicities, categories, metric and hinge | Display dates, common coarsenings and permitted Key-return indices |
| First decimal inversion | Original component boundaries, selector anchors, decimal and placeholder policy, admitted source manifest | Reversed components, digit gains and generated endpoints |
The complete source packets remain the evidence record. A compact reconstruction may instead read a smaller parameter basis, but its source masks, coefficients and exceptions remain part of the explanation. Do not count both the full source rows and their extracted parameters as independent inputs. In a conditional inverse problem, an output may become a retained observation; label that change of role explicitly.
Examples of equal numbers that retain different roles:
| Value | Roles |
|---|---|
| 130 | Adam’s MT begetting age; Cainan’s begetting age; Terah’s selected begetting age; the generated Arphaxad–Reu total |
| 60 | Terah’s variant; Isaac’s begetting age; Nahor’s MT/LXX lifespan difference |
| 100 | The repeated MT/LXX age-difference scale; Abraham’s begetting age |
| 70 | NT slot metric; Terah’s minimum begetting age; the generated Cainan-minus-Terah variant gap |
| 460 | Cainan’s lifespan; the measured Covenant path; the first-five SP begetting sum |
| 950 | Noah’s lifespan; the generated midpoint of the 1250/650 pair |
The inherited C1131 register can remain useful as a local interface register. In the new synthesis, identify its cached Rounded coordinates, inverse endpoints and other generated quantities by their dependencies. They should not appear to be additional global premises merely because a later module reads them.
This is consolidation of the certified work, not another numerical investigation or a claim to have found a globally minimal input set.