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    {
      "id": "SP_FIELD",
      "source": "File_18.md",
      "line_start": 1571,
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      "text": "#### 3.2.1 SP Noah/Shem field and named bindings\n\nEach slash-pair below is ordered primary / lower companion. The companion is one year farther forward in time. The rows display ordinary Gear combined with SP-local person-station adjacency; they are not six independently attested source states or a new unrestricted execution generator.\n\n| Gear | Noah birth | Noah death | Shem birth | Shem death |\n|---|---|---|---|---|\n| G1 | 3491/3490 | 2541/2540 | 2991/2990 | 2391/2390 |\n| G2 | 3493/3492 | 2543/2542 | 2993/2992 | 2393/2392 |\n| G3 | 3495/3494 | 2545/2544 | 2995/2994 | 2395/2394 |\n\nAdd `215` for the reports’ equalized dates. Noah’s primary death column carries the inclusive/harmonic qualification and the lower column the ordinary-companion qualification. Matched birth/death endpoints preserve Noah `950` and Shem `600`; matched Noah/Shem births preserve `500`. The mixed G2 companion-Noah / primary-Shem path is `3492−2993=499`, the ordinal 500th-year alternative.\n\nThe native G2 post-Flood spans are `2893−2543=350` and `2892−2542=350`. The second uses Flood close and Noah’s companion death; it does not type the Flood close as a companion. The cross-pair `2893−2542=351` is not an unqualified `350`.\n\nThe following bindings preserve the prior usable stations while making their Gears explicit:\n\n| Shem station / binding | Birth BC | Death BC | Qualified relation |\n|---|---:|---:|---|\n| G2 primary, Noah/Flood comparison | 2993 | 2393 | G2 primary Noah `3493−500=2993`; `2993−100=2893`, Flood start. |\n| G2 companion, Noah/Flood comparison | 2992 | 2392 | G2 companion Noah `3492−500=2992`; ordinal `2992−99=2893`, Flood start. |\n| G1 primary, Arphaxad-bound | 2991 | 2391 | `2991−100=2891`, fixed Arphaxad; also `3493−502=2991` from G2 primary Noah. |\n| G1 companion, Noah-bound comparison | 2990 | 2390 | `3492−502=2990` from G2 companion Noah; it does not replace the full-100 Arphaxad-bound row. |\n\nG2 primary Shem `2993` is `102` from fixed Arphaxad `2891`. These comparisons retain their endpoint roles and bindings. Noah/Shem alone have the full qualified cross-Gear endpoint-comparison permission in this domain; other patriarchs retain coherent-Gear biographies. Qualified Noah↔Flood comparisons are allowed, while the Flood remains an event start/close structure.\n\nThe post-Flood begetting table selects the G1 primary / Arphaxad-bound Shem row:",
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      "id": "VARIANTS",
      "source": "File_18.md",
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      "text": "\nTradition-scope clarification:\nThis multiplication is not MT-local. MT, SP, and LXX encounter the fork sequence at the same genealogical locations: the Sojourn / Egypt-position `+215` fork, the `+60 Terah` fork, and the 2nd Cainan `+130` boundary. The arithmetic status differs by tradition. MT / SP receive Cainan by restoration when that state is opened. LXX already contains Cainan in its regular baseline, so the LXX form is a native-Cainan boundary state unless a theoretical removal / reinsertion state is explicitly opened.\n\n| Epoch / boundary | Active variants | Possible explicit date states | Handling |\n|---|---|---:|---|\n| Adam → Arphaxad / Flood | `±215 Sojourn × +60 Terah × restored 2nd Cainan` where opened | eight states | Active only if restored 2nd Cainan is explicitly inserted. Arphaxad is synonymous with the Flood / Ark-exit conception boundary and is the first upstream row to absorb the Cainan hinge. |\n| 2nd Cainan → Terah | `±215 Sojourn × +60 Terah` | four states | 2nd Cainan, Shelah, Eber, Peleg, Reu, Serug, Nahor, and Terah remain four-position. |",
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      "id": "SP_LOCALITY",
      "source": "File_18.md",
      "line_start": 433,
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      "text": "Machine Guard [FILE_18 SP NOAH/SHEM LOCALITY + FLOOD GEAR SEPARATION]:\n\nThe SP companion operator is primary minus one for Noah/Shem person-stations only. Native G2 Noah is `3493/3492`, Shem `2993/2992`, Noah death `2543/2542`, and Shem death `2393/2392`. G1 Shem `2991/2990` with deaths `2391/2390` remains available under named bindings; only `2991→2891` is the displayed full-100 Arphaxad-bound relation. Do not propagate the companion into Adam through Lamech or Arphaxad onward, and do not transfer it to MT/LXX. Native G2 Lamech is `3545→2893`, `653` inclusive. Flood `2893→2892` is a start→close event pair, not a companion pair. All three traditions retain ordinary Flood Gears and independent one-year Flood spans; §3.1.4 supplies the exact table. LXX is native Cainan ON in that comparison. Keep the G2 `654+654` midpoint to fixed Arphaxad separate from the G1 Lamech-death / Flood-start / Arphaxad coordinate convergence.",
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    {
      "id": "LXX_REMOVAL",
      "source": "File_18.md",
      "line_start": 1140,
      "line_end": 1147,
      "text": "\n| Tradition / method | Handling |\n|---|---|\n| LXX Regular | Cainan is already in the baseline. `5279 BC` Adam minimum includes his `130` begetting years. No adjustment is needed. |\n| MT / SP Regular | To restore Cainan, insert 2nd Cainan by adding the `+130` begetting-age hinge between Arphaxad and Shelah. Shelah and the downstream Terah field remain four-position; Arphaxad / Flood through Adam shift by `+130` and become eight-position where the restored-Cainan state is explicitly opened. MT with Cainan: `3899 + 130 = 4029 BC`. SP with Cainan: `4199 + 130 = 4329 BC`. |\n| LXX Cumulative | Cainan is already in the baseline. His `460`-year lifespan is included in the chain. No adjustment is needed. |\n| MT / SP Cumulative | To restore Cainan, insert the `+460` lifespan hinge between Arphaxad and Shelah. In the cumulative table this shifts Adam through Arphaxad / Flood by `+460`; Shelah and downstream rows remain unchanged. MT cumulative with Cainan: `14006 + 460 = 14466 BC`, Moses line center. |\n| LXX theoretical removal | LXX could have Cainan removed: `5279 − 130 = 5149 BC`, Regular. This is not tracked in standard tables but remains architecturally valid. |",
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    {
      "id": "FLOOD_GEAR_SCOPE",
      "source": "File_18.md",
      "line_start": 1540,
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      "text": "#### 3.1.4 Ordinary Flood Gears, fixed Arphaxad, and the SP midpoint\n\nThis table uses the full-430 comparison frame, Terah `+60` OFF, MT/SP second Cainan OFF, and LXX native second Cainan ON. The LXX G2 Creation head is `5494`, consistent with `5494−3238=2256`; Cainan-OFF `5364` must not be paired with native-ON Flood `3238`.\n\n| Tradition | G3 Flood start→close | G2 Flood start→close | G1 Flood start→close | Fixed Arphaxad |\n|---|---|---|---|---:|\n| MT | 2460→2459 | 2458→2457 | 2456→2455 | 2456 |\n| LXX — native Cainan ON | 3240→3239 | 3238→3237 | 3236→3235 | 3236 |\n| SP | 3110→3109 | 3108→3107 | 3106→3105 | 3106 |\n\nEvery row has the ladder `G3 start → G2 start → G1 start → G1 close = 2+2+1 = 5`. At this layer LXX is MT `+780`, including Arphaxad. Each Flood close arises from that Gear’s one-year event span, independently of SP Noah/Shem primary→companion. At held Sojourn, Terah, and Cainan settings, regular Arphaxad onward through Moses does not move with Gear; the separately scoped variant mechanisms retain their own permissions.\n\nSubtract `215` from this table for the corresponding minimum/native frames. The native SP starts G3/G2/G1 are `2895/2893/2891`, with closes `2894/2892/2890`; fixed Arphaxad is `2891`.",
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    {
      "id": "E_RATIO_CORRECTED",
      "source": "File_46.md",
      "line_start": 117,
      "line_end": 133,
      "text": "### L3. Priestly Ratio (25/23)\n\nActive state: Key-of-23 Priestly Expansion state.\n\n```markdown\n4830 × 25/23 = 5250\n```\n\nbecause `4830/23 = 210` and `210 × 25 = 5250`.\n\nTherefore:\n\n```markdown\n5256 BC → 6 BC = 5256 − 6 = 5250\n```\n\nThe source associates this operator with Luke (the Luke / Priestly expansion); the association is developed in §4.2.",
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  "local_midpoint": {
    "coordinate": 3188,
    "record_indices": [
      245
    ],
    "outer_radius": 432,
    "inner_radius": 18,
    "ratio": 24
  },
  "counts": {
    "label_assignments": 16,
    "same_record_returns": 8,
    "alias_switches": 8,
    "all_SP_paths": 1,
    "unchanged_context_paths": 0
  },
  "limits": "Local midpoint is an existing record and derived comparison, not a new global Mirror axis. The old E/J/P return graph has a different declared source/pivot menu; no global novelty claim or chronological cycle follows."
}