write manuscript keys.py

"""Prepare reader-facing Key modules; no journal or canonical edits."""
from pathlib import Path
import json

MODULES = [
    {
        "title": "Different calendar counts, one schematic measure",
        "text": "The three calendar Keys connect different year counts through one declared measure. Write E=25/23 for the Priestly Key, P=70/69 for the Prophetic Key, and J=300/299 for the Enochian Key. Their matching calendar lengths satisfy 336E=360P=364J=8400/23. Multiplying a span by a Key therefore changes its count while preserving the same modeled day-volume when the corresponding unit accompanies the result.\n\nFor the shared span 12558, the outputs are 13650, 12740 and 12600. Multiplying these respectively by 336, 360 and 364 gives 4586400 in every case. This existing calibration explains why different numerical totals can belong to one mathematical family.\n\nUnit labels also matter when separate components receive different Keys. The inherited comparison built from the 299|161 partition gives 300|175 under J on the first part and E on the second. With their matching units, 300×364+175×336=168000. Swapping the units changes that volume to 164500 although the numerical sum remains 475.\n\nThe connection is exact but conditional: it describes a schematic calendar realization, not proof that a chronology literally elapsed in mixed historical calendars. A complete comparison consequently carries both the number and its declared unit. Equal numbers without matching units, and unequal numbers with matching measures, tell different stories.",
        "sources": [
            {"file": "490d_Unification_Research_Strategy_v0_2_20260906.md", "section": "§3.3"},
            {"file": "File12 Calendrical Physics", "section": "Active Enochian Key clarification, line263"},
            {"file": "File63 Scale-Neutral 480/483/490 Carrier", "section": "§9.7"},
            {"file": "File60 Levitical Covenant Spine", "section": "§5; component161→175 reconciliation"},
            {"file": "c532_c631/journal.json", "section": "C533: assembled300|175 comparison"},
        ],
        "steps": [988, 1004, 1005, 1006, 1007],
        "key_claims": [
            "336E=360P=364J=8400/23 is inherited exact calibration.",
            "Matching units make all nine assignments on299|161 preserve168000 by one componentwise identity.",
            "The assembled475 comparison is inherited C533; a literal mixed-calendar timeline is not asserted.",
        ],
    },
    {
        "title": "Selective expansion and successive Keys",
        "text": "A Key can act on a selected part while the rest remains fixed. This produces a different operation from applying a Key to the whole span. The distinction links two source families. In the 483 carrier, the final 80.5 is one sixth of the total: expanding that part by E produces 402.5+87.5=490, the same total as applying P to all 483. In the 12558 path, the final 483 is one twenty-sixth: expanding that part by E produces 12075+525=12600, the same total as applying J to the whole.\n\nThe general rule is simple. If fraction f receives factor k, the effective total factor is 1+f(k−1). This explains the selected fractions 1/6 and 1/26 without treating their source boundaries as interchangeable. The computed intermediate fraction 3/13 connects P to J, but calculation alone does not appoint a corresponding chronological cut.\n\nNested selection multiplies selection fractions: one sixth followed by three thirteenths selects one twenty-sixth. Successive whole-span conversion instead multiplies the Keys themselves; P followed by J gives 7000/6877, not J.\n\nTogether with calendar calibration, the two inherited completion relations form four equations with three independent constraints. Solving them backward recovers the Keys, but supplies an equivalent description of established relationships, not independent evidence for their historical origin.",
        "sources": [
            {"file": "File63 Scale-Neutral 480/483/490 Carrier", "section": "§1.3; §§7.3–7.4; §9.7"},
            {"file": "490d_Unification_Research_Strategy_v0_2_20260906.md", "section": "§3.3; §5E"},
        ],
        "steps": [984, 985, 986, 987, 989, 990, 991, 992],
        "key_claims": [
            "A_f(k)=1+f(k−1); A_g(A_f(k))=A_(gf)(k).",
            "The source-selected fractions1/6 and1/26 differ in status from computed3/13.",
            "The four-equation calibration/completion system has rank3; its backward solution is not an independent derivation from partitions alone.",
        ],
    },
    {
        "title": "What retained parts let us recover",
        "text": "Several apparently separate families follow the same retained-part construction. Let u denote the component that receives a Key and v the component held unchanged. Their native, Prophetic and Priestly totals are T₀=u+v, Tₚ=Pu+v and Tₑ=Eu+v. Because E−1=6(P−1), the gains obey Tₑ−T₀=6(Tₚ−T₀). The three totals therefore contain only two independent numerical measurements.\n\nTwo totals recover the components exactly: u=69(Tₚ−T₀), then v=T₀−u. The third total checks the same relationship rather than adding a third independent fact. This one construction covers all three 690-core brackets: with retained flanks of 0, 30 or 60, the native/P/E totals are respectively 690/700/750, 720/730/780 and 750/760/810.\n\nSupplement A’s cumulative calendar-body family uses the same construction on a larger scale. Its converted upper segment is 9660 and its fixed lower segment is 2940. The resulting totals are 12600, 12740 and 13440. These source-defined components make the family intelligible without treating its three totals as unrelated coincidences.\n\nNumerical recovery still leaves chronological information to the source. It does not identify which named interval occupies each role, their order, their absolute placement, or permission to apply the operation. Recovering two magnitudes is therefore one part of reconstructing a declared chronological object.",
        "sources": [
            {"file": "14-file_70-supplement-a-key-of-23-fine-resolution-720-30-rail-2-.md", "section": "§1.2: complete690/30 bracket table"},
            {"file": "14-file_70-supplement-a-key-of-23-fine-resolution-720-30-rail-2-.md", "section": "§10.3: cumulative calendar-body matrix, lines2130–2185"},
        ],
        "steps": [995, 996, 997, 1007],
        "key_claims": [
            "The native/P/E measurement matrix has rank2 and left dependency(5,−6,1).",
            "Two measurements recover the converted and retained magnitudes on every declared row.",
            "Supplement A §10.3 controls9660|2940; latest File52c is not its controlling source.",
            "Numerical identifiability does not recover source identities, order, anchor or authorization.",
        ],
    },
    {
        "title": "When a total preserves the full comparison",
        "text": "Combining several components into one total can hide exactly the information that distinguishes two chronological paths. There is a precise test for when this simplification is harmless. If every component in a combined block receives the same conversion factor, we may add first and convert afterward, or convert each component and then add. The two procedures agree for every possible set of component values.\n\nIf the factors differ inside a block, this universal agreement fails. A particular source total may still agree because its component weights make the differences cancel. That is a property of the supplied arrangement, not permission to forget its internal boundary.\n\nThe 483 carrier makes the distinction concrete. Keeping 402.5 fixed and expanding the final 80.5 by E gives 402.5|87.5. Applying P uniformly gives 408⅓|81⅔. Both total 490, but their two components differ by −35/6 and +35/6. The total erases a real internal displacement.\n\nThis is why a family comparison should retain intermediate boundaries as well as endpoints. An equal total answers a narrower question than an equal path. The same discipline helps relate regular, cumulative and Rounded objects: first specify the components and measurement, then state which internal distinctions the chosen total preserves and which it loses.",
        "sources": [
            {"file": "File63 Scale-Neutral 480/483/490 Carrier", "section": "§1.3"},
            {"file": "c532_c631/journal.json", "section": "C609: inherited internal-defect example"},
            {"file": "490d_Unification_Research_Strategy_v0_2_20260906.md", "section": "§§3.1–3.2; §5E"},
        ],
        "steps": [993, 994, 997, 1007],
        "key_claims": [
            "For a declared partition-summing map C, C diag(k_i)=diag(k_B) C for every input iff each block has a common factor.",
            "The inherited490 completion has zero total defect but component defect(−35/6,+35/6).",
            "A shared total does not establish identical interior paths or interchangeable measurement rules.",
        ],
    },
    {
        "title": "Pivots place the whole field",
        "text": "A duration ratio does not determine a date transformation until a held pivot is declared. Around pivot a, factor k sends coordinate x to a+k(x−a). Differences between points scale by k, while their absolute placement still depends on a. This separates the shape of a chronological field from where it sits.\n\nFor two successive Keys, integer placement has an exact test. Let their reduced ratios be p₁/q₁ and p₂/q₂, with integer pivots a and b. An integer input can have integer outputs at both stages only when gcd(p₁,q₂) divides b−a. If that condition holds, the admissible inputs form one residue class with spacing q₁q₂/gcd(p₁,q₂). A complete field belongs to that class when one point has the right placement and every internal difference is a multiple of the spacing.\n\nFor the fixed pivots 14006 and 4836, the diagnostic J→P composition has no such integer inputs: gcd(300,69)=3 does not divide their difference. This identifies a domain limit without inventing replacement pivots or authorizing new chronological routes.\n\nFractions themselves remain exact coordinates. The full File46 head pattern, with indices 92,89,46,43,0 on a ten-unit mesh, survives E expansion on mesh 250/23. Preserving that entire rational image explains the family more faithfully than discarding points to retain only integer endpoints.",
        "sources": [
            {"file": "File46 Harmonic Expansion Protocols", "section": "§§2–3:14006 and4836 pivots; §6A.5: complete head field"},
            {"file": "490d_Unification_Research_Strategy_v0_2_20260906.md", "section": "§5C: transformations and domains"},
            {"file": "c482_c531/journal.json", "section": "C506–C507: inherited placement witnesses"},
        ],
        "steps": [998, 999, 1000, 1001, 1002, 1003],
        "key_claims": [
            "Stagewise integer domains depend on both reduced ratios and declared pivots.",
            "Whole-field membership separates one placement residue from all internal differences.",
            "The nine fixed-pivot pairs are diagnostics, not nine newly authorized routes.",
            "Rational images preserve the complete field without date repair or a new historical calendar.",
        ],
    },
    {
        "title": "The structural role of 529",
        "text": "The number 529 has a specific role in the Priestly expansion family: it is 23², the denominator needed for two applications of E=25/23 to produce integral duration widths. A width 529n therefore follows the ladder 529n→575n→625n. The inherited examples 1058→1150→1250 and 10580→11500→12500 share that duration grammar, with the second ten times the first. Their agreement follows from the same operation and scale relation.\n\nWidths alone do not determine endpoints. Holding the same integer pivot for both stages requires each starting point’s offset from that pivot to be divisible by 529. With different pivots, the allowed residue changes. Two fields can therefore share a 529-multiple width while only one has integral endpoints under its declared pivots. The successful inherited small example and the fixed-12026 comparison exhibit exactly this distinction.\n\nThe Rounded macro family also supplies a particular endpoint realization: with AD 12026 held, AD 1446→AD 526→476 BC accompanies the widths 10580→11500→12500. Its last crossing uses the declared Rounded coordinate convention; substituting ordinary civil counting changes the final display.\n\nThus 529 connects these families through a reusable two-stage duration structure. It does not license a universal date conversion, supply a missing pivot, or establish independent evidence merely because another multiple follows the same inherited ladder.",
        "sources": [
            {"file": "File_52c.Rounded_Whole_Span_Inverse_Detailed_Study_Draft (2)(1).md", "section": "§§3.8–3.9; coordinate convention in§1 and§6"},
            {"file": "c482_c531/journal.json", "section": "C505–C507: duration ladder and placement; C510–C511: Rounded endpoint realization"},
            {"file": "c932_c1131/journal.json", "section": "C1001: inherited width/placement distinction"},
        ],
        "steps": [505, 506, 507, 510, 511, 998, 1001, 1007],
        "key_claims": [
            "529n→575n→625n is an inherited duration identity under E twice, not a new discovery.",
            "A529-multiple width does not by itself guarantee integral endpoint placement.",
            "File52c supplies a particular Rounded endpoint realization with its source-appointed pivot and count convention.",
            "No second decimal inversion, universal date map, or new source authorization is introduced.",
        ],
    },
]

out = Path(__file__).resolve().parent / "manuscript_keys.json"
for module in MODULES:
    count = len(module["text"].split())
    if not 150 <= count <= 250:
        raise ValueError((module["title"], count))
out.write_text(json.dumps(MODULES, ensure_ascii=False, indent=2) + "\n")
print(json.dumps({"output": str(out), "word_counts": {m["title"]: len(m["text"].split()) for m in MODULES}}, ensure_ascii=False))