File: File_09
Title: Cumulative Architecture
Legacy source title: CUMULATIVE_ARCHITECTURE.md
Entity: CUMULATIVE TIMELINE
Classification: The Master Structure
UUID: SYS_CUMULATIVE
Status: Final; post-final pressure tested; File_18 section-reference cross-file update applied; File_16 / File_18 1876 Cainan macro-vector cross-file update applied
Publication-cleanup status: Public-clean Markdown source; archival amendment history routed to Repository_Change_Archive.
Pressure-test status: Current; focused pressure test complete for the File_18 section-reference update and public-clean cleanup.
Register Agreement status: Checked against State_Vocabulary_Register v1.17 and active companion controls; convergence / pointer update only; no arithmetic, anchors, modal states, node-classes, operators, sign conventions, slash-pairs, ranges, envelopes, Mirror protocols, Machine Guards, claim-status labels, theological claims, or dependency boundaries changed.
Primary domain: Cumulative; Comparative; Prophetic; Theological; Mirror; Calendar
Traditions: MT; SP; NT / Luke by dependency
Canonical source: Markdown
Primary anchors: 4115t/4114n BC; AD 1406t/1407n; 4114 BC source shorthand; 1407t/1406n BC; 1406 BC; AD 1406; 5296–5289 BC; 5289 BC; 1859 BC; 1782 BC
Related files: `File_00`; `File_02`; `File_04`; `File_06`; `File_07`; `File_16`; `File_17`; `File_18`; `File_22`; `File_54`; Restart Capsule v11.15; 490d Repository Style Guide v2.5; Project Procedures v3.2
Major operators: Jubilee `49`; `110 × 110`; Cainan macro-vector dependency; Cainan / Famine projection `2520`; Enochian lower-bound vector `2730`; Daniel 12 Cainan sandwich `1260 → 1290 → 1260`; audit-controlled `2307`; phase-resolved Mirror coordinate-completion; civil cross-axis span `BC + AD − 1`; precise numeric-year Mirror node; paired-versus-single Mirror span distinction; formal phase-consistency proof for paired Mirror dates; Julian phase-coordinate proof with Oct 1 / Jan 1 / Apr 1 mapping; standalone phase-polarity caution for single-date Mirror nodes; `25/23`; `70/69`; cumulative 2nd Cainan `+460`; Danielic `2300`; same-side BC span; source-display Levi `+77`; direction-aware BC subtraction display
Major modal states: cumulative MT; SP cumulative; restored cumulative 2nd Cainan Flood Week; Cainan macro-vector dependency state; Cainan / Famine envelope projection state; Conquest / New Eden phase-resolved Mirror coordinate-completion; generic phase-resolved Mirror suffix-inversion rule; paired-versus-single Mirror span state; formal paired Mirror phase-consistency proof state; Julian Jan-1 Mirror-axis phase model; t/n January-centered pair state; n/t July-centered contrast state; standalone Tishri/Nisan single-date polarity-flip caution state; precise numeric-year Mirror node; East-side / West-side Conquest phase pair; Arphaxad-Jacob-Levi arc; Danielic 2300-cycle state; NT / Luke comparative state by dependency
Major claim-status labels: source-retained chronology datum; author-clarified chronology datum; arithmetic fact; structural inference; shared-tradition evidence; theological note; Mirror coordinate-completion; Mirror source-label; dependency-controlled; audit note
Revision basis: 490d Repository Style Guide v2.5; Restart Capsule v11.15; State Vocabulary Register v1.17; Project Procedures v3.2; prior finalized source; listed file dependencies; Repository_Change_Archive (non-controlling history).
Current refresh note: Public-clean trust-status equalization aligns active control pointers to 490d Repository Style Guide v2.5, Restart Capsule v11.15, State_Vocabulary_Register v1.17, and Project Procedures v3.2. Register Agreement status is recorded in the header; no arithmetic, anchors, modal states, node-classes, operators, sign conventions, slash-pairs, ranges, envelopes, Mirror protocols, Machine Guards, claim-status labels, theological claims, or dependency boundaries are changed. Detailed pass logs, pressure-test records where applicable, pointer-refresh history, and replacement-workflow notes are preserved in Repository_Change_Archive.

# File_09 — Cumulative Architecture

## Related Repository Files

| File | Function for `File_09` |
|---|---|
| `File_00` | Foundational controls for cumulative chronology, civil cross-axis span `BC + AD − 1`, slash-pair expansion, calendar-state suffixes, Mirror / civil / inverse firewalling, file-level source-map discipline, and argument-control layering. |
| `File_02` | Flood terminology, cumulative Flood Week controls, restored cumulative 2nd Cainan Flood Week precedent, `+460` cumulative Cainan distinction, and shared-tradition claim-status restraint. |
| `File_04` | Jacob as Jubilee standard, `147 = 3 × 49`, Jacob death-state, Levi death-state handling, and argument-control precedent for arithmetic facts versus theological / typological meaning. |
| `File_06` | Conquest process state, Aaron/Moses death-phase anchors, land-rest envelope, and Creation-week / cumulative Creation-week straddle precedent. |
| `File_07` | Creation-week endpoint slash-pairs, Nisan/Tishri suffix handling, phase-resolved Mirror suffix inversion, and component-wise civil cross-axis Mirror checks. |
| `File_16` | Cainan mechanism, regular `+130` versus cumulative `+460`, `1876 BC` Nexus, local numeric-year Mirror label precedent, dependency-boundary precedent, and Mirror / civil firewalling. |
| `File_17` | Danielic time-span component grammar, especially `490`, `2300`, Key-of-23 conversion, prophetic span anatomy, and component-status restraint. |
| `File_18` | Cumulative data verification tables, especially §6A for MT cumulative trunk, §6B for MT cumulative + 2nd Cainan, §6C for SP cumulative, and §6D for LXX cumulative. |
| `File_22` | Jacobean Completion, cumulative architecture, and Priestly expansion dependency. |
| `File_54` | Luke / BJ / Rounded claim-status control, Lukan 77-generation comparative restraint, shared-tradition evidence, and Mirror classification precedent. |
| Restart Capsule v11.15 | Repository-wide anchors, operators, modal states, Cainan distinction, cumulative Flood Week controls, civil-span / Mirror guards, and File_54 Luke / BJ claim controls. |
| 490d Repository Style Guide v2.5 | Canonical Markdown, number formatting, heading hierarchy, terminology, modal-state auditing, arithmetic controls, calendar-state suffixes, slash-pair discipline, and claim-status standards. |
| Project Procedures v3.2 | Pass sequence, authorial-direction protocol, audit-note discipline, and Finalization Pass controls. |

## 0. File-function

`File_09` records the cumulative master architecture of the repository in compressed form. It preserves the tripartite cumulative epochs, the SP cumulative square, the Conquest / New Eden harmonic, the Arphaxad-Jacob-Levi arc, and the Danielic Creation cycles under the cumulative 2nd Cainan variant.

Final-source note:
This Final source incorporates the author decisions that resolved prior audit items. It resolves the node-class of `5289 BC`, classifies the `5520` Conquest harmonic as phase-resolved Mirror coordinate-completion, preserves `AD 1406` as a precise numeric-year Mirror node distinct from the Rounded / Protocol 1 target, states the East-side / West-side Conquest phase distinction, states the generic phase-resolved Mirror suffix-inversion rule for `.5` Tishri/Nisan dual dates, distinguishes paired Mirror spans from single-date exact Mirror spans, preserves the formal phase-consistency proof, preserves the Julian phase-coordinate proof, and preserves the standalone single-date polarity caution. Final pressure-test status is preserved in the file header. Detailed pressure-test records are archived rather than repeated in the public body.

Modal-state rule:
A shared date-label, number, span, suffix, slash-pair, target-state, or harmonic value does not create identity unless state, node-class, tradition, and operator agree.

Argument-control rule:
Arithmetic facts and source-retained chronology data carry the base layer of `File_09`. Structural inferences explain how the checked spans interlock. Theological notes explain why a structure matters but do not replace arithmetic or dependency control. Luke-related comparative claims are classified as structural inference and shared-tradition evidence by dependency, not as proof of direct literary dependence.

Author-decision rule:
The author-clarified `5289 BC`, `AD 1406`, `4115t/4114n BC → AD 1406t/1407n`, generic phase-resolved Mirror suffix-inversion states, paired-versus-single Mirror span distinction, formal phase-consistency proof, Julian Jan-1 phase-coordinate proof, and standalone single-date polarity-flip caution are now active source controls in `File_09`. They should not be downgraded back to unresolved audit notes in this Final source.

### 0.1 Working state register

The following states are active in `File_09`. They are simultaneous, non-competing states unless a local section explicitly narrows the working state.

| State | Primary values / forms | Node-class / function | Handling in `File_09` |
|---|---:|---|---|
| File identity state | `File_09`; `CUMULATIVE_ARCHITECTURE.md`; CUMULATIVE TIMELINE | cumulative master-structure file | Preserved. Current source is Final. |
| Cumulative master-architecture state | whole file | compressed architecture register | The file gathers cumulative MT, SP cumulative, Conquest / New Eden, Arphaxad-Jacob-Levi, and Danielic Cainan material. Do not force all sections into one chronology. |
| Cumulative MT tripartite state | Creation → Shem; Flood → Abraham; Abraham → Conquest | cumulative epoch structure | Source-retained. Endpoints remain dependency-controlled by `File_18`, §6A and `File_22`. |
| Creation → Shem state | 175 Jubilees | cumulative Creation-to-Shem span | Source-retained chronology datum. Shem is a cumulative endpoint / boundary node in this section. Do not substitute a regular Shem birth or death state unless a dependency opens it. |
| Flood → Abraham state | 2401 years | cumulative Flood-to-Abraham span | Source-retained chronology datum. Flood and Abraham node-classes remain dependency-controlled. |
| Abraham → Conquest / Jacobean Completion state | 21 Jubilees; `1029`; `7 × 147` | Abrahamic promise-to-Conquest completion | Source-retained chronology datum plus structural inference. The `147` value invokes Jacob’s lifespan as Jubilee standard by dependency through `File_04` and `File_22`. |
| SP cumulative square state | `12100 = 110 × 110` | SP cumulative square | Arithmetic fact inside SP cumulative state. This is SP cumulative, not SP regular chronology and not cumulative MT unless a dependency explicitly links them. |
| Creation endpoint phase-pair state | `4115t/4114n BC` | MT Standard-Normal Creation-week endpoint pair | Author-clarified by dependency: the seven years of Creation may be viewed Tishri-to-Tishri and/or Nisan-to-Nisan. The pair is not collapsed into unsuffixed `4114 BC`. |
| Conquest phase-pair state | `1407t/1406n BC` | East-side / West-side Jordan Conquest pair | Author-clarified chronology datum. `1407t BC` marks the East side of Jordan Conquest start and occupation by the 2.5 tribes; `1406n BC` marks the later West side crossing and occupation by the other 10 tribes. |
| Aaron/Moses terminal phase state | Aaron death shortly before `1407t BC`; Moses death shortly before `1406n BC`; each mourned 30 days | wilderness-terminal phase distinction | Author-clarified chronology datum. The approximately six-month gap is important to the East-side / West-side Conquest phase pair and must not be collapsed. |
| Conquest / New Eden phase-resolved Mirror coordinate-completion state | `4115t/4114n BC → AD 1406t/1407n = 5520 years` | Eden-to-New-Eden Mirror coordinate-completion | Author decision applied. The compressed source line `4114 BC + AD 1406 = 5520` is now treated as shorthand for the phase-resolved component checks, not as an unsuffixed coordinate-sum proof. |
| Generic phase-resolved Mirror suffix-inversion rule | `Yt/(Y−1)n BC → AD (Y−1)t/Y n` | phase-preserving Mirror display rule for `.5` Tishri/Nisan dual dates | Author decision applied. When a BC dual date is separated by a half-year from Tishri to Nisan, the AD Mirror display must preserve the half-year relation by suffix inversion. The AD display is therefore `t/n`, not `n/t`, unless a local file explicitly opens a different phase-state. |
| Paired-versus-single Mirror span state | single exact mirrors: `1407t BC → AD 1407t = 2813`; `1406n BC → AD 1406n = 2811`; paired Mirror: `1407t/1406n BC → AD 1406t/1407n = 2812` | distinction between non-paired exact Mirror nodes and phase-resolved paired Mirror coordinate-completion | Author decision applied. Single dates mirror to their own numeric-year AD counterpart. A paired `.5` slash-pair mirrors cross-component with suffix inversion, yielding the equal paired checks `1407 + 1406 − 1 = 2812` and `1406 + 1407 − 1 = 2812`. |
| Formal paired Mirror phase-consistency proof state | proof notation: `n = 0`; `t = 0.5`; phase correction `q − p` applied only after the civil-year skeleton | proof that suffix inversion preserves `.5` phase distance and equal component spans | Author decision applied. The valid paired display gives equal exact components: `1407t BC → AD 1406t = 2812` and `1406n BC → AD 1407n = 2812`. The invalid same-order display would produce `2811.5` and `2812.5`, and its AD-side internal width is `1.5` years rather than `.5`. This proof is a phase-consistency check, not a new civil-span operator. |
| Julian Jan-1 Mirror-axis phase model | Oct 1 = `t`; Apr 1 = `n`; Jan 1 = Mirror-axis / center point | simplified Julian phase-coordinate model for exact paired-date work | Author decision applied. The model maps Tishri to the start of Oct 1 and Nisan to the start of Apr 1. The `t/n` pair is January-centered. This supplies the exact calendar reason that paired Mirror dates use suffix inversion. |
| Second-Adam / circumcision hinge state | Dec 25, 1 BC → Jan 1, AD 1 | repository Mirror hinge / Day-8 naming and circumcision tradition | Preserved as theological / calendrical hinge. The Mirror axis is the start of Jan 1, AD 1; it is not a July-centered axis. |
| January-centered `t/n` pair state | `Yt/(Y−1)n BC`; AD Mirror `AD (Y−1)t/Y n` | half-year pair centered on Jan 1 | Active for phase-resolved Mirror work. The pair’s BC center is Jan 1 of `(Y−1) BC`; its AD center is Jan 1 of `AD Y`. The self-mirrored pair brackets the Jan 1, AD 1 hinge. |
| July-centered `n/t` contrast state | same-year `Yn/Yt` | half-year pair centered on July 1 | Contrast state only. It is not active for Creation / Conquest paired Mirror work because it would center the pair on July 1 rather than Jan 1. |
| Standalone phase-date polarity caveat | single exact `t` or `n` Mirror dates; odd single-date spans | polarity-flip warning for non-paired phase dates | Author decision applied as a compact caveat. Standalone Nisan or Tishri dates may flip phase polarity across their own midpoint because exact single-date Mirror spans such as `2813` and `2811` are odd. This does not contradict the paired `t/n` state, whose Jan-1 average is even. Full mechanics are recommended for a later Mirror-control file. |
| Plague-period phase-pair example | `1447t/1446n BC → AD 1446t/1447n` | example of the generic suffix-inversion rule by dependency | Source-control example only in `File_09`. The plague-period pair is not a new File_09 anchor. It illustrates that `AD 1446n/1447t` would not preserve the `.5` relation and must not replace the phase-resolved Mirror display. |
| Precise numeric-year Mirror node state | `1407t BC → AD 1407t = 2813`; `1406n BC → AD 1406n = 2811`; unsuffixed `1406 BC → AD 1406 = 2811` | precise single-date Mirror nodes | Author decision applied. Single exact Mirror nodes are valid, but they do not define the paired slash-pair Mirror span. The paired state has its own component checks and yields `2812`. |
| Standalone single-date polarity-flip caution state | Tishri single midpoint: Nisan-side polarity; Nisan single midpoint: Tishri-side polarity | caution note for non-paired exact Mirror nodes | Author clarification applied as a bounded note. A single exact Tishri or Nisan date mirrored to its own AD counterpart yields an odd span and therefore a half-span midpoint that flips phase polarity. This is not an inconsistency with the paired `t/n` Jan-1 Mirror state; it is a distinct single-date state whose fuller mechanics belong to a future Mirror-control file. |
| MT Standard-Normal Creation endpoint dependency state | 4114 BC source shorthand | Creation endpoint / Eden-side anchor | Source-retained chronology datum by dependency. In the `5520` harmonic it must be expanded to `4115t/4114n BC` when the phase-resolved Mirror state is active. |
| Priestly conversion state | `5520 × 25/23 = 6000` | Priestly Key-of-23 conversion display | Arithmetic fact under exact `25/23`: `5520 ÷ 23 = 240`; `240 × 25 = 6000`. |
| Theological Sabbath-rest state | 6 Days / `6000` years / 7th Day of Rest | theological reading of the Conquest harmonic | Preserved as Theological note. It explains the meaning of the numeric structure but does not replace arithmetic or endpoint-state controls. |
| Restored cumulative 2nd Cainan Flood Week state | `5296–5289 BC`; `+460` | restored cumulative Flood Week envelope | Active author decision. `5289 BC` belongs to the terminal member of this restored cumulative Flood Week. |
| Arphaxad-Jacob arc state | 5289 BC → 1859 BC; `3430`; `70 × 49`; `7 × 490` | restored cumulative Flood Week terminal / Arphaxad-side boundary to Jacob death | Arithmetic fact under same-side BC span and Jubilee / Danielic factorization. The `5289 BC` label is now resolved as the terminal member of the restored cumulative 2nd Cainan Flood Week and retained as the source’s Flood / Arphaxad boundary label. |
| Jacob death state | 1859 BC | Jacob death under the standard `+215` Jacob state | Source-retained chronology datum by dependency. Do not collapse with MT Minimum Jacob death or LXX `−33` Jacob death states. |
| Levi death state | 1782 BC | Levi death under the `+215` Levi death state | Source-retained chronology datum by dependency. Do not collapse with the LXX `−33` Levi death state or with Jacob’s death. |
| Levi `+77` source-display state | `1859 BC + 77 years = 1782 BC` | forward-time BC extension display | Source-display sign preserved. Direction-aware BC arithmetic checks as `1859 − 77 = 1782`. Argument role: arithmetic fact plus structural inference where compared with the Lukan `77` field. |
| NT / Luke comparative state | Lukan “77-generation” harmonic | comparative genealogy / heptadic harmonic | Controlled as structural inference and shared-tradition evidence by dependency. No direct-dependence claim is made. |
| Cumulative restored 2nd Cainan state | `+460` | cumulative lifespan insertion | Active in the Danielic Cainan section and in the restored cumulative Flood Week state. Must not be collapsed with regular restored 2nd Cainan `+130`. |
| Cainan macro-vector dependency state | `4851 → 2551 = 2300`; `4391 → 2091 = 2300`; `4398–4391 → 1878–1871` by `2520`; `4391 → 1661` by `2730`; `4396 → 586` through `1260 → 1290 → 1260` | cumulative-to-regular Cainan / Nexus support | `File_09` registers the cumulative architecture dependency only. `File_16` controls the Nexus proof and Category B classification; `File_18` supplies the source table values. The inclusive `2307` companion and solar comparison remain audit-controlled. |
| Danielic 2300-cycle state | `7 × 2300`; `7.5 × 2300`; `15870`; `16100`; `17250` | Danielic Creation-cycle display | Arithmetic facts under exact operators. Endpoints remain dependency-controlled. |
| Danielic “Mirror” source-label state | The `7 × 2300` Mirror | local cycle / Mirror display label | Preserved as Mirror source-label / dependency-controlled terminology. It is not Protocol 1 or Protocol 2 Mirror unless a later dependency explicitly opens that protocol. |
| Prophetic conversion state | `15870` solar years → `16100` Prophetic | Prophetic-cycle conversion display | Arithmetic fact under `70/69`: `15870 ÷ 69 = 230`; `230 × 70 = 16100`. |
| Priestly Danielic conversion state | `15870` solar years → `17250` Priestly | Priestly-cycle conversion display | Arithmetic fact under `25/23`: `15870 ÷ 23 = 690`; `690 × 25 = 17250`. |
| Calendar-suffix state | `n`; `t` | Nisan / Tishri state labels | Active in the Creation and Conquest Mirror coordinate-completion. Suffixes are state labels and must be preserved. |
| Slash-pair state | `4115t/4114n BC`; `AD 1406t/1407n`; `1407t/1406n BC` | ordered phase-pairs | Active in §3. Do not collapse, average, reorder, or unsuffix these pairs. |

### 0.2 File map

| Section | Function | Active state / operator |
|---|---|---|
| Related Repository Files | Identifies controlling dependencies and source-boundary files | dependency tracking |
| §0 | Defines file function, working-state register, File map, node-class controls, Machine Guards, arithmetic controls, claim-status controls, author-decision integration result, and finalization control | file-level cumulative state; phase-resolved Mirror coordinate-completion; author-decision controls |
| §1 | Records the tripartite cumulative epochs | cumulative MT; Jubilee `49`; Jacobean Completion; structural inference |
| §2 | Records the SP cumulative square | SP cumulative; `110 × 110`; arithmetic fact; endpoint dependency |
| §3 | Records the `5520` Conquest harmonic after author clarification | core phase-resolved Mirror coordinate-completion; civil cross-axis component checks; `25/23`; Theological note; Appendix A controls detailed Mirror mechanics |
| §4 | Records the Arphaxad-Jacob-Levi arc after author clarification | restored cumulative 2nd Cainan Flood Week terminal; same-side BC arc; `70 × 49`; `7 × 490`; Jacob-Levi `+77`; Luke comparative state |
| §5 | Records the Danielic Creation cycles under the Cainan variant | cumulative MT + 2nd Cainan `+460`; Danielic `2300`; Mirror source-label; Key-of-23 conversions |
| §6 | Preserves the source cross-reference index | dependency tracking |
| §7 | Records audit and dependency notes retained in the Final source | audit / dependency control |
| Appendix A | Retains phase-resolved Mirror mechanics for paired / single dates, suffix inversion, Julian Jan-1 center, and standalone polarity caution | source-active Mirror addendum |
| Revision and archive note | Records public-clean archive routing and preservation controls | publication cleanup |

### 0.3 Node-class and display-state register

| Date / value / display | Node-class | Active state | Do not collapse with |
|---|---|---|---|
| 4115t/4114n BC | phase-resolved Creation-week endpoint pair | Conquest / New Eden phase-resolved Mirror coordinate-completion | unsuffixed `4114 BC` shorthand; `4116 BC` Year-6; Rounded `4106 BC`; cumulative Creation `14006 BC`; SP / LXX Creation states |
| 4114 BC | compressed source shorthand for the Eden-side anchor | MT Standard-Normal Creation endpoint dependency state | full phase-resolved pair when §3 is active |
| AD 1406t/1407n | phase-resolved New Eden Mirror coordinate pair | Conquest / New Eden phase-resolved Mirror coordinate-completion | Protocol 1 `AD 1405`; unsuffixed `AD 1406` precise node unless the active display collapses suffixes by author decision |
| AD 1406 | precise numeric-year Mirror node and compressed source target | precise Mirror node of unsuffixed `1406 BC`; Tishri member of `AD 1406t/1407n` when suffixes are opened | Rounded / Protocol 1 `AD 1405`; ordinary unsuffixed elapsed span to `4114 BC` |
| 1407t/1406n BC | East-side / West-side Jordan Conquest pair | Conquest phase-pair state | unsuffixed `1406 BC` anchor alone; land-rest endpoint `1399 BC` |
| `Yt/(Y−1)n BC → AD (Y−1)t/Y n` | generic phase-resolved Mirror suffix-inversion rule | `.5` Tishri/Nisan Mirror display state | same-order AD display `AD (Y−1)n/Yt`, which would stretch the phase pair to about `1.5` years |
| Oct 1 / Jan 1 / Apr 1 | simplified Julian phase-coordinate points | Julian Jan-1 Mirror-axis model | astronomical month-length corrections unless a local day-count section opens them |
| `Yt/(Y−1)n BC` | January-centered source pair | Tishri-to-Nisan cross-year half-year pair | same-year `Yn/Yt`, which is July-centered |
| `Yn/Yt` | July-centered same-year contrast pair | non-active contrast state | January-centered `Yt/(Y−1)n BC` pair |
| 1407t BC → AD 1407t | single-date exact Mirror node | non-paired Tishri Conquest node | paired Mirror span `2812`; Nisan single node `2811` |
| 1406n BC → AD 1406n | single-date exact Mirror node | non-paired Nisan Conquest node | paired Mirror span `2812`; Tishri single node `2813` |
| 1407t/1406n BC → AD 1406t/1407n | paired phase-resolved Mirror coordinate-completion | Conquest pair / New Eden pair | single-date exact Mirror spans `2813` and `2811`; same-order AD display `AD 1406n/1407t` |
| 2813 | single-date exact Mirror span | `1407t BC → AD 1407t` | paired span `2812`; Nisan single span `2811` |
| 2812 | paired phase-resolved Mirror span | `1407t/1406n BC → AD 1406t/1407n`; average of `2813` and `2811` | single-date spans by themselves; arbitrary slash-pair averaging |
| 2811 | single-date exact Mirror span | `1406n BC → AD 1406n`; unsuffixed `1406 BC → AD 1406` | paired span `2812`; Rounded / Protocol 1 `2810` |
| 1447t/1446n BC → AD 1446t/1447n | plague-period phase-pair example | generic Mirror suffix-inversion example by dependency | `AD 1446n/1447t`; wilderness death pair; Conquest-side pair unless state is named |
| 1407t BC | East side of Jordan Conquest start / occupation by 2.5 tribes | Conquest phase-pair state | West side crossing / occupation `1406n BC` |
| 1406n BC | West side Jordan crossing and occupation by the other 10 tribes | Conquest phase-pair state | East-side start `1407t BC`; unsuffixed `1406 BC` when suffixes are not active |
| 5520 | phase-resolved civil cross-axis harmonic value | local Mirror coordinate-completion | old unsuffixed coordinate sum; ordinary elapsed civil span from `4114 BC` to `AD 1406`, which would be `5519` |
| 5519 | obsolete civil contrast for compressed unsuffixed pair | audit-history value only | active `5520` phase-resolved component checks |
| 6000 | Priestly-converted display value | `25/23` conversion state; Theological note field | civil-year span or unconverted solar span |
| 2811 | precise numeric-year Mirror span | `1406 BC → AD 1406` | Rounded / Protocol 1 comparison `2810` |
| 2810 | Rounded / Protocol 1 comparison span | `1406 BC → AD 1405` comparison only | precise numeric-year Mirror span `2811` |
| 5296–5289 BC | restored cumulative 2nd Cainan Flood Week | cumulative `+460` Flood Week state | base rounded cumulative Flood Week `4836–4829 BC`; regular Flood states |
| 5289 BC | terminal member of restored cumulative 2nd Cainan Flood Week; Flood / Arphaxad-side boundary label | Arphaxad-Jacob arc | base cumulative Flood `4836 BC`; restored cumulative Flood Week opening `5296 BC`; ordinary Arphaxad begetting row unless dependency opens it |
| 1859 BC | Jacob death | standard Jacob `+215` death-state by dependency | Jacob Entry; Jacob birth; LXX `−33` Jacob death; MT Minimum Jacob death |
| 1782 BC | Levi death | `+215` Levi death state | Jacob death `1859 BC`; LXX `−33` Levi death; Conquest anchor |
| `+77` | source-display temporal extension | Levi extension state | ordinary upstream BC addition unless direction-aware BC arithmetic is also stated |
| `−77` in direction-aware BC display | arithmetic movement from Jacob death to Levi death | Levi extension arithmetic check | source narrative `+77` display; do not treat as change of claim |
| `+460` | cumulative restored 2nd Cainan insertion | cumulative Cainan state | regular restored 2nd Cainan `+130` |
| 15870 | solar-year cycle span | Danielic 2300-cycle state | date anchor or ordinary civil span without endpoints |
| 16100 | Prophetic converted cycle value | Danielic Prophetic conversion state | date anchor; Priestly `17250` state |
| 17250 | Priestly converted cycle value | Danielic Priestly conversion state | date anchor; Prophetic `16100` state |
| `7 × 2300` Mirror | source label for Danielic cycle display | local Danielic Mirror source-label state | Protocol 1; Protocol 2; civil cross-axis span; inverse-number reversal |

### 0.4 Modal-state processing rules

1. Cumulative MT, SP cumulative, regular chronology, and phase-resolved Mirror coordinate-completion are distinct states. Shared numbers do not merge them.
2. Date-label identity requires agreement in state, node-class, tradition, suffix, and operator.
3. `4114 BC` is retained as the source’s compressed Eden-side anchor, but §3 expands it to `4115t/4114n BC` when the phase-resolved Mirror coordinate-completion is active.
4. The executable `5520` harmonic is no longer the old unsuffixed display `4114 + 1406 = 5520`. It is the component-wise civil cross-axis pair: `4115 + 1406 − 1 = 5520` and `4114 + 1407 − 1 = 5520`.
5. `AD 1406t/1407n` is the phase-resolved Mirror coordinate-completion of the Conquest-side pair `1407t/1406n BC`. The display inverts across the Mirror.
6. Generic phase-resolved Mirror rule: when a BC dual date is separated by a half-year as `Yt/(Y−1)n BC`, the AD Mirror display preserves the `.5` relation as `AD (Y−1)t/Y n`. It must not be written as `AD (Y−1)n/Yt`, because that changes the AD-side internal phase distance to about `1.5` years.
7. Formal proof rule: for proof-only phase notation, set `n = 0` and `t = 0.5`. The whole-year civil skeleton remains `BC + AD − 1`; the phase-consistency check compares target phase `q` and source phase `p`. Valid paired suffix inversion makes `q − p = 0` on both components. The invalid same-order AD display makes one component `−0.5` and the other `+0.5`, proving that the same-order display cannot support exact month/day work.
8. Unsuffixed `AD 1406` is also retained as the precise numeric-year Mirror node of unsuffixed `1406 BC`: `1406 + 1406 − 1 = 2811`. This must not be confused with the Rounded / Protocol 1 target `AD 1405`: `1406 + 1405 − 1 = 2810`.
9. Single-date exact Mirror nodes and phase-resolved paired Mirror states are distinct. A single date mirrors to its own numeric-year AD counterpart, while a `.5` paired slash-pair mirrors cross-component with suffix inversion. For the Conquest pair: `1407 + 1407 − 1 = 2813`; `1406 + 1406 − 1 = 2811`; but `1407 + 1406 − 1 = 2812` and `1406 + 1407 − 1 = 2812` when the pair is mirrored as `1407t/1406n BC → AD 1406t/1407n`. The relation `(2813 + 2811) ÷ 2 = 2812` is explanatory for this paired state; it is not a general averaging operator for slash-pairs.
10. `1407t BC` and `1406n BC` are not invented replacement dates. They preserve the East-side / West-side Jordan Conquest phase distinction: East-side occupation by the 2.5 tribes, followed about six months later by the West-side crossing and occupation by the other 10 tribes.
11. Aaron’s death shortly before `1407t BC` and Moses’ death shortly before `1406n BC`, with each mourned 30 days, are retained as author-clarified terminal phase controls.
12. The SP cumulative square, `12100 = 110 × 110`, remains a separate SP cumulative state. Its endpoints must not be inferred from MT cumulative architecture.
13. `5289 BC` is resolved as the terminal member of the restored cumulative 2nd Cainan Flood Week, `5296–5289 BC`, and as the source’s Flood / Arphaxad-side boundary label.
14. `1859 BC` and `1782 BC` belong to the Jacob-Levi `+215` death-state field. Do not mix them with LXX `−33`, MT Minimum, or other Jacob / Levi comparison states.
15. The Levi `+77` line preserves the source’s forward-time extension display. Arithmetic-control display may add the direction-aware BC check `1859 − 77 = 1782` without changing the source claim.
16. Regular restored 2nd Cainan `+130` and cumulative restored 2nd Cainan `+460` are related Cainan states but not interchangeable operators.
17. The Danielic “Mirror” label in §5 is a source-retained cycle label. It does not open Protocol 1, Protocol 2, civil cross-axis Mirror arithmetic, 10x Mirror scaling, or inverse-number reversal.
18. The theological reading of `6000` years leading to the 7th Day of Rest is preserved as theological meaning. It does not carry the arithmetic burden.
19. In the simplified Julian phase-coordinate model, `t` is the start of Oct 1, `n` is the start of Apr 1, and the Mirror hinge is the start of Jan 1. The pair `Yt/(Y−1)n BC` is January-centered; a same-year `Yn/Yt` pair is July-centered and is not the active Creation / Conquest paired Mirror state.
20. In a self-mirrored `t/n` pair, the BC pair-center and AD pair-center bracket Jan 1, AD 1 exactly. In File_09's `5520` Conquest harmonic, the same phase-coordinate rule instead supplies equal component spans from the Creation endpoint pair to the New Eden / Conquest Mirror pair.

### 0.5 Machine Guards for `File_09`

Machine Guard [FILE_09 CUMULATIVE / REGULAR]:

Cumulative MT, SP cumulative, and regular chronology are distinct. Do not use a regular Creation, Flood, Abraham, Jacob, Levi, or Conquest state to replace a cumulative state unless the active section states the conversion and dependency.

Machine Guard [FILE_09 5520 PHASE-RESOLVED MIRROR]:

The source line `4114 BC + AD 1406 = 5520 years` is a compressed source display. The active Final source form is the phase-resolved Mirror coordinate-completion:

```markdown
4115t/4114n BC → AD 1406t/1407n = 5520 years
4115 + 1406 − 1 = 5520
4114 + 1407 − 1 = 5520
```

Do not return the file to the unsuffixed coordinate-sum explanation unless the author explicitly reverses this decision.

Machine Guard [FILE_09 AD 1406 PRECISE MIRROR NODE]:

`AD 1406` is the precise numeric-year Mirror node of the unsuffixed `1406 BC` Conquest:

```markdown
1406 + 1406 − 1 = 2811
```

It is not the Rounded / Protocol 1 target `AD 1405`, where:

```markdown
1406 + 1405 − 1 = 2810
```

Machine Guard [FILE_09 CONQUEST PHASE PAIR]:

`1407t/1406n BC` is the Conquest-side phase pair. `1407t BC` marks the East side of Jordan Conquest start and occupation by the 2.5 tribes. `1406n BC` marks the later West side crossing and occupation by the other 10 tribes. Aaron died shortly before `1407t BC`; Moses died shortly before `1406n BC`; each was mourned 30 days. Preserve the approximately six-month gap.

Machine Guard [FILE_09 MIRROR SUFFIX INVERSION]:

Phase-resolved `.5` Tishri/Nisan dual dates invert their suffix display across the Mirror in order to preserve the half-year phase distance.

Generic form:

```markdown
Yt/(Y−1)n BC → AD (Y−1)t/Y n
```

Therefore:

```markdown
1407t/1406n BC → AD 1406t/1407n
1447t/1446n BC → AD 1446t/1447n
```

Do not use the same-order AD display `AD (Y−1)n/Yt` for a phase-resolved Mirror pair unless a local section explicitly opens a different phase-state. The same-order AD display expands the AD-side internal phase distance to about `1.5` years rather than preserving the source pair's `.5` relation.

Proof-only phase notation:

```markdown
n = 0
t = 0.5
```

The whole-year civil skeleton remains:

```markdown
BC + AD − 1
```

When an exact phase-state is opened, compare source phase `p` with target phase `q`. Valid paired suffix inversion gives `q − p = 0` on both components. Same-order AD display gives one component with `q − p = −0.5` and the other with `q − p = +0.5`. That is why exact day/month calculations fail under the same-order display even if the integer labels look superficially balanced.

Example rejected form:

```markdown
1447t/1446n BC → AD 1446n/1447t
```

The AD-side pair `AD 1446n/1447t` is about `1.5` years apart. Therefore it is not the Mirror of the `.5` phase-pair `1447t/1446n BC`.

`AD 1406t/1407n` reflects the Conquest-side pair `1407t/1406n BC` by phase-resolved Mirror coordinate-completion. The AD-side display is intentionally ordered by Mirror relation and suffix inversion. Do not collapse it into unsuffixed `AD 1406` or treat it as a Rounded / Protocol 1 mod-5 target.

Machine Guard [FILE_09 JULIAN JAN-1 PHASE MODEL]:

For the simplified Julian phase-coordinate proof, use:

```markdown
Oct 1 = Tishri 1 = `t`
Apr 1 = Nisan 1 = `n`
Jan 1 = Mirror-axis / center point
```

The repository's phase-resolved paired Mirror state is January-centered:

```markdown
Yt/(Y−1)n BC → AD (Y−1)t/Y n
```

The same-year display `Yn/Yt` is July-centered and is not the active Creation / Conquest paired Mirror state. The July-centered `n/t` form must not replace the Jan-1-centered `t/n` form in exact month/day work.

The simplified Julian phase-coordinate model is a proof model for repository phase logic. It does not open astronomical month-length corrections unless a local day-count section explicitly opens that state.

Machine Guard [FILE_09 PAIRED / SINGLE MIRROR DATES]:

Single exact Mirror dates and paired phase-resolved Mirror dates are distinct states.

Single-date checks:

```markdown
1407t BC → AD 1407t
1407 + 1407 − 1 = 2813

1406n BC → AD 1406n
1406 + 1406 − 1 = 2811
```

Paired phase-resolved Mirror check:

```markdown
1407t/1406n BC → AD 1406t/1407n
1407 + 1406 − 1 = 2812
1406 + 1407 − 1 = 2812
```

The paired value `2812` is the average of the two non-paired single-date Mirror spans:

```markdown
2813 + 2811 = 5624
5624 ÷ 2 = 2812
```

This average explains why the paired state sits between the two single-date exact Mirror spans. It must not be turned into a general slash-pair averaging operator. The active paired calculation remains component-wise civil cross-axis arithmetic after suffix inversion.

Machine Guard [FILE_09 STANDALONE POLARITY FLIP]:

Standalone exact Mirror dates and paired phase-resolved Mirror dates must remain separate.

A standalone Tishri date mirrored to its own AD numeric-year counterpart yields an odd span:

```markdown
Yt BC → AD Yt
Y + Y − 1 = 2Y − 1
```

A standalone Nisan date mirrored to its own AD numeric-year counterpart also yields an odd span:

```markdown
(Y−1)n BC → AD (Y−1)n
(Y−1) + (Y−1) − 1 = 2Y − 3
```

Because these spans are odd, each standalone single-date midpoint is a half-span. In exact phase work, that half-span flips phase polarity at the midpoint: a Tishri-to-Tishri single-date Mirror has a Nisan-side midpoint, and a Nisan-to-Nisan single-date Mirror has a Tishri-side midpoint.

This is not an inconsistency. It is a different modal state from the paired `t/n` Mirror. In `File_09`, the Jan-1 Mirror-axis proof applies to the paired `t/n` state as an average / center-state. Full treatment of standalone Nisan or Tishri polarity inversion should be controlled by a future Mirror-mechanics file, likely `File_51b` or a repository glossary entry.

Formal necessity proof for the Conquest pair:

```markdown
Valid paired display:
1407t BC → AD 1406t = 2812
1406n BC → AD 1407n = 2812

Invalid same-order AD display:
1407t BC → AD 1406n = 2811.5
1406n BC → AD 1407t = 2812.5
```

The invalid display does not preserve equal component spans once the `.5` phase is opened. It also changes the AD-side internal distance from `.5` to `1.5` years. Therefore the paired Mirror display is not arbitrary: it is mathematically required by the phase-state.

Machine Guard [FILE_09 CAINAN +460 / +130]:

Cumulative restored 2nd Cainan uses `+460`. Regular restored 2nd Cainan uses `+130`. `File_09` activates the cumulative `+460` state in the restored cumulative Flood Week and Danielic Cainan sections and must not exchange it for the regular `+130` insertion.

Machine Guard [FILE_09 CAINAN MACRO-VECTOR DEPENDENCY]:

The Cainan macro-vector may be cited only with its active dependency. `File_18` supplies the cumulative and regular Cainan table values; `File_16` controls the Nexus proof through `2300`, `2520`, `2730`, and `1260 → 1290 → 1260`. Do not treat `2307` or solar comparison material as active File_09 operators.

Machine Guard [FILE_09 5289 FLOOD / ARPHAXAD]:

`5289 BC` is the terminal member of the restored cumulative 2nd Cainan Flood Week, `5296–5289 BC`. The source label “Flood / Arphaxad” is preserved as a combined Flood Week terminal / Arphaxad-side boundary label. Do not treat it as an ordinary regular Arphaxad begetting row unless a controlling dependency explicitly opens that row.

Machine Guard [FILE_09 ARPHAXAD-JACOB-LEVI]:

`5289 BC`, `1859 BC`, and `1782 BC` are state-tagged nodes in the Arphaxad-Jacob-Levi arc. `5289 BC` is the restored cumulative Flood Week terminal / Arphaxad-side boundary label; `1859 BC` is Jacob death; `1782 BC` is Levi death. Shared span logic does not collapse the nodes.

Machine Guard [FILE_09 DANIELIC MIRROR LABEL]:

The phrase `7 × 2300 Mirror` is preserved as source terminology for the Danielic cycle display. It is not Protocol 1 Mirror, Protocol 2 Mirror, civil cross-axis arithmetic, 10x scaling, or inverse-number reversal unless a later dependency explicitly opens that protocol.

Machine Guard [FILE_09 LUKE CLAIM-STATUS]:

The Lukan “77-generation” harmonic is preserved as a comparative source claim. In this file it is classified as structural inference and shared-tradition evidence by dependency. Do not turn it into a direct-dependence claim or a proof of Luke’s source use unless a later source-critical dependency supplies that evidence.

Machine Guard [FILE_09 THEOLOGY / ARITHMETIC BURDEN]:

The Sabbath-rest reading in §3 explains the theological meaning of the `6000`-year Priestly conversion. It must not replace the arithmetic operator, endpoint state, phase-pair state, or civil-span guard.

### 0.6 Arithmetic-control summary

Arithmetic-control scope:
This Final source retains the completed arithmetic checks and integrates the author-clarified controls. It updates the active operators and node-classes for prior audit items. Final pressure-test status is preserved in the file header. Detailed pressure-test records are archived rather than repeated in the public body.

| Arithmetic field | Calculation | Result | Claim-status / handling |
|---|---|---:|---|
| Creation → Shem | `175 × 49` | `8575` | Arithmetic fact; endpoints dependency-controlled. |
| Flood → Abraham | `2401 = 49 × 49` | `2401` | Arithmetic fact; endpoints dependency-controlled. |
| Abraham → Conquest | `21 × 49` | `1029` | Arithmetic fact. |
| Jacobean Completion | `7 × 147` | `1029` | Arithmetic fact supporting structural inference. |
| SP cumulative square | `110 × 110` | `12100` | Arithmetic fact; SP endpoints dependency-controlled. |
| Conquest / New Eden Tishri component | `4115 + 1406 − 1` | `5520` | Arithmetic fact under phase-resolved Mirror coordinate-completion. |
| Conquest / New Eden Nisan component | `4114 + 1407 − 1` | `5520` | Arithmetic fact under phase-resolved Mirror coordinate-completion. |
| Compressed source shorthand | `4114 BC + AD 1406 = 5520` | source-history shorthand | Preserved as compressed display, not the final executable operator. |
| Obsolete unsuffixed civil contrast | `4114 + 1406 − 1` | `5519` | Audit-history contrast only; superseded by phase-resolved expansion. |
| Single-date Tishri Mirror node | `1407 + 1407 − 1` | `2813` | Arithmetic fact; non-paired exact Mirror node. |
| Single-date Nisan Mirror node | `1406 + 1406 − 1` | `2811` | Arithmetic fact; non-paired exact Mirror node and unsuffixed `AD 1406` precise Mirror node. |
| Paired Conquest Mirror, Tishri component | `1407 + 1406 − 1` | `2812` | Arithmetic fact under paired phase-resolved Mirror coordinate-completion. |
| Paired Conquest Mirror, Nisan component | `1406 + 1407 − 1` | `2812` | Arithmetic fact under paired phase-resolved Mirror coordinate-completion. |
| Paired average explanation | `(2813 + 2811) ÷ 2` | `2812` | Explanatory relation for this paired Mirror state; not a general slash-pair averaging operator. |
| Rounded / Protocol 1 comparison | `1406 + 1405 − 1` | `2810` | Comparison state only; not the active `AD 1406` node. |
| Priestly conversion, Conquest harmonic | `5520 × 25/23` | `6000` | Arithmetic fact. |
| Six-day theological display | `6 × 1000` | `6000` | Arithmetic display supporting Theological note. |
| Restored cumulative Flood Week shift | `5296 − 4836`; `5289 − 4829` | `460`; `460` | Arithmetic fact; confirms `+460` week shift. |
| Arphaxad-Jacob same-side span | `5289 − 1859` | `3430` | Arithmetic fact; `5289 BC` node-class resolved as restored cumulative Flood Week terminal / Arphaxad-side boundary. |
| 70-Jubilee factorization | `70 × 49` | `3430` | Arithmetic fact. |
| Danielic factorization | `7 × 490` | `3430` | Arithmetic fact. |
| Levi extension direction-aware display | `1859 − 77` | `1782` | Arithmetic fact; source `+77` sign preserved as narrative extension display. |
| Danielic Prophetic conversion | `15870 × 70/69` | `16100` | Arithmetic fact. |
| Danielic Priestly conversion | `15870 × 25/23` | `17250` | Arithmetic fact. |
| Danielic `2300` display | `7 × 2300` | `16100` | Arithmetic fact. |
| Danielic exact-half display | `7.5 × 2300` | `17250` | Arithmetic fact; exact `.5` retained. |

Arithmetic-control result:
All locally executable arithmetic statements in the revised source check under their stated or guarded operators after the author decisions. The prior `5520` issue is resolved by phase-resolved civil cross-axis component checks, not by a raw unsuffixed coordinate sum. No theological claim or cross-file dependency is changed.

### 0.7 Claim-status register for `File_09`

| Label | Function in `File_09` |
|---|---|
| Source-retained chronology datum | A date, span, or target-state preserved from the source or a controlling dependency where `File_09` does not locally re-prove the full table row. |
| Author-clarified chronology datum | A previously audit-controlled value or state resolved by author clarification during revision. |
| Arithmetic fact | Direct calculation from stated values under a stated operator, such as `21 × 49 = 1029`, `4115 + 1406 − 1 = 5520`, `1407 + 1406 − 1 = 2812`, or `5289 − 1859 = 3430`. |
| Structural inference | Pattern inferred from checked arithmetic and state-controlled alignment, such as the Jacobean Completion or the Arphaxad-Jacob `70-Weeks` super-cycle. |
| Shared-tradition evidence | Comparative heptadic or Lukan material preserved by dependency without claiming direct literary dependence. |
| Theological note | The six-days-to-seventh-day Sabbath-rest reading attached to the `6000`-year Priestly conversion. |
| Mirror coordinate-completion | Mirror material that supplies the cross-axis counterpart needed to understand the full coordinate identity of a node, block, rail, or state. |
| Mirror source-label | Source terminology such as `7 × 2300 Mirror` retained without opening Protocol 1, Protocol 2, civil Mirror arithmetic, 10x scaling, or inverse-number reversal. |
| Dependency-controlled | Material retained because another file supplies the endpoint table, source row, or broader proof. |
| Audit note | Operator, target-state, or node-class matter that remains controlled but should not be silently resolved. |

Claim-status rule:
Claim-status labels are used where needed to prevent arithmetic facts, structural inference, theological meaning, comparative Luke material, and Mirror labels from collapsing into one evidential layer. They are not attached mechanically to every sentence.

### 0.8 Argument-control summary

`File_09` argues by layering source-retained cumulative data, arithmetic facts, structural inferences, theological meaning, and dependency-controlled comparative claims.

| Argument layer | Function in `File_09` | Control |
|---|---|---|
| Source-retained chronology data | Preserves the compressed source architecture: tripartite epochs, SP square, Conquest harmonic, Arphaxad-Jacob-Levi arc, Danielic Cainan cycles. | Retained, but missing endpoints remain dependency-controlled. |
| Author-clarified controls | Resolves `5289 BC`, `AD 1406`, the phase-resolved `5520` Mirror coordinate-completion, the paired-versus-single Mirror span distinction, and the formal proof for `.5` Mirror suffix inversion. | Integrated as author-clarified source controls; not retained as unresolved finalization blockers. |
| Arithmetic facts | Verify the visible products, spans, exact ratios, factorisations, phase-resolved cross-axis checks, and same-side BC spans. | May support the main cumulative architecture when state and operator are explicit. |
| Structural inference | Explains why checked spans matter: Jacobean Completion, `70-Weeks` super-cycle, Conquest / New Eden completion, and Danielic cycle structure. | Supports the argument after arithmetic and modal state are stated. |
| Theological note | Interprets the `6000` Priestly conversion as 6 Days leading to the 7th Day of Rest. | Preserved; does not carry arithmetic burden. |
| Shared-tradition evidence | Places the `77` Levi extension beside the Lukan `77-generation` harmonic. | Comparative only; no direct-dependence claim. |
| Mirror coordinate-completion | Expands the compressed `5520` line into phase-resolved Creation / Conquest slash-pairs. | Main-body coordinate-completion because the Mirror supplies the correct counterpart for the `5520` identity. |
| Mirror source-label | Preserves “`7 × 2300` Mirror” as local terminology. | Not Protocol 1, Protocol 2, civil Mirror arithmetic, or inverse-number logic unless a future dependency opens that exact protocol. |
| Dependency-controlled proof | Keeps full endpoint tables in `File_18`, `File_16`, `File_22`, and related files. | Do not infer missing endpoints from factorization alone. |

Argument-control result:
The file’s strongest local claim is that its visible cumulative architecture is internally coherent under the stated operators after the author decisions. The higher-order claims — Jacobean Completion, Lukan 77-generation correspondence, New Eden / Sabbath-rest theology, and Danielic Mirror terminology — are preserved but claim-status controlled.

### 0.9 Author-decision integration result

Author-decision integration retained in Final source:

- `5289 BC` is resolved as the terminal member of the restored cumulative 2nd Cainan Flood Week, `5296–5289 BC`, and as the source’s Flood / Arphaxad-side boundary label;
- `AD 1406` is resolved as the precise numeric-year Mirror node of unsuffixed `1406 BC`, not the Rounded / Protocol 1 target `AD 1405`;
- the compressed `5520` source line is expanded to the phase-resolved form `4115t/4114n BC → AD 1406t/1407n = 5520`;
- the executable `5520` checks are now `4115 + 1406 − 1 = 5520` and `4114 + 1407 − 1 = 5520`;
- the Conquest-side pair `1407t/1406n BC` is explicitly stated as East-side / West-side Jordan Conquest phase material;
- the generic phase-resolved Mirror suffix-inversion rule is stated: `Yt/(Y−1)n BC → AD (Y−1)t/Y n`;
- the paired-versus-single Mirror distinction is stated explicitly: single exact mirrors give `1407 + 1407 − 1 = 2813` and `1406 + 1406 − 1 = 2811`, while the paired phase-resolved Mirror gives `1407 + 1406 − 1 = 2812` and `1406 + 1407 − 1 = 2812`;
- the formal phase-spacing proof is stated: an AD-side `t/n` pair preserves the `.5` Tishri/Nisan interval, while the same-order `n/t` display stretches the AD pair to about `1.5` years;
- the plague-period example is retained as a source-control illustration: `1447t/1446n BC → AD 1446t/1447n`, while `AD 1446n/1447t` is rejected for this state because it does not preserve the `.5` phase relation;
- Aaron and Moses terminal death-phase controls are explicitly stated: Aaron died shortly before `1407t BC`, Moses died shortly before `1406n BC`, and each was mourned 30 days;
- no contradiction to `File_54` is introduced by the Lukan `77-generation` language, which remains structural inference / shared-tradition evidence only;
- the Julian phase-coordinate proof is integrated: Oct 1 = `t`, Apr 1 = `n`, and Jan 1 is the Mirror-axis center; `t/n` pairs are Jan-1-centered, whereas same-year `n/t` pairs are July-centered;
- the standalone phase-date polarity caveat is integrated: single exact Nisan or Tishri Mirror spans may be odd and may flip polarity at their half-year midpoint, while the paired `t/n` state averages the single-date spans into the even Jan-1-centered value;
- the Conquest self-mirror pair checks as `1407t/1406n BC → AD 1406t/1407n = 2812`, while the File_09 Conquest / New Eden coordinate-completion checks as `4115t/4114n BC → AD 1406t/1407n = 5520` component-wise and center-to-center;
- these decisions are retained as active source controls in the Final source.

## 1. Tripartite epochs

Active state:
cumulative MT tripartite state.

Node-class note:
Creation, Shem, Flood, Abraham, and Conquest function here as cumulative architecture nodes. This section does not open ordinary regular biography rows or regular Flood / Creation endpoint rows unless a dependency supplies them.

| Span | Source value | Arithmetic check | Claim-status / handling |
|---|---:|---:|---|
| Creation → Shem | 175 Jubilees | `175 × 49 = 8575` | Source-retained chronology datum; arithmetic fact; endpoints dependency-controlled. |
| Flood → Abraham | 2401 years | `2401 = 49 × 49` | Source-retained chronology datum; arithmetic fact; endpoints dependency-controlled. |
| Abraham → Conquest | 21 Jubilees | `21 × 49 = 1029` | Source-retained chronology datum; arithmetic fact; source `1029` retained. |

Structural inference:
The `1029`-year span is also exactly `7 × 147` (Jacob’s lifespan). This supports the source’s identification of the Conquest as the “Jacobean Completion” of the Abrahamic promise. See `File_22`.

Arithmetic check:

```markdown
21 × 49 = 1029
7 × 147 = 1029
147 = 3 × 49
```

Arithmetic-control note:
The `1029` value checks both as 21 Jubilees and as seven Jacob lifespans. The Jacob-lifespan datum `147 = 3 × 49` remains controlled by `File_04` and `File_22`; this file verifies only the visible multiplication.

Arithmetic-control note:
The local arithmetic also gives:

```markdown
2401 + 1029 = 3430
```

This is a direct sum of the source-retained Flood → Abraham and Abraham → Conquest spans. It does not infer missing endpoints or reclassify the Arphaxad-Jacob `3430` arc.

Argument-control note:
The Jacobean Completion claim belongs to the Abraham → Conquest cumulative state. It does not convert Jacob’s own biography row into the Abraham → Conquest span. The arithmetic fact supports the structural inference; the structural inference does not replace the endpoint dependency.

Dependency note:
The endpoints for Creation → Shem, Flood → Abraham, and Abraham → Conquest remain dependency-controlled until `File_18`, §6A and `File_22` supply or confirm the cumulative table rows. This file does not infer missing endpoints.

## 2. The SP cumulative square

Active state:
SP cumulative state.

Node-class note:
The `12100` square is an SP cumulative structure. It is not an SP regular chronology row and not an MT cumulative row unless a dependency explicitly relates the states.

| Value | Source expression | Arithmetic check | Claim-status / handling |
|---:|---|---:|---|
| 12100 years | `110 × 110` | `110 × 110 = 12100` | Arithmetic fact; source-retained SP cumulative square; endpoints dependency-controlled. |

Argument-control note:
The square expression may support SP cumulative architecture once the endpoints are supplied. In this file, the square itself checks arithmetically, but the endpoint proof remains dependency-controlled.

Dependency note:
The source does not state the SP cumulative square endpoints. Endpoint identification remains dependency-controlled by `File_18`, §6C or another SP cumulative table dependency.

## 3. The 5520 Conquest harmonic: Eden to New Eden

Active state:
Conquest / New Eden phase-resolved Mirror coordinate-completion.

Source-history note:
The source line is compressed:

```markdown
4114 BC + AD 1406 = 5520 years
```

Author-decision handling:
The compressed source line is expanded to its phase-resolved slash-pair form:

```markdown
4115t/4114n BC → AD 1406t/1407n = 5520 years
```

This is not a deletion of the source value. It is a state-expansion of the source shorthand.

### 3.1 Phase-resolved Creation and Conquest pairs

Creation-side basis:
The `4115t/4114n BC` pair exists because the seven years of Creation are viewed Tishri-to-Tishri and/or Nisan-to-Nisan. The pair is the phase-resolved form of the MT Standard-Normal Creation-week endpoint state.

Conquest-side basis:
The Conquest-side pair is `1407t/1406n BC`. `1407t BC` marks the East side of Jordan Conquest start and occupation by the 2.5 tribes. About six months later, `1406n BC` marks the crossing to the West side of Jordan and the beginning of occupation by the other 10 tribes.

Aaron/Moses phase note:
Aaron died shortly before `1407t BC` and was mourned 30 days. Moses died shortly before `1406n BC` and was mourned 30 days. This six-month terminal phase is important throughout the repository and must not be collapsed into a single unsuffixed Conquest date.

Mirror inversion note:
In the Mirror, `AD 1406t/1407n` reflects the Conquest-side pair `1407t/1406n BC`. The AD-side display is a phase-resolved Mirror coordinate-completion of the Conquest pair, not a Rounded / Protocol 1 mod-5 target.

Generic suffix-inversion note:
This is the local Conquest form of the generic phase-resolved Mirror rule for any `.5` Tishri/Nisan dual date:

```markdown
Yt/(Y−1)n BC → AD (Y−1)t/Y n
```

The rule preserves the half-year relation after the date-pair crosses the Mirror. It applies, for example, to the plague-period pair:

```markdown
1447t/1446n BC → AD 1446t/1447n
```

The display `AD 1446n/1447t` is not valid for this phase-resolved Mirror state because it is about `1.5` years apart rather than `.5` years apart. The issue is a suffix-inversion / Mirror-coordinate display state, not a second civil-span operator.

Formal phase-consistency proof:
For proof-only notation, let:

```markdown
n = 0
t = 0.5
```

The whole-year skeleton remains the normal civil cross-axis count:

```markdown
BC + AD − 1
```

When the exact phase-state is opened, the component check also preserves the phase relation between source phase `p` and target phase `q`. Valid suffix inversion keeps `q − p = 0` on both paired components:

```markdown
1407t BC → AD 1406t:
1407 + 1406 − 1 + (0.5 − 0.5) = 2812

1406n BC → AD 1407n:
1406 + 1407 − 1 + (0 − 0) = 2812
```

If the AD-side display is not inverted, the components no longer match at exact phase resolution:

```markdown
1407t BC → AD 1406n:
1407 + 1406 − 1 + (0 − 0.5) = 2811.5

1406n BC → AD 1407t:
1406 + 1407 − 1 + (0.5 − 0) = 2812.5
```

Therefore `AD 1406n/1407t` is not merely a different display choice. It breaks the exact paired state. The same logic applies to the plague-period example: `1447t/1446n BC → AD 1446t/1447n` preserves the `.5` relation, while `AD 1446n/1447t` expands the AD-side pair to about `1.5` years.

Paired-versus-single note:
Single exact Mirror dates and paired phase-resolved Mirror dates are distinct states. A single date mirrors to its own numeric-year AD counterpart:

```markdown
1407t BC → AD 1407t = 2813 years
1407 + 1407 − 1 = 2813

1406n BC → AD 1406n = 2811 years
1406 + 1406 − 1 = 2811
```

When the two dates are paired as a `.5` Tishri/Nisan slash-pair, the Mirror display changes to the suffix-inverted pair:

```markdown
1407t/1406n BC → AD 1406t/1407n = 2812 years
1407 + 1406 − 1 = 2812
1406 + 1407 − 1 = 2812
```

The paired `2812` is also the average of the two non-paired single-date spans:

```markdown
2813 + 2811 = 5624
5624 ÷ 2 = 2812
```

This explains the paired Conquest state, but it does not create a general averaging operator for slash-pairs. The executable paired checks remain component-wise civil cross-axis calculations after suffix inversion.

### 3.2 The executable `5520` checks

Operator:
Civil cross-axis component checks use `BC + AD − 1` after the phase-resolved Mirror counterpart has been stated.

| Component | Calculation | Result | Claim-status / handling |
|---|---:|---:|---|
| Tishri component | `4115 + 1406 − 1` | `5520` | Arithmetic fact under phase-resolved Mirror coordinate-completion. |
| Nisan component | `4114 + 1407 − 1` | `5520` | Arithmetic fact under phase-resolved Mirror coordinate-completion. |
| Priestly conversion | `5520 × 25/23` | `6000` | Arithmetic fact under exact `25/23`. |
| Theological reading | 6 Days (`6000` years) of work lead to the 7th Day of Rest, identified with the Conquest. | `6 × 1000 = 6000` | Theological note supported by arithmetic display. |

Arithmetic checks:

```markdown
4115 + 1406 − 1 = 5520
4114 + 1407 − 1 = 5520
5520 ÷ 23 = 240
240 × 25 = 6000
```

Theological note:
The six-days-to-seventh-day reading is preserved as theological interpretation of the `6000`-year Priestly conversion. It does not replace the stated phase-resolved Mirror operator or target-state.

### 3.3 Addendum pointer: phase-resolved Mirror mechanics

The detailed paired-versus-single Mirror distinction, generic suffix-inversion proof, Julian Jan-1 phase-coordinate proof, precise `AD 1406` note, and standalone polarity caution are retained in Appendix A.

These controls remain active for `File_09`. They are placed in Appendix A so the main `5520` harmonic remains compact while future files can cite the phase-resolved Mirror mechanics directly.

## 4. The Arphaxad-Jacob arc

### 4.1 The “70-Weeks” super-cycle

Active state:
Arphaxad-Jacob arc under restored cumulative 2nd Cainan Flood Week terminal state.

Node-class note:
`5289 BC` is the terminal member of the restored cumulative 2nd Cainan Flood Week, `5296–5289 BC`, generated by applying the cumulative 2nd Cainan `+460` lifespan state to the base rounded cumulative Flood Week `4836–4829 BC`. The source label “Flood / Arphaxad” is preserved as a combined Flood Week terminal / Arphaxad-side boundary label.

| Element | Source value | Arithmetic check | Claim-status / handling |
|---|---:|---:|---|
| Restored cumulative Flood Week | 5296–5289 BC | `5296 − 4836 = 460`; `5289 − 4829 = 460` | Arithmetic fact; author-clarified `+460` cumulative Cainan state. |
| Anchor | 5289 BC, Flood / Arphaxad | terminal member of `5296–5289 BC` | Author-clarified chronology datum; combined source label retained. |
| Target | 1859 BC, death of Jacob | — | Source-retained chronology datum; Jacob death-state by dependency. |
| Span | 3430 years | `5289 − 1859 = 3430` | Arithmetic fact under same-side BC subtraction. |
| Logic | `3430 = 70 × 49`, or `7 × 490` | `70 × 49 = 3430`; `7 × 490 = 3430` | Arithmetic fact supporting structural inference. |

Structural inference:
The `3430` span functions as a “70-Weeks” super-cycle because it checks as both `70 × 49` and `7 × 490`. This classification depends on the active Arphaxad-Jacob arc state and does not automatically classify every other `3430` span in the repository.

State note:
`1859 BC` is Jacob death under the standard Jacob `+215` state by dependency. It is not Jacob Entry and not a comparison-state death under MT Minimum or LXX `−33`.

### 4.2 The Levi extension

Active state:
Jacob-Levi extension.

Node-class note:
`1782 BC` is Levi death under the `+215` Levi death state by dependency. It is not a second Jacob death date and not a Conquest date.

| Element | Source / revised statement | Arithmetic check | Claim-status / handling |
|---|---|---:|---|
| Levi extension | Source display: `1859 BC` (Jacob death) `+ 77` years = `1782 BC` (Levi death) | direction-aware BC display: `1859 − 77 = 1782` | Arithmetic fact; source `+77` extension sign preserved. |
| Lukan harmonic | The Levi extension supports the Lukan “77-generation” harmonic. | no direct arithmetic check beyond the `77` relation | Structural inference; shared-tradition evidence by dependency; no direct-dependence claim. |

Sign-convention note:
The source display `1859 BC + 77 years = 1782 BC` is retained as a forward-time BC extension display. Arithmetic-control display adds the direction-aware same-side BC form:

```markdown
1859 − 77 = 1782 BC
```

This is not a correction to the source sign. It is an arithmetic clarification of forward movement within BC date labels.

Argument-control note:
The source’s “validates” language is controlled as structural inference and shared-tradition evidence. The local fact is the Jacob-Levi `77`-year extension. The Luke-related claim is comparative and dependency-controlled, not a claim that Luke directly depended on this local `File_09` structure.

Dependency note:
The Lukan “77-generation” harmonic remains dependency-controlled by the Luke / genealogy branch, especially `File_54`. No direct-dependence claim is made in `File_09`.

## 5. Danielic Creation cycles: the Cainan variant

Active state:
Cumulative MT with restored cumulative 2nd Cainan.

Cainan state:
The local Cainan operator is cumulative restored 2nd Cainan `+460`. Regular restored 2nd Cainan `+130` is not active in this section.

Mirror-label state:
The source phrase `7 × 2300 Mirror` is preserved as a Danielic cycle / Mirror source-label. It is not Protocol 1 or Protocol 2 Mirror unless a later dependency explicitly opens those protocols.

| Element | Source statement | Arithmetic check | Claim-status / handling |
|---|---|---:|---|
| Source | Cumulative MT + 2nd Cainan (`+460` years). | no local endpoint check | Source-retained chronology datum; cumulative Cainan state; endpoints dependency-controlled. |
| Prophetic conversion | `15870` solar years → `16100` Prophetic (`7 × 2300`) | `15870 × 70/69 = 16100`; `7 × 2300 = 16100` | Arithmetic fact under `70/69`. |
| Priestly conversion | `15870` solar years → `17250` Priestly (`7.5 × 2300`) | `15870 × 25/23 = 17250`; `7.5 × 2300 = 17250` | Arithmetic fact under `25/23`; exact `.5` retained. |
| Mirror / cycle label | The `7 × 2300` Mirror | no formal Mirror protocol opened | Mirror source-label; dependency-controlled. |

Detailed arithmetic checks:

```markdown
15870 ÷ 69 = 230
230 × 70 = 16100
7 × 2300 = 16100
```

```markdown
15870 ÷ 23 = 690
690 × 25 = 17250
7.5 × 2300 = 17250
```

Exact-half note:
The `7.5` value is retained as an exact half-state display. No decimal drift or rounding is introduced.

Argument-control note:
The Prophetic and Priestly display values both check as arithmetic facts. The source does not state the endpoints for the `15870` solar-year span, so the endpoint set remains dependency-controlled. The “Mirror” label is preserved as terminology but does not carry the local burden of proof.

Dependency note:
The source does not state the endpoints for the `15870` solar-year span. This file preserves the statement and leaves endpoint identification to a controlling cumulative / Danielic dependency.

Dependency note:
The `+460` Cainan value is retained as the cumulative 2nd Cainan state. It must not be collapsed with the regular restored 2nd Cainan `+130` state.

## 6. Cross-reference index

| Area | Cross-reference | Dependency handling |
|---|---|---|
| Data verification | `File_18`, §§6A–6D, Cumulative Tables | Controls missing cumulative table endpoints and verification rows. Use §6A for MT cumulative trunk, §6B for restored cumulative 2nd Cainan, §6C for SP cumulative, and §6D for LXX cumulative. |
| Variant logic | `File_16`, §3, Cainan Mechanism | Controls regular `+130` versus cumulative `+460` Cainan distinctions. |
| Jacobean Completion | `File_22` | Controls the `1029 = 7 × 147` completion framing. |
| Luke comparative claim-status | `File_54` | Controls Lukan 77-generation comparative restraint and no-direct-dependence language. |
| Creation-week endpoint phase pair | `File_07` | Controls `4115t/4114n BC` Creation-week endpoint slash-pair precedent and suffix handling. |
| Conquest phase pair | `File_06` and author clarification | Controls Aaron/Moses terminal phase anchors and the `1407t/1406n BC` East-side / West-side Conquest distinction. |

## 7. Audit and dependency notes retained in the Final source

Audit note:
The `5520` Conquest harmonic is resolved in the Final source as phase-resolved Mirror coordinate-completion:

```markdown
4115t/4114n BC → AD 1406t/1407n = 5520 years
4115 + 1406 − 1 = 5520
4114 + 1407 − 1 = 5520
```

The old unsuffixed contrast `4114 + 1406 − 1 = 5519` remains only as audit history.

Audit note:
The generic phase-resolved Mirror suffix-inversion rule is now active in `File_09`:

```markdown
Yt/(Y−1)n BC → AD (Y−1)t/Y n
```

This rule explains why `1407t/1406n BC` mirrors as `AD 1406t/1407n`, and why the plague-period label-state `1447t/1446n BC` mirrors as `AD 1446t/1447n` rather than `AD 1446n/1447t`.

Audit note:
The paired-versus-single Mirror distinction is now active in `File_09`:

```markdown
1407t BC → AD 1407t = 2813
1406n BC → AD 1406n = 2811
1407t/1406n BC → AD 1406t/1407n = 2812
2813 + 2811 = 5624
5624 ÷ 2 = 2812
```

The `2812` value belongs to the paired phase-resolved Mirror state. It is not a correction of the single-date `2813` or `2811` checks and not a general averaging operator.

Audit note:
The formal phase-consistency proof is now active in `File_09`. It shows that suffix inversion is mathematically necessary for `.5` paired Mirror states, because the valid display gives equal exact components:

```markdown
1407t BC → AD 1406t = 2812
1406n BC → AD 1407n = 2812
```

The invalid same-order AD display gives unequal exact components:

```markdown
1407t BC → AD 1406n = 2811.5
1406n BC → AD 1407t = 2812.5
```

and changes the internal AD-side pair width to `1.5` years. This proof confirms the phase-state; it does not introduce a second civil-span operator.

Audit note:
The Julian phase-coordinate proof is now active in `File_09`. Under the simplified Julian phase model, Oct 1 = `t`, Apr 1 = `n`, and Jan 1 = the Mirror-axis center. Therefore `Yt/(Y−1)n BC` is January-centered, while same-year `Yn/Yt` is July-centered and is not the active Creation / Conquest paired Mirror state.

Audit note:
The standalone single-date polarity-flip caution is now active in `File_09`. Standalone exact Tishri or Nisan Mirror nodes are valid, but they yield odd spans and half-span midpoints that flip phase polarity. This is not an inconsistency with the paired `t/n` Jan-1 average state. It is a distinct modal state, and fuller treatment belongs to a future Mirror-mechanics file.

Audit note:
`AD 1406` is retained as the precise numeric-year Mirror node of `1406 BC`, not the Rounded / Protocol 1 target `AD 1405`.

```markdown
1406 + 1406 − 1 = 2811
1406 + 1405 − 1 = 2810
```

Audit note:
The Levi extension line retains the source `+77` display. The direction-aware BC arithmetic checks as:

```markdown
1859 − 77 = 1782
```

This clarification does not change the source claim or sign convention.

Audit note:
The Danielic `7 × 2300 Mirror` phrase is retained as source terminology but not classified as Protocol 1, Protocol 2, civil Mirror arithmetic, 10x Mirror scaling, or inverse-number reversal.

Dependency note:
The tripartite epoch endpoints, SP cumulative square endpoints, and Danielic `15870` endpoint set remain dependency-controlled. Do not infer them from factorization alone.

Dependency note:
The `5289 BC` Flood / Arphaxad label is no longer unresolved as to its local node-class. It is the terminal member of the restored cumulative 2nd Cainan Flood Week, `5296–5289 BC`. Full cumulative-table proof remains controlled by `File_18`, §6B and related cumulative dependencies.

Dependency note:
The Lukan 77-generation relation is claim-status controlled as structural inference and shared-tradition evidence by dependency. It is not an unresolved author-decision blocker unless the author wants to assert a stronger source-critical or direct-dependence claim.

Argument-control note:
All interpretive claims in this file are tied to the appropriate claim-status layer: arithmetic fact, structural inference, theological note, Mirror coordinate-completion, Mirror source-label, shared-tradition evidence, or dependency-controlled proof.

## Appendix A. Phase-resolved Mirror mechanics

Appendix status:
This appendix is source-active. It preserves the author-clarified mechanics for `.5` Tishri/Nisan phase-pairs, paired-versus-single Mirror dates, suffix inversion, Julian Jan-1 phase coordinates, and standalone polarity caution. Appendix placement is a readability decision, not evidential demotion.

### A.1 Paired versus single Mirror spans

Active state:
paired-versus-single Mirror span distinction.

| Mirror form | Calculation | Result | Handling |
|---|---:|---:|---|
| Single Tishri date | `1407 + 1407 − 1` | `2813` | `1407t BC → AD 1407t`; exact single-date Mirror node. |
| Single Nisan date | `1406 + 1406 − 1` | `2811` | `1406n BC → AD 1406n`; exact single-date Mirror node. |
| Paired Tishri component | `1407 + 1406 − 1` | `2812` | `1407t BC → AD 1406t`; paired phase-resolved Mirror component. |
| Paired Nisan component | `1406 + 1407 − 1` | `2812` | `1406n BC → AD 1407n`; paired phase-resolved Mirror component. |
| Paired average explanation | `(2813 + 2811) ÷ 2` | `2812` | Explains the paired state; not a general averaging operator. |

State note:
The single-date checks are true when the dates are not paired. The paired Conquest state is a different modal state: the half-year slash-pair crosses the Mirror and preserves its `.5` relation through suffix inversion. Therefore the paired Mirror display is `AD 1406t/1407n`, not `AD 1407t/1406n` and not a collapse into a single unsuffixed AD date.

Formal proof note:
The paired state is not arbitrary. The proof is that the suffix-inverted display preserves both equal component spans and the `.5` internal distance of the pair. If the AD-side suffixes are kept in same-order form, exact month/day work breaks.

Proof-only phase notation:

```markdown
n = 0
t = 0.5
```

Valid paired display:

```markdown
1407t BC → AD 1406t
1407 + 1406 − 1 + (0.5 − 0.5) = 2812

1406n BC → AD 1407n
1406 + 1407 − 1 + (0 − 0) = 2812
```

Invalid same-order AD display:

```markdown
1407t BC → AD 1406n
1407 + 1406 − 1 + (0 − 0.5) = 2811.5

1406n BC → AD 1407t
1406 + 1407 − 1 + (0.5 − 0) = 2812.5
```

The invalid same-order display also gives the wrong internal AD-side pair width:

```markdown
AD 1406n → AD 1407t = 1.5 years
```

The valid suffix-inverted display preserves the half-year internal pair width:

```markdown
AD 1406t → AD 1407n = 0.5 year
```

Therefore the paired Mirror state must be:

```markdown
1407t/1406n BC → AD 1406t/1407n = 2812 years
```

The same formal proof governs the plague-period example:

```markdown
1447t/1446n BC → AD 1446t/1447n
```

and rejects:

```markdown
1447t/1446n BC → AD 1446n/1447t
```

because `AD 1446n → AD 1447t` is about `1.5` years rather than `.5` years.

### A.2 Formal proof of suffix inversion and paired span necessity

Active state:
formal phase-distance proof for paired Mirror dates.

Proof statement:
The AD-side suffix inversion is not arbitrary. It is required when a paired Tishri/Nisan date is treated as a `.5` phase-resolved slash-pair across the Mirror.

Definition:
A phase-resolved `.5` Tishri/Nisan BC pair has the form:

```markdown
Yt/(Y−1)n BC
```

The first member is the Tishri member. The second member is the Nisan member about six months later. In BC chronology, forward movement in time lowers the year label: Tishri of `Y` moves forward to Nisan of `Y−1`. The pair therefore preserves an internal phase distance of about `.5` year.

Required AD-side condition:
The AD Mirror counterpart must preserve the same internal phase distance. In AD chronology, forward movement in time raises the year label. Therefore Tishri of `Y−1` moves forward to Nisan of `Y`, and the valid AD-side pair is:

```markdown
AD (Y−1)t/Y n
```

Invalid same-order display:
The same-order AD display is:

```markdown
AD (Y−1)n/Yt
```

This display moves from Nisan of `AD (Y−1)` to Tishri of `AD Y`, which is about `1.5` years. It fails the defining `.5` phase-distance condition. Equal-looking integer totals cannot rescue the display, because the state being mirrored is not merely two year labels; it is a Tishri/Nisan pair separated by about half a year.

Phase-distance table:

| Display | Internal phase relation | Status |
|---|---:|---|
| `Yt BC → (Y−1)n BC` | about `.5` year | valid BC source pair |
| `AD (Y−1)t → AD Yn` | about `.5` year | valid AD Mirror pair |
| `AD (Y−1)n → AD Yt` | about `1.5` years | invalid same-order AD display for this Mirror state |

Formal span proof:
For a single exact Tishri date:

```markdown
Yt BC → AD Yt
Y + Y − 1 = 2Y − 1
```

For a single exact Nisan date:

```markdown
(Y−1)n BC → AD (Y−1)n
(Y−1) + (Y−1) − 1 = 2Y − 3
```

For the paired phase-resolved Mirror:

```markdown
Yt BC → AD (Y−1)t
Y + (Y−1) − 1 = 2Y − 2

(Y−1)n BC → AD Yn
(Y−1) + Y − 1 = 2Y − 2
```

Thus both paired components return the same span. The paired span is also the midpoint of the two non-paired single-date spans:

```markdown
((2Y − 1) + (2Y − 3)) ÷ 2 = 2Y − 2
```

For the Conquest pair, `Y = 1407`:

```markdown
1407t BC → AD 1407t
2 × 1407 − 1 = 2813

1406n BC → AD 1406n
2 × 1407 − 3 = 2811

1407t/1406n BC → AD 1406t/1407n
2 × 1407 − 2 = 2812
```

Therefore:

```markdown
2813 + 2811 = 5624
5624 ÷ 2 = 2812
```

Conquest component checks:

```markdown
1407 + 1406 − 1 = 2812
1406 + 1407 − 1 = 2812
```

Plague-period instance:

```markdown
1447t/1446n BC → AD 1446t/1447n
```

Rejected display:

```markdown
1447t/1446n BC → AD 1446n/1447t
```

Reason for rejection:
`AD 1446n → AD 1447t` is about `1.5` years, not `.5` years. Therefore it is not the Mirror counterpart of the `.5` BC pair `1447t/1446n BC`.

Conclusion:
The paired value `2812` is not arbitrary and is not borrowed from either single-date Mirror node. It is forced by two requirements operating together: the AD-side pair must preserve the `.5` Tishri/Nisan phase distance, and each paired component must check by the civil cross-axis operator `BC + AD − 1`. The average relation explains why the paired value sits between the two single-date spans, but the executable paired calculation remains component-wise civil cross-axis arithmetic after suffix inversion.

### A.3 Julian phase-coordinate proof: Jan 1 center versus July 1 center

Active state:
Julian Jan-1 phase-coordinate proof for paired Mirror dates.

Purpose:
This section formalizes the author clarification that the phase-resolved Mirror pair is not arbitrary. It also explains why the repository uses a `t/n` pair for Creation / Conquest paired Mirror work rather than a same-year `n/t` pair.

Simplified Julian phase convention:

```markdown
start of Oct 1 = Tishri 1 = `t`
start of Apr 1 = Nisan 1 = `n`
start of Jan 1 = civil / Mirror center
```

Theological / calendrical hinge:
The repository Mirror is centered on the start of Jan 1, AD 1, traditionally associated with Christ's Day-8 circumcision and naming after the Dec 25, 1 BC birth placement. This is the Jan-1 hinge, not a July-1 hinge.

Proof-only coordinate notation:
Measure time in years from the start of Jan 1, AD 1. Then:

```markdown
A(AD y, Jan 1) = y − 1
A(y BC, Jan 1) = −y
A(AD y, n) = y − 3/4
A(AD y, t) = y − 1/4
A(y BC, n) = −y + 1/4
A(y BC, t) = −y + 3/4
```

January-centered BC source pair:
For a Tishri/Nisan pair:

```markdown
Yt/(Y−1)n BC
```

The two coordinates are:

```markdown
A(Yt BC) = −Y + 3/4
A((Y−1)n BC) = −Y + 5/4
```

Therefore the internal pair width is:

```markdown
(−Y + 5/4) − (−Y + 3/4) = 1/2
```

and the pair-center is:

```markdown
((−Y + 3/4) + (−Y + 5/4)) ÷ 2 = −Y + 1
```

That center is Jan 1 of `(Y−1) BC`.

Valid AD Mirror pair:
The phase-preserving AD counterpart is:

```markdown
AD (Y−1)t/Y n
```

The two coordinates are:

```markdown
A(AD (Y−1)t) = Y − 5/4
A(AD Y n) = Y − 3/4
```

Therefore the internal pair width is:

```markdown
(Y − 3/4) − (Y − 5/4) = 1/2
```

and the pair-center is:

```markdown
((Y − 5/4) + (Y − 3/4)) ÷ 2 = Y − 1
```

That center is Jan 1 of `AD Y`.

Self-mirror center check:
For a self-mirrored `t/n` pair, the BC center and AD center bracket Jan 1, AD 1 exactly:

```markdown
BC pair-center = −Y + 1
AD pair-center = Y − 1
((-Y + 1) + (Y − 1)) ÷ 2 = 0
```

`A = 0` is the start of Jan 1, AD 1.

Component span proof:
The component spans are equal:

```markdown
A(AD (Y−1)t) − A(Yt BC)
= (Y − 5/4) − (−Y + 3/4)
= 2Y − 2
```

```markdown
A(AD Y n) − A((Y−1)n BC)
= (Y − 3/4) − (−Y + 5/4)
= 2Y − 2
```

Conquest example, `Y = 1407`:

```markdown
1407t/1406n BC → AD 1406t/1407n
```

Pair centers:

```markdown
1407t/1406n BC center = Jan 1, 1406 BC
AD 1406t/1407n center = Jan 1, AD 1407
```

Self-mirror span:

```markdown
1407 + 1406 − 1 = 2812
1406 + 1407 − 1 = 2812
```

Single-date contrast:

```markdown
1407t BC → AD 1407t
1407 + 1407 − 1 = 2813

1406n BC → AD 1406n
1406 + 1406 − 1 = 2811
```

The paired value sits between the two single-date values:

```markdown
2813 + 2811 = 5624
5624 ÷ 2 = 2812
```

This average explains the paired state, but it does not replace the component-wise civil cross-axis calculations.

Invalid same-order AD display:
If the AD side is written as same-order `AD (Y−1)n/Yt`, its coordinates are:

```markdown
A(AD (Y−1)n) = Y − 7/4
A(AD Yt) = Y − 1/4
```

The AD-side internal width is:

```markdown
(Y − 1/4) − (Y − 7/4) = 3/2
```

Therefore it is a `1.5`-year AD-side pair, not the required `.5`-year Mirror pair.

The component spans also fail to match:

```markdown
A(AD (Y−1)n) − A(Yt BC)
= (Y − 7/4) − (−Y + 3/4)
= 2Y − 5/2
```

```markdown
A(AD Yt) − A((Y−1)n BC)
= (Y − 1/4) − (−Y + 5/4)
= 2Y − 3/2
```

For `Y = 1407`, this gives:

```markdown
2811.5
2812.5
```

Thus the same-order AD display is not a valid exact phase-resolved Mirror display.

July-centered contrast:
A same-year `n/t` pair is a different state. Its center is July 1, not Jan 1:

```markdown
A(Yn BC) = −Y + 1/4
A(Yt BC) = −Y + 3/4
((−Y + 1/4) + (−Y + 3/4)) ÷ 2 = −Y + 1/2
```

That center is July 1 of year `Y BC`. Therefore a same-year `n/t` pair does not place the Mirror on the Jan-1 hinge. It must not replace the January-centered `t/n` pair used for Creation / Conquest paired Mirror work.

File_09 `5520` application:
The Conquest harmonic is not the self-mirror of the Creation pair. It is a Conquest / New Eden coordinate-completion from the Creation endpoint pair to the phase-resolved AD Conquest pair. The same Jan-1 phase mechanics still make both components exact:

```markdown
A(4115t BC) = −4115 + 3/4 = −16457/4
A(AD 1406t) = 1406 − 1/4 = 5623/4
5623/4 − (−16457/4) = 22080/4 = 5520
```

```markdown
A(4114n BC) = −4114 + 1/4 = −16455/4
A(AD 1407n) = 1407 − 3/4 = 5625/4
5625/4 − (−16455/4) = 22080/4 = 5520
```

The pair centers also check:

```markdown
4115t/4114n BC center = Jan 1, 4114 BC = −4114
AD 1406t/1407n center = Jan 1, AD 1407 = 1406
1406 − (−4114) = 5520
4114 + 1407 − 1 = 5520
```

Conclusion:
The `t/n` order is mathematically required for Jan-1-centered paired Mirror states. The same-year `n/t` order is July-centered and therefore belongs to a different modal state.

### A.4 The precise `AD 1406` node and the Rounded contrast

Active state:
precise numeric-year Mirror node.

The unsuffixed `AD 1406` source target is retained in two controlled senses:

1. as the `AD 1406t` member of the phase-resolved paired Mirror field `AD 1406t/1407n`;
2. as the precise numeric-year Mirror node of the unsuffixed `1406 BC` Conquest anchor.

The suffixed single-date form is also preserved as `1406n BC → AD 1406n = 2811`. This is a non-paired exact Mirror node and must not be used to overwrite the paired `2812` state.

Precise numeric-year Mirror check:

```markdown
1406 BC → AD 1406
1406 + 1406 − 1 = 2811
```

Rounded / Protocol 1 contrast:

```markdown
1406 BC → AD 1405
1406 + 1405 − 1 = 2810
```

Argument-control note:
The precise `AD 1406` node must not be confused with Rounded mod-5 Mirror arithmetic. The rounded comparison is retained only as a contrast state.

Audit-history note:
The old compressed-display contrast `4114 + 1406 − 1 = 5519` is retained only as an audit-history marker showing why the unsuffixed source display required expansion. It is not the active calculation after the author decision.

### A.5 Standalone polarity flip versus paired Jan-1 average

Active state:
standalone single-date polarity caution contrasted with paired `t/n` Jan-1 Mirror state.

Scope note:
This subsection prevents the paired-date proof from being misread as a denial of valid standalone exact Mirror nodes. It does not attempt to give the full standalone polarity theory. That fuller explanation belongs to a future Mirror-mechanics file.

Standalone Tishri node:

```markdown
1407t BC → AD 1407t = 2813 years
1407 + 1407 − 1 = 2813
2813 ÷ 2 = 1406.5
```

In exact phase terms, a Tishri-to-Tishri standalone Mirror has a half-span midpoint. Under the simplified Julian model from Appendix A.3, that midpoint lands on the Nisan-side polarity of the hinge field.

Standalone Nisan node:

```markdown
1406n BC → AD 1406n = 2811 years
1406 + 1406 − 1 = 2811
2811 ÷ 2 = 1405.5
```

In exact phase terms, a Nisan-to-Nisan standalone Mirror also has a half-span midpoint. Under the simplified Julian model from Appendix A.3, that midpoint lands on the Tishri-side polarity of the hinge field.

Formal coordinate note:
Using the proof-only Julian coordinates from Appendix A.3:

```markdown
A(Yt BC) = −Y + 3/4
A(AD Yt) = Y − 1/4
((−Y + 3/4) + (Y − 1/4)) ÷ 2 = 1/4
```

The value `1/4` is the Nisan / Apr 1 side of the Jan-1 hinge field.

```markdown
A((Y−1)n BC) = −Y + 5/4
A(AD (Y−1)n) = Y − 7/4
((−Y + 5/4) + (Y − 7/4)) ÷ 2 = −1/4
```

The value `−1/4` is the Tishri / Oct 1 side of the hinge field.

Paired state contrast:
The paired `t/n` state is different. The source pair and its Mirror counterpart are each internally `.5` years wide and the pair-centers bracket Jan 1, AD 1:

```markdown
Yt/(Y−1)n BC → AD (Y−1)t/Y n
BC pair-center = −Y + 1
AD pair-center = Y − 1
((-Y + 1) + (Y − 1)) ÷ 2 = 0
```

`A = 0` is the start of Jan 1, AD 1.

Therefore, the Jan-1 Mirror-axis claim in `File_09` applies to the paired `t/n` state as an average / center-state. Standalone single-date Nisan or Tishri mirrors are valid exact Mirror nodes, but they flip phase polarity at their own midpoint and must not be used to overwrite the paired `t/n` state.

Audit note:
This polarity flip is not an inconsistency error. It is a modal-state distinction between standalone exact Mirror nodes and paired phase-resolved Mirror coordinate-completion. `File_09` records the caution because the distinction affects exact day/month work, but the broader reason should be handled in a future Mirror-control file.

## Revision and archive note

This public-clean Markdown source removes only archival amendment history, pass logs, pressure-test repetition, pointer-refresh records, and obsolete replacement-workflow notes.

Detailed revision history is preserved in the `Repository_Change_Archive`.

Final pressure-test status is preserved in the file header. Detailed pressure-test records are archived rather than repeated in the public file body.

No arithmetic, anchors, modal states, node-classes, sign conventions, operators, slash-pairs, ranges, envelopes, Mirror protocols, Machine Guards, claim-status labels, theological claims, or dependency boundaries are changed.