File: File_49
Title: Prime-Quadruplet Cycle-Alignment Axiom and Test Protocol — Repository Summary and External-Source Pointer
Status: Revised; summary / external-source pointer; Finalization author-invoked
Publication-cleanup status: Public-clean Markdown source; archival amendment history routed to Repository_Change_Archive.
Pressure-test status: Current; publication-clean verification complete for the repository-side summary / external-source pointer; external raw source not reverified in this pass.
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: Methodological; Statistical; Prime
Traditions: MT; SP; LXX
Canonical source: Markdown (repository-side summary); full raw form hosted externally — see §5
Primary anchors: none introduced (target dates are MT/SP/LXX chronology outputs controlled elsewhere)
Related files: File_00; File_32; File_48; File_50-series; File_51a; Restart Capsule v11.15; State Vocabulary Register v1.17; 490d Repository Style Guide v2.5; Project Procedures v3.2
Major operators: prime-quadruplet rails `B = Q − 11`, `M = B + 30`, `−B`, `−M`; decadal admission gate (±2); mod-30 step lattice; uniform shift-null; hit-counting score
Major modal states: protocol-lock state; P2 naturalization (−6) state; P1 no-naturalization state; regular vs cumulative target state; LXX(P1) split-polarity state; baseline cycle-set C_BASE lock
Revision basis: 490d Repository Style Guide v2.5; Restart Capsule v11.15; State Vocabulary Register v1.17; Project Procedures v3.2; File_49 summary-and-source-pointer source; File_48 statistical-candor controls; 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_49 — Prime-Quadruplet Cycle-Alignment Axiom and Test Protocol (Repository Summary and External-Source Pointer)

## 0. File-function

This file is the repository-side summary of File_49 and a pointer to its full raw form. The full File_49 — axioms, prime tables, prime-quadruplet start lists (Pn), chronology-derived target lists, the 10x scaling-experiment report, and the companion polarity-comparison Python script — is held externally as the source of record (§5), not carried in the repository, by author decision.

It lets a reader or AI system identify what File_49 governs, recover the reusable protocol locks without the full apparatus, read the protocol's own epistemic constraints, and follow the pointer for full detail. It does not regenerate, re-verify, or revise the external content: where this summary and the raw article differ, the raw article is authoritative for its own data and the controlling files in §4 are authoritative for shared prime-architecture states.

### 0.1 Claim-status control

Style Guide §2B labels as used here:

| Label | Function here |
|---|---|
| Methodological datum | The locks, rails, gates, and null model defining the protocol — specification, not chronology. |
| Statistical result | Z-scores and family rankings reported by the external article — reported outputs of a defined test, not proof. |
| Structural inference | The article's two-regime ("two-octave") and handoff reading. |
| Theological note | The article's punishment-number and order/complement readings — meaning-context, not arithmetic burden. |
| Audit note | Items routed to the raw article or a controlling file for verification. |

Primary-burden rule: prime-aligned anchoring is a provisional organizing heuristic (per the protocol's §0.1), not an established chronological anchor. No statistical result, structural inference, or theological note in File_49 carries a chronological claim on its own.

## 1. Summary of the raw protocol

File_49 fixes the test conditions — rails, targets, cycles, polarity, null model — so prime-quadruplet cycle-alignment runs do not drift. The reusable core is the locks below.

### 1.1 Protocol axioms (locks)

| Lock | Content |
|---|---|
| A1 Calendar | Civil BC/AD, no year 0; `BC + AD − 1 = Total` across the boundary; any astronomical year-0 use is a separate named experiment family. |
| A2 Rail base | From each quadruplet-start prime `Q`: `B = Q − 11`, `M = B + 30`. Any other base (e.g. `Q − 5`) is a new family and must be renamed. |
| A3 Step lattice | Null shifts act on one discrete lattice: `STEP = 30`; shifts only `r ↦ r + k·30`. |
| A4 Null distribution | Uniform shift over the fundamental period: `k` uniform on `[0, K)`, `s = k·STEP`; `K = LCM` of the per-cycle shift periods. |
| A5 Cycle lock | Baseline claims use `C_BASE = [2300, 2520, 3430]` only; any other cycle-set is non-baseline and must be renamed and reported separately. |

### 1.2 Rails, targets, and the decadal admission gate

Rails are generated per `Q` from the A2 base in fixed configurations (`no_mod30`, `pos_mod30`, `neg_mod30`, `both_mod30`, and cross variants). The prime table is admissible only on declared columns; `Minus Interim` is excluded as noise.

Targets are integer lists from chronology tables for six constructions (MT, SP, LXX × regular and cumulative), governed by the Naturalization-First Decadal Admission Gate:

- P2 lanes (MT/SP): naturalize first, `Y_nat = Y − 6`, before any admission.
- P1 lane (LXX): no naturalization, `Y_nat = Y`.
- Admission is a gate, not rounding: regular placements admit a decade only within `[Y_nat − 2, Y_nat + 2]`; cumulative placements are a 7-year band expanded by ±2 to an 11-year window, admitting every decade inside.

Forced anchors always unioned in: 1446 BC (Exodus), 1406 BC (Conquest), 1870 (decadal representative for the 1876 BC entry into Egypt), Enoch's Ascension. LXX(P1) uses split polarity (Adam→Terah negative; Abraham→Moses and later positive); other lanes are positive-polarity unless defined otherwise.

### 1.3 Scoring and significance

Observed score = hit count: for cycles `C`, rails `R`, targets `T`, the triples where `(t − r) ≡ 0 (mod c)`. Significance is a Monte-Carlo Z under the A4 shift-null, optionally cross-checked by an analytical mean/variance from the same residue structure. A run is a new (renamed) experiment family if the step lattice, rail base, rail generators, null shift domain, target-derivation rules, or cycle list change.

## 2. The 10x scaling experiment (reported in the same article)

The source page also carries an experiment report (draft, February 2026) on whether the alignment persists when cycle periods are ×10. Carried here as statistical results and structural inferences, not verified or proof-bearing:

| Reported finding | Article's stated result |
|---|---|
| Dominant 10x signal | Ezekiel cycle 39000 (= 390 × 100): peak Z ≈ +4.84 at P29, sustaining Z > 3.5 through P50 (both_mod30). |
| Scale "throne swap" | TRIO strongest at 1x and weakening at 10x; Ezekiel weak at 1x and strongest at 10x — opposite responses to scale. |
| P16 handoff | P6–P16 read as a TRIO regime, P16–P30 as an Ezekiel regime, meeting near P16. |
| Polarity reversal | `neg_mod30` dominant at 1x; `pos_mod30` dominant at 10x. |
| Target-list robustness | Family ranking stable across three MT-derived target lists (65, 72, 76 entries). |

The article frames the Ezekiel result as independent of the TRIO reference frame, with a two-octave structural reading and a theological reading (390 and 430; the `390 = 3 × 130` order/complement motif) — structural inference and theological note under §0.1.

## 3. Epistemic status and permitted claims

Restated from the protocol's own §0.1. File_49 is not proof of any causal or historical relationship between prime-quadruplet structure and biblical chronology. The bounded claim: under the locked axioms, multiple independent target constructions have repeatedly produced nontrivial positive Z-scores on the baseline cycle-set, suggesting the alignment may exceed naive intuition.

- Provisional anchor policy: prime-aligned anchoring may serve as a tentative organizing heuristic until contradicted by stronger counter-evidence or by failures under the same locked protocol.
- Non-finality: absence of detected faults establishes only that the protocol has not yet produced a contradiction in the tested space — not truth.
- What counts as contradiction: sustained null-like or negative results under the same axioms across comparable target families, or a protocol flaw that inflates significance (leakage, improper null, phase bias, target-selection bias).

The article's §12 caveats hold by reference: interpretive scaling/grouping choices; the 10x multiplier is one of several; target-set uncertainty; randomized-target, alternative-scaling, and replication tests would strengthen the conclusions.

## 4. Cross-file relationships and dependency boundaries

- File_32 controls the prime-architecture states this protocol depends on: the prime-quadruplet scaffold, the `B`/`M`/`−B`/`−M` rail system, positive/negative polarity date outputs, Mod-30 / Mod-210 corridor logic, and the Formation Wobble. The File_49 rails are the File_32-controlled coordinate system, not a new operator.
- File_48 is the sibling cumulative-prime-harmonic file and nearest statistical control; its candor cluster (reproduce-or-remove; floors as floors; one null per section; no proof-promotion) governs how File_49's Z-scores are reported. Route statistical-verification questions there and to the raw article.
- File_50-series continues the prime branch (mod-30, polarity, bilateral-symmetry).
- File_51a controls the Rounded Scaffold (mod-5); adjacent but distinct — do not collapse the prime work into it.
- File_00 carries the canonical File_49 publication reference in its source-history link table.

Dependency note: target dates are MT/SP/LXX chronology outputs controlled in the chronology files; File_49 consumes them. The decadal admission gate and naturalization shifts are File_49-local conventions and must be cited as such if reused.

## 5. Pointer to the full raw article

Full raw File_49 — axioms, prime tables, Pn lists, target lists, the 10x experiment report, and the companion script — is held at:

https://490d.com/file_49-prime-quadruplet-cycle-alignment-axiom-and-test-protocol-ai-reference/

Source of record for all detail not reproduced here. Per the repository link-normalization plan, this conformed file points to the current publication URL; update the link only if the page is divided or relocated, without altering protocol content.

## Audit notes

- Verification scope: this summary does not re-run or re-verify the article's Z-scores, family rankings, or tier figures; they are the article's reported statistical results. Verification, if needed, runs against the raw article and the File_48 candor controls.
- Narrative vs script discrepancy (raw article): the report prose and its companion script do not fully agree on some run parameters and labels (e.g. the Monte-Carlo sample count; whether "TRIO" denotes the 1x baseline `[2300, 2520, 3430]` or the script's 10x cycle pair). Recorded as an audit note; it belongs to the external source and to any future revision of the script.

## 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`.

The external raw article pointer in §5 is retained as source-control content. This summary does not re-run or re-verify the external article's statistical outputs.

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.