FILE_49 — Prime-Quadruplet Cycle-Alignment Axiom and Test Protocol (AI reference)

Part 1, THE 490d UNIFIED CHRONOLOGY: KNOWLEDGE GRAPH REPOSITORY

For Part 2: Files_31-46 about Pi, Primes and Berossus +50 are found in a separate document due to length constraints.)

Part-3-Files_47-forward_machine-reference-document-for-490d-unified-chronology-repository/

File_49: Comprehensive Technical Reference for AI Systems

0) Scope and intent

This file defines the axioms (locks) and test protocol used in the prime-quadruplet cycle-alignment experiments: rail construction, target construction (including decadal admission), scoring, null model, polarity handling, and invariants that must not drift between runs.

This is a protocol specification. Full prime tables, full prime-quad lists (Pn), full chronology tables, and run logs are stored in separate files.

Add a short epistemic-status lock near the top (Scope/Intent), so an AI reader cannot misread File_49 as a proof document.

0.1 Epistemic status and permitted claims

This file is not presented as proof of any causal or historical relationship between prime-quad structure and biblical chronology. It is a protocol specification for repeatable tests, written to prevent drift in rails, targets, cycles, polarity, and null models.

The working claim is limited to this:

  • Under the locked axioms in this file, multiple independent target constructions (regular and cumulative; MT/SP/LXX variants) have repeatedly produced nontrivial positive Z-scores on the baseline cycle-set (C_BASE), suggesting the observed alignment may exceed naive intuition.

Accordingly:

  1. Provisional anchor policy: prime-aligned anchoring may be used as a tentative organizing heuristic for chronology exploration until contradicted by stronger counter-evidence or by failures under the same locked protocol.
  2. Non-finality: absence of detected faults in the author’s testing does not establish truth; it only establishes that the protocol has not yet produced a contradiction within the tested space.
  3. What would count as contradiction: a sustained pattern of null-like results (or negative results) under the same axioms across comparable target families, or identification of a protocol flaw that inflates significance (e.g., leakage, improper null, phase bias, or target-selection bias).
  4. A5 (Cycle lock): Baseline claims use C_BASE=[2300,2520,3430] only; any other cycle-set is non-baseline and must be explicitly renamed and reported separately.

This section constrains interpretation: File_49 defines how to test, not what must be concluded.

1) Core axioms (locks)

A1. Calendar convention lock (civil BC/AD; no year 0)

All civil placements use BC/AD with no year 0:

  • 1 BC is immediately followed by AD 1.
  • Any span that crosses the boundary uses the identity
    BC + AD − 1 = Total.

If an “astronomical year-0” convention is ever used, it is a separate named experiment family (see §7).

A2. Prime-node station lock (P2 rail base)

Rails are constructed from each prime-quadruplet start Q using the locked base:

  • B = Q − 11
  • M = B + 30

This is a P2-calibrated rail coordinate system. Any alternative base (e.g., Q−5) is a new experiment family and must be renamed.

A3. Step-lattice lock (discrete translation group)

All null shifts act on the same discrete lattice as the observed evaluation:

  • STEP = 30 (decadal lattice)

Shifts are only of the form r ↦ r + k·30, never arbitrary offsets.

A4. Null-distribution lock (uniform shift over the fundamental period)

For fixed rails R, targets T, cycles C, define score S(s) after a shift s.

Null model:

  • choose k uniformly from {0,1,…,K−1}
  • set s = k·STEP
  • evaluate S(s)

where K is the LCM of the per-cycle shift periods:

  • period(c) = c / gcd(c, STEP)
  • K = LCM(period(c) for c ∈ C)

Changing STEP, C, or the shift domain changes the probability space → new experiment.

2) Rails

2.1 Pn lists (quadruplet starts)

A “Pn” list is the first n quadruplet-start primes from the standard quadruplet-start sequence used in the scripts (A007530-style starts). This file does not restate those lists; it only locks how rails are generated from them.

2.2 Rail construction (allowed configs)

For each quadruplet start Q:

  • B = Q − 11
  • M = B + 30

Allowed rail configs per Q:

ConfigRails per Q
no_mod30[B, −B]
pos_mod30[B, M, −B]
neg_mod30[B, −B, −M]
both_mod30[B, M, −B, −M]
cross_pos[B, −M]
cross_neg[M, −B]
cross_both[B, −M, M, −B]

No other rail generators are permitted unless introduced under a new config name and new experiment family.

3) Prime table dependency (canonical table; admissible columns only)

The prime table is a reference artifact that may contain auxiliary or diagnostic columns. This protocol may only depend on columns declared admissible below. Any other column is protocol-invalid (cannot be used in computations, validations, or argumentation for this protocol).

3.1 Admissible columns (protocol-valid)

  • Index
  • Prime
  • −5 (Regular)
  • −11 (Gap)
  • Cumulative Sum
  • Gap Difference
  • Interim Cum Sum
  • Decadal Interim (if used as a precomputed decade representative)

3.2 Explicitly excluded (protocol-invalid / noise)

  • Minus Interim (evaluated and rejected as noise; not used)

If the external prime table contains excluded columns, they may remain present as diagnostics, but File_49 prohibits using them.

4) Targets (chronology-derived integer lists)

Targets are finite integer lists (typically decadal) derived from chronology tables under locked rules. This file defines legality and the decadal admission algorithm.

4.1 Six tested chronologies (three traditions × regular/cumulative)

Each tradition is tested in regular and cumulative (lifespan) form:

  1. MT Regular
  2. MT Cumulative (lifespan)
  3. SP Regular
  4. SP Cumulative (lifespan)
  5. LXX Regular
  6. LXX Cumulative (lifespan)

4.2 Prime-favorable Creation anchors (six)

The “prime-favorable” Creation anchors are the Creation dates (as decadal targets) that best aligned in the tests for each of the six chronologies. These are treated as empirical outcomes (not theological claims).

  • MT Regular: 4110
  • SP Regular: 4410
  • LXX Regular: 5490
  • MT Cumulative: 14000
  • SP Cumulative: 13910
  • LXX Cumulative: 14890

Important correction (SP cumulative 13910):
13910 is not shorthand for “(+60+130).” It is the SP cumulative (lifespan) creation anchor in the prime-favorable lane (see variant matrix §4.5). The “+130” issue belongs to regular chronology (R130/R0), not to the definition of SP cumulative.

4.3 Target legality conditions

A target list T is legal for this protocol only if:

  1. It is versioned and reproducible (hard-coded list or generated by a documented rule).
  2. It is integer valued (signed integers allowed where polarity is defined).
  3. If decadalized, the admission rule is explicitly the ±2 gate (and cumulative 7-year band gate), not generic rounding (see §4.4).
  4. Any base correction (e.g., P2 naturalization −6) is explicitly recorded (see §4.4).
  5. Exclusion lock: “cumulative dates embedded with begetting ages” (hybrids that encode begetting-age structure inside cumulative coordinates) are out of scope and illegal for TARGETS here. If explored, they must be defined as a new experiment family.

4.4 Decadal admission algorithm (the ±2 gate)

Decadalization is not rounding; it is an admission test.

4.4.1 Station-dependent normalization step

  • P2-base targets: apply naturalization first:
    Y_nat = Y − 6
  • P1-base targets: no naturalization step:
    Y_nat = Y

This normalization applies before any decadal admission for both regular and cumulative targets.

4.4.2 Regular chronology: ±2 admission window (Gear 2)

For each relevant node year Y (typically the birth year in regular chronology):

  1. compute Y_nat (station rule above)
  2. define window W = [Y_nat − 2, Y_nat + 2]
  3. include any decade(s) (years ending in 0) that fall inside W
  4. if none fall in W, the node contributes no decadal target
  5. if two decades fall in W (rare), include both

4.4.3 Cumulative chronology: 7-year band plus ±2 (Gear 1 / lifespan)

Cumulative placement is treated as a 7-year band per node:

  • conceptual band: B7 = [Y0, Y0 + 6]

Admission rule:

  1. apply station normalization to the band (P2 shifts the whole band by −6)
  2. expand by ±2 to form acceptance region:
    B_accept = [B7_start − 2, B7_end + 2]
  3. include every decade that falls inside B_accept
  4. if two decades fall inside, include both (per policy)

4.5 Variant matrix (tested settings; no interpretation)

Toggles (notation fixed; no “+” notation in labels):

  • T60 / T0: Terah lifespan 205 (T60) vs 145 (T0)
  • C460 / C0: 2nd Cainan cumulative lifespan reinsertion (+460) included vs excluded (cumulative only)
  • R130 / R0: 2nd Cainan regular begetting-age insertion (+130) included vs excluded (regular only)
  • A70 / A130: Terah→Abraham begetting age 70 vs 130 (regular only)

Prime-favorable configurations (as tested):

TrackTraditionStationCainan cumulativeCainan regularTerah lifespanTerah→Abraham
CumulativeLXXP1C460n/aT60n/a
CumulativeSPP2C460n/aT60n/a
CumulativeMTP2C460 and C0 both favorablen/aT60n/a
RegularLXXP1n/aR130n/aA70
RegularSPP2n/aR0n/aA70
RegularMTP2n/aR0n/aA70

Untested / explicitly not covered in this protocol record:

  • MT regular with R130 (“MT +130”) was not tested.

5) Forced anchors and duplicate policy

5.1 Always-included anchors (forced into targets)

After decadal admission, targets are unioned with forced anchors that must be present in every run (even if not admitted by the ±2 gate):

  • 1446 BC (Exodus)
  • 1406 BC (Conquest)

Additional privileged anchors used in regular chronology testing:

  • Entry into Egypt (“the nexus”): represented decadal as 1870 (historical rationale: 1876 BC)
    Policy lock: store 1870 as the forced decadal representative to avoid ambiguity.
  • Enoch’s Ascension: included as a privileged narrative anchor.
    The civil year is taken from the corresponding regular chronology table(s) and then treated as forced-in (decadal representative if your table encodes it as such).

(“Creation” and “Flood” are automatically present via the Adam / Arphaxad nodes in the tables and need no special casing.)

5.2 Duplicate suppression (dates-only targets) with a narrow exception

Default: a target list is a set of dates; do not include the same signed date twice.

Exception: a duplicate date may be retained only if it represents different nodes (different patriarchs/events) and node-identity is explicitly preserved in that run mode. This is rare.

Operationally (recommended):

  • internally represent candidates as (date, node_id)
  • export standard targets as dates-only, deduped by date
  • if a special run intends node multiplicity, it must be named as a separate experiment mode

Explicit corner case lock: if a date appears in both regular and cumulative for the same node/event (e.g., Moses 1526 BC), it is deduplicated in combined runs.

6) Polarity rules (signed targets)

6.1 LXX(P1) split polarity (Adam→Terah negative)

In the LXX(P1) construction:

  • Adam → Terah segment uses negative polarity (negative integers).
  • Abraham → Moses and later uses positive polarity.

All other traditions and tracks in this protocol are treated as positive-polarity targets unless explicitly defined otherwise.

6.2 Structural signed band in the 14000 / 90+900 module

Where the “14000 / 90+900” structural mapping is invoked, the target construction includes a signed band spanning −90 to +900 (using the module’s own discrete admission rule). This is treated as structural (part of the polarity design), not an accidental byproduct.

7) Scoring statistic (observed score)

Given cycles C, rails R, targets T, define:

[
S = \sum_{c\in C}\ \sum_{r\in R}\ \sum_{t\in T}\ \mathbf{1}\big[(t-r)\equiv 0\ (\mathrm{mod}\ c)\big].
]

This is the hit-counting score used in the scripts.

8) Significance procedures

8.1 Monte-Carlo Z (shift-null on the STEP lattice)

Compute S_obs = S(0). Sample many shifts s = k·30 with k uniform on [0,K) (see §1.4). From the sampled scores compute mean μ, standard deviation σ, and:

[
Z = \frac{S_{\text{obs}}-\mu}{\sigma}.
]

Multi-seed MC repeats the process across seeds and reports mean Z, SD(Z), and CI.

8.2 Analytical mean/variance (residue-count method)

An analytical mean/variance method is permitted only if computed from the same residue structure implied by (R, T, C, STEP) and checked against MC within expected tolerance. If both are reported, they are treated as separate outputs.

8.3 Cycle “family” decomposition

Cycle lists may be grouped into families (e.g., Year-type; Key-of-23; Danielic/7-fold) and tested separately under the same locked rails/targets/null.

8.4 Year-zero diagnostics are separate experiment families

Any year-zero exploration is not a reinterpretation of §1.1. It must be implemented only by explicitly named configs and treated as a new experiment family.

9) What counts as a new experiment (required renaming)

A run must be treated as a new experiment family if any of the following change:

  1. STEP lattice (e.g., 30 → other).
  2. Rail base (anything other than B = Q − 11) without a new config name.
  3. Rail generator rules (adding/removing rails per Q beyond §2.2).
  4. Null shift domain (anything other than uniform k∈[0,K) with s=k·STEP).
  5. Target derivation rules (including P2 naturalization −6, ±2 gate, cumulative 7-year band rule, forced anchors, polarity rules).
  6. Cycle list C or the policy for assembling it.
  7. Introduction of any hybrid target construction explicitly excluded in §4.3 (e.g., embedded begetting-age cumulative targets).

10) Integration notes (non-procedural)

  • File_49 is protocol-centric.
  • Prime tables, Pn lists, chronology tables, and run logs are external artifacts referenced by this protocol.

IndexPrime−5 (Regular)−11 (Gap)Cumulative SumGap DifferenceInterim Cum SumDecadal Interim
150−60660
211606909690
310196909690186180
4191186180276630906900
5821816810108666017461740
6148114761470255639029462940
7187118661860441621046264620
82081207620706486117076567650
9325132463240972621099369930
103461345634501317621901536615360
115651564656401881637802259622590
129431942694202823635703180631800
131300112996129904122626404386643860
1415641156361563056856905694656940
15157311572615720725763307290672900
161606116056160508862619809060690600
17180411803618030106656870107526107520
18189111890618900125556510126066126060
191942119416194101449661590146556146550
202101121006210001659661260167226167220
212227122266222601882263030191256191250
222530125296252902135166420219936219930
233172131716317102452263120248346248340
243484134836348302800568940288996288990
254378143776437703238267560331386331380
265134151336513303751563990379146379140
275533155326553204304767650438126438120
286298162976629704934464230497676497670
296721167206672005606462280562926562920
30694916948669480630126———
IndexPrime−5 (Regular)−11 (Gap)Cumulative SumGap DifferenceInterim Cum SumMinus Interim (**Not Used in Tests!**
150−60660
2116069096−84
310196909690186−84
4191186180276630906−534
582181681010866601746−384
614811476147025563902946696
7187118661860441621046262346
82081207620706486117076563246
9325132463240972621099366276
10346134563450131762190153667536
11565156465640188163780225969396
129431942694202823635703180615246
131300112996129904122626404386625596
1415641156361563056856905694641136
15157311572615720725763307290656526
161606116056160508862619809060670596
1718041180361803010665687010752687756
18189111890618900125556510126066106146
191942119416194101449661590146556123966
202101121006210001659661260167226143706
212227122266222601882263030191256162936
222530125296252902135166420219936181806
233172131716317102452263120248346210396
243484134836348302800568940288996236286
254378143776437703238267560331386272496
265134151336513303751563990379146319836
275533155326553204304767650438126367506
286298162976629704934464230497676426246
296721167206672005606462280562926491166
30694916948669480630126———

PRIME QUADRUPLET CYCLE ALIGNMENT WITH BIBLICAL CHRONOLOGY: Comprehensive Technical Reference for AI Systems