490d C275 — provenance of the 529 placement premises

24 September 2026. Continuation through C274. Completed bounded provenance audit.

Finding

The three placement premises have explicit support in the supplied Mirror construction. Their documentary roles differ from their roles in C274's algebra:

• The comprehensive handoff supplies the shared MT/LXX translation 5290 and then displays the MT closing join after the additional Shem translation 598.
• It supplies cumulative SP translation 4715 and then displays the SP/MT global reflection.
• The bilateral report proves that the MT placement is uniquely recovered if the closing join is required, with the week length and 600−598 residual held.

These passages establish a documented, internally coherent construction. They do not make the original placement and its algebraic consequences separate independent determinations.

A useful reduction is now explicit: with the common MT/LXX shift held, the MT closing join is equivalent to placing the LXX OFF opening at the existing global Mirror origin. No additional placement constraint is obtained by counting both descriptions.

The older 3K+7K chain adds an identified SP Noah intermediate to the selected 5290 span. Its text calls that span already established and retains the 6 BC target. It supports the source-qualified partition, while leaving the choice of that target in place.

1. Scope, source roles and notation

C275 follows the proposal in C274: trace premises A/B/C to exact passages in the supplied original Mirror/529 documents and immediate references. Source coordinates, the global Mirror, physical phase convention and translation increment 598 remain fixed. No parameter is fitted and no event register is enlarged.

Thirteen existing inputs are frozen. The documentary audit uses nineteen passage records, P01–P19. A separate five-passage set, S01–S05, supports Dean's corrected LXX observation. Those supplemental records are excluded from the A/B/C assessment.

The exact passage ledger includes source filename, section, line range, complete excerpt and SHA-256 identity. References such as [P08] below resolve to that ledger. “Source” here means a supplied project document or chronology table; the audit is not a new textual-critical verification of ancient manuscripts.

Use K=529 and E=25/23 in this report. The older axis report sometimes calls the expansion factor K; its quoted text is preserved unchanged, with that older symbol understood as E here.

Let m, l and s denote the MT ON, LXX OFF and cumulative SP OFF Flood translations. Their Shem translations are each Flood translation plus 598. The three C274 conditions are:

C274's result is retained: all three give m=l=5290 and s=4715; each single omission leaves one free parameter. C275 does not rerun that omission campaign.

2. What the underlying tables control

The three fields each span seven elapsed years. Corresponding MT ON and LXX OFF source boundaries differ by six years. Corresponding MT ON and SP OFF boundaries differ by 580.

These are chronology inputs. They do not alone specify how far each field must be translated.

File_18's MT restored Flood row also contains the compressed note “5290 → Christ, Key of 23” [P01]. That is a relevant prior association. The note does not itself specify a complete departure/landing phase pair or fully define its operator; those details are supplied by the expanded Mirror handoff. It should neither be ignored nor promoted into a standalone derivation of all three translations.

3. Premise A: MT closing join

The comprehensive handoff §8 explicitly instructs advancement of the middle MT ON and LXX OFF weeks by 5290. Its table gives MT opening 7t/6n BC and closing AD 1t/2n [P08].

Section 9 then uses source displacement 600 and translation increment 598. MT's Shem field is advanced by 5888, reflected, and displayed from AD 1t/2n to AD 8t/9n. The two intervals therefore share AD 1t/2n, centered on January AD 2 [P09].

The documentary chain is:

source fields → declared 5290 translation and +598 increment → displayed closing join.

The bilateral report supplies the reverse conditional argument. For F=[a,a+w] and residual r, the reflected partner is [r−a−w,r−a]. It explicitly introduces the condition that they “meet end-to-start,” then obtains

With w=7 and r=2, this gives a=−6 and junction x=1 [P10]. The requirement that the intervals meet is essential. The week length and residual alone give the relation between the intervals; they do not require that specific placement.

Thus A is both a displayed consequence of the supplied translation and a condition sufficient to recover it. These two valid directions are not two independent witnesses.

The source-qualified 3K+7K support

The axis report §16 routes to its S11 branch and preserves the chain

Its labels are MT cumulative ON Flood opening, SP regular G3 companion Noah birth, and the retained 6 BC Christ anchor [P15–P18]. It must not be recast as an LXX cumulative source or an LXX personal companion.

The branch explicitly introduces this as a division of the established 5290-year comparison. It also records the earlier 5K+5K partition of the same outer span [P17, P19]. The named intermediate makes the 3K+7K division source-qualified. It does not independently choose the original endpoint at 6 BC.

The inspected branch is the retained, previously hash-verified copy with upload suffix “(1).” The axis bibliography names a “(2)” upload. Identification rests on the matching title, date, explicit chain and source roles; byte identity with the uninspected “(2)” copy is not asserted.

This is positive support with a stated dependency, not a finding that A is unsupported.

4. Premise B: the common MT/LXX translation

The clearest support is the same §8 instruction to advance both middle weeks by 5290 [P08]. It declares one operation applied to the two selected source fields.

The underlying six-year displacement explains the resulting six-year separation:

for corresponding endpoints. Setting l=m preserves six. The source displacement does not itself force equal translations when separate translations are allowed.

The 5290 value also has a source-controlled axis role. The LXX OFF opening has radius 5290 from the fixed Mirror origin, and E carries it to native ON radius 5750 [P07]. The later axis report retains 5290=10K as a Flood-related marker while leaving its broader domain assignment open [P14].

That supplies a coherent reason to investigate the number. A source radius, a translation duration and a specific event landing are nonetheless different roles. The presence of 5290 as a radius does not, without the chosen action, require that both source fields advance by it.

Equivalent origin-centered description

Define residuals

Here R_D=0 means the LXX OFF opening −5290 lands at the existing global Mirror origin. Exact arithmetic gives

Consequently, with B held,

Equivalently, A puts the MT opening at x=−6. These descriptions expose the same anchor condition. They do not add a new axis or an independent constraint.

The global origin remains January AD 1; the local Flood/reflected-Shem junction remains x=1, January AD 2. The equivalence does not identify those two centers.

5. Premise C: cumulative SP reflected against MT

The comprehensive handoff §14.1 explicitly lists SP OFF Flood translation 4715 and Shem translation 5313 [P11]. Section 14.2 then tabulates the translated intervals and states the exact SP/MT global reflection identity [P12].

The SP source interval [−4716,−4709] becomes [s−4716,s−4709]. The Mirror of translated MT is [5289−m,5296−m]. Equating corresponding ordered endpoints gives

Both endpoint equations are the same constraint. Once m=5290 is held, C uniquely gives s=4715.

The source fields determine a corresponding-boundary separation of 580. The chosen translation difference is 5290−4715=575=EK, leaving a transformed separation of five. The source 580 alone does not select that five-year landing difference; it becomes five through the declared placement.

The reflection identity concerns the transformed intervals. It does not identify original MT and SP source events or calendars, a qualification the handoff states explicitly [P12].

This audit concerns cumulative SP. It does not alter C274's result that the regular SP maps come through LXX and the retained 17K correspondence. Releasing C moves cumulative SP while leaving those regular maps fixed when l stays fixed.

6. Assessment and consequence for the research

The passages establish a sourced construction and its exact consequences. Within this bounded documentary set, no separate argument was found deriving all three placement requirements from the raw chronology coordinates alone.

This is not a claim that such support is absent everywhere, that the construction has no explanatory value, or that every C274 free-parameter state is historically admissible. It also does not decide Dean's providential interpretation. It clarifies which claims belong to the same dependency chain.

Document presentation order is not reconstructed discovery history. Saying that §8 supplies a translation before §9 displays a consequence describes the written argument.

The remaining question is narrower: does an independently documented source 598 relation require the assignment of 598 as the difference between Flood and Shem translation parameters? C275 held that assignment fixed. A source duration of 598 and a transformation-parameter difference of 598 need an explicit connecting argument; equal numbers alone do not supply it.

7. Supplemental LXX correction — recorded separately

Dean's corrected comparison is fully retained in the accompanying supplemental note and evidence:

• LXX Creation 5494 BC, +8464 → AD2970 base; difference from reflected Conquest AD1406 base is 1564=68×23, expanding to 1700.
• LXX Jared 4534 BC, +8464 → AD3930 base; difference from reflected Exodus AD1446 base is 2484=108×23, expanding to 2700.
• LXX Creation→Jared is 960; MT is 460. Offsets are 1380 at Creation and 880 at Jared. The comparison-gap difference is 960−40=920, expanding to 1000.

The full t/n pairs preserve the existing no-year-zero convention. The old AD3746/2300 claim is superseded for this observation. These comparisons are supplemental awareness and are not used as evidence for A, B or C or as a new research direction.

8. Evidence and integrity

72 targeted checks passed, covering thirteen frozen inputs, predecessor binding, exact passages, referenced evidence identifiers, elementary affine restatements and the supplemental arithmetic. Five generated outputs replayed byte identically. Documentary classification remains an authored assessment, not a machine-proved historical result.

The evidence packet includes the exact passage ledger in Markdown and JSON, authored premise assessment, algebraic restatements, supplemental results and note, executable verifier, review notes, scope, source and artifact manifests, replay record, report, checkpoint and certificate.

All thirteen original inputs remain unchanged. File_18 remains at SHA-256 68301ab760bfbe2e874aedc5c8d943ced7a6219d34bc2859332a70713f9630d5; File_09 remains at 45851004c5864229ebf6a896f9099819a08d8926715d3e97e4bc3985c4a3876e. The C127 graph retains 208 nodes and 382 duration edges. The C265 certificate is unchanged.

C275 chains to C274 certificate SHA-256 23ab41af374a05812d024b1be7ef9b141086b11bbf9ca456b2255efd8b5968f6. Review is author provenance and mathematical consistency review; no new independent-agent review is claimed.

No historical campaign, new endpoint scan, primer study, parameter fitting, chart recalibration, canonical amendment or upstream Gear transport was undertaken. Capture now, canonize later.

Best next bounded step

C276: audit the transfer from the retained 598/600 source rectangle to the assigned translation increment. Keep its existing source nodes and phase labels fixed. Distinguish a 598 span between selected source indices from a 598 difference between the two translation parameters, and determine whether the source paths fix that difference without reinstating the desired local join. Use the existing 17K correspondence; add no source events or fitted landing.

High is sufficient. C276 is proposed, not executed.