# 490d C470–C479 reading index

25 September 2026 UTC. **All ten authorized steps and all30 individual deliverables are complete. C480 is unexecuted.**

Read the C479 synthesis and checkpoint first. Use the C479 compact restart kit as the active packet. The C470–C479 continuation archive preserves every full packet and individual deliverable. Older archives remain selective reference libraries; current source/scope decisions override stale next-step paragraphs.

The complete1150 interval census gives51 coordinate pairs and three admitted fixed-E expansions, only one with a sourced2K predecessor. The1250 census gives74 coordinate pairs/130 label pairs in seven source classes. Family translations preserve endpoint structure without ensuring sourced factors. The primary/companion and fixed-Mirror path boundaries are explicit.

| Step | Report | Checkpoint | Evidence |
|---|---|---|---|
| C470 | [490d_C470_Complete_1150_to_1250_Fixed_Pivot_Census_20260925.md](sandbox:/workspace/scratch/2cd312e78692/deliverables/490d_C470_Complete_1150_to_1250_Fixed_Pivot_Census_20260925.md) | [490d_Mirror_Checkpoint_After_C470_20260925.md](sandbox:/workspace/scratch/2cd312e78692/deliverables/490d_Mirror_Checkpoint_After_C470_20260925.md) | [490d_C470_Evidence_20260925.zip](sandbox:/workspace/scratch/2cd312e78692/deliverables/490d_C470_Evidence_20260925.zip) |
| C471 | [490d_C471_Source_Bindings_and_Inverse_Ancestry_of_1250_Outputs_20260925.md](sandbox:/workspace/scratch/2cd312e78692/deliverables/490d_C471_Source_Bindings_and_Inverse_Ancestry_of_1250_Outputs_20260925.md) | [490d_Mirror_Checkpoint_After_C471_20260925.md](sandbox:/workspace/scratch/2cd312e78692/deliverables/490d_Mirror_Checkpoint_After_C471_20260925.md) | [490d_C471_Evidence_20260925.zip](sandbox:/workspace/scratch/2cd312e78692/deliverables/490d_C471_Evidence_20260925.zip) |
| C472 | [490d_C472_Complete_1250_Role_and_Context_Grammar_20260925.md](sandbox:/workspace/scratch/2cd312e78692/deliverables/490d_C472_Complete_1250_Role_and_Context_Grammar_20260925.md) | [490d_Mirror_Checkpoint_After_C472_20260925.md](sandbox:/workspace/scratch/2cd312e78692/deliverables/490d_Mirror_Checkpoint_After_C472_20260925.md) | [490d_C472_Evidence_20260925.zip](sandbox:/workspace/scratch/2cd312e78692/deliverables/490d_C472_Evidence_20260925.zip) |
| C473 | [490d_C473_Typed_500_and_499_Correspondences_of_1250_Families_20260925.md](sandbox:/workspace/scratch/2cd312e78692/deliverables/490d_C473_Typed_500_and_499_Correspondences_of_1250_Families_20260925.md) | [490d_Mirror_Checkpoint_After_C473_20260925.md](sandbox:/workspace/scratch/2cd312e78692/deliverables/490d_Mirror_Checkpoint_After_C473_20260925.md) | [490d_C473_Evidence_20260925.zip](sandbox:/workspace/scratch/2cd312e78692/deliverables/490d_C473_Evidence_20260925.zip) |
| C474 | [490d_C474_Equal_Overall_Maps_and_Different_Source_Admission_20260925.md](sandbox:/workspace/scratch/2cd312e78692/deliverables/490d_C474_Equal_Overall_Maps_and_Different_Source_Admission_20260925.md) | [490d_Mirror_Checkpoint_After_C474_20260925.md](sandbox:/workspace/scratch/2cd312e78692/deliverables/490d_Mirror_Checkpoint_After_C474_20260925.md) | [490d_C474_Evidence_20260925.zip](sandbox:/workspace/scratch/2cd312e78692/deliverables/490d_C474_Evidence_20260925.zip) |
| C475 | [490d_C475_Four_Inherited_Noah_Ladders_and_Split_Factorizations_20260925.md](sandbox:/workspace/scratch/2cd312e78692/deliverables/490d_C475_Four_Inherited_Noah_Ladders_and_Split_Factorizations_20260925.md) | [490d_Mirror_Checkpoint_After_C475_20260925.md](sandbox:/workspace/scratch/2cd312e78692/deliverables/490d_Mirror_Checkpoint_After_C475_20260925.md) | [490d_C475_Evidence_20260925.zip](sandbox:/workspace/scratch/2cd312e78692/deliverables/490d_C475_Evidence_20260925.zip) |
| C476 | [490d_C476_Primary_and_Companion_Conditions_for_Noah_Held_Ladders_20260925.md](sandbox:/workspace/scratch/2cd312e78692/deliverables/490d_C476_Primary_and_Companion_Conditions_for_Noah_Held_Ladders_20260925.md) | [490d_Mirror_Checkpoint_After_C476_20260925.md](sandbox:/workspace/scratch/2cd312e78692/deliverables/490d_Mirror_Checkpoint_After_C476_20260925.md) | [490d_C476_Evidence_20260925.zip](sandbox:/workspace/scratch/2cd312e78692/deliverables/490d_C476_Evidence_20260925.zip) |
| C477 | [490d_C477_Fixed_Mirror_Images_of_the_Noah_Held_Family_20260925.md](sandbox:/workspace/scratch/2cd312e78692/deliverables/490d_C477_Fixed_Mirror_Images_of_the_Noah_Held_Family_20260925.md) | [490d_Mirror_Checkpoint_After_C477_20260925.md](sandbox:/workspace/scratch/2cd312e78692/deliverables/490d_Mirror_Checkpoint_After_C477_20260925.md) | [490d_C477_Evidence_20260925.zip](sandbox:/workspace/scratch/2cd312e78692/deliverables/490d_C477_Evidence_20260925.zip) |
| C478 | [490d_C478_Alternate_Arithmetic_Verification_and_Sealed_Batch_Audit_20260925.md](sandbox:/workspace/scratch/2cd312e78692/deliverables/490d_C478_Alternate_Arithmetic_Verification_and_Sealed_Batch_Audit_20260925.md) | [490d_Mirror_Checkpoint_After_C478_20260925.md](sandbox:/workspace/scratch/2cd312e78692/deliverables/490d_Mirror_Checkpoint_After_C478_20260925.md) | [490d_C478_Evidence_20260925.zip](sandbox:/workspace/scratch/2cd312e78692/deliverables/490d_C478_Evidence_20260925.zip) |
| C479 | [490d_C479_Interval_Families_Sourced_Factorizations_and_Mirror_Limits_Synthesis_20260925.md](sandbox:/workspace/scratch/2cd312e78692/deliverables/490d_C479_Interval_Families_Sourced_Factorizations_and_Mirror_Limits_Synthesis_20260925.md) | [490d_Mirror_Checkpoint_After_C479_20260925.md](sandbox:/workspace/scratch/2cd312e78692/deliverables/490d_Mirror_Checkpoint_After_C479_20260925.md) | [490d_C479_Evidence_20260925.zip](sandbox:/workspace/scratch/2cd312e78692/deliverables/490d_C479_Evidence_20260925.zip) |

## Result locator

**C470 — All Sourced 1150 Intervals and Fixed-Pivot Expansion to 1250.** All 51 sourced 1150-year coordinate pairs (101 label pairs) produce 408 fixed-pivot E trials: 16 have integer outputs and three have both outputs sourced. The admitted pairs are1955/3105→1805/3055 at3680,2020/3170→1956/3206 at2756, and2148/3298→2020/3270 at3620. Only the middle case has a complete sourced2K predecessor,2148/3206 at3620.

**C471 — Source Bindings and Ancestry Gates of the Three 1250 Outputs.** All three1250 outputs have a matched-context MT Shem-death versus SP-primary/LXX-OFF Shem-birth binding, giving600+650. Their endpoint changes are−150/−50,−64/+36 and−128/−28. The first two-K ancestry fails at missing2093/3151; the third fails integrality at every fixed first pivot; only the established middle case has a sourced predecessor.

**C472 — Complete 1250 Source-Pair Inventory and Role Families.** The complete1250 inventory contains74 coordinate pairs and130 label pairs. Three disjoint matched-context families contribute24 coordinate pairs each: MT Shem-death/SP-primary-or-LXX Shem-birth; MT Flood-start/SP-primary-or-LXX Noah-birth; and MT Flood-close/SP-companion Noah-birth. Two extra MT Noah-death/SP-companion Shem-birth pairs complete the coordinate inventory; eight additional label pairs are aliases of core coordinates. All three admitted E outputs lie in the Shem family.

**C473 — Typed Translations Between the Three 1250 Families.** All24 matched1250 contexts form typed triplets: Shem-family A maps to Flood-start/Noah-primary family C by+500; SP C maps to Flood-close/Noah-companion family B by−1, so B=A+499. There are48 typed+500 maps and24 qualified−1 maps. None of the six translated admitted E comparisons has its full input/anchor source support.

**C474 — Equal Overall E-Square Maps With Different Source Admission.** The +500-translated split word and the inherited C429 Noah-held word E_3706² have the same full affine map, slope625/529 and effective pivot3706. The translated word needs absent pivots4120/3256 and absent upper intermediate3670; the inherited held word2648/3706→2556/3706→2456/3706 is fully sourced. Its input is the inherited C287 i3 17K corner.

**C475 — Four Inherited Noah Ladders and Their Split Factorizations.** Sixteen factorizations associated with the four inherited Noah-held ladders have five fully sourced profiles: the four original held words and the established Shem split partner of3706. Only that split partner uses the active eight-pivot menu. The3491 partner has sourced endpoints and intermediate but lacks pivot3405; the3708 partner has sourced pivots but lacks both intermediate endpoints.

**C476 — Primary and Companion Source Conditions for Noah-Held Ladders.** Across24 Noah contexts per SP rail, primary-held1058→1150→1250 paths have24 sourced middles/finals and exactly four sourced inputs, hence four complete paths. Companion-held paths have24 sourced finals but no sourced middle; five inputs are sourced, including the inherited3899/2841 Noah-role alias in addition to four matched Flood-close inputs.

**C477 — Fixed Mirror Images of the Source-Qualified Noah-Held Family.** The18 fixed-Mirror trials on nine Noah-held source-endpoint cases reproduce exactly the five inherited input images, including the original i3/i5 17K corners. No cumulative middle is sourced; none of the five complete input images has a sourced expanded final. Two isolated final images belong to the3899 alias case and lack pivot, input and middle.

**C478 — Alternate Arithmetic Verification and Sealed Batch Audit.** A different root-agent implementation passes98 checks, regenerating all528 regular labels/373 coordinates and48 cumulative records. Reverse interval-to-pivot enumeration, direct integer polynomial evaluation, typed family classification and Mirror comparison agree with C470–C477. The eight sealed packets and24 publications pass the integrity audit with no discrepancies.

**C479 — Complete Interval Families, Sourced Factorizations and Mirror Limits.** C470–C479 are complete. The51 sourced1150 intervals admit exactly three fixed-E expansions to1250; only one has a complete2K predecessor. The74 coordinate/130 labelled1250 pairs reduce to seven source classes dominated by three matched24-context families. Whole-map equality does not ensure sourced factors. Four primary Noah-held ladders remain complete; five companion endpoint cases lack every middle. Fixed Mirror images retain the two inherited17K corners but no cumulative E ladder in the48-record menu. C480 is unexecuted.

## Verification and provenance

All30 individual publications succeeded. The final audit verifies 360 packet payloads, 120 certificate bindings, 230 frozen source entries, ten predecessor links and ten ZIPs. The batch records 1,316 calculation checks and 290 source/authentication checks. C478’s98 different-implementation checks are included in the main total. These are verification counts, not independent historical witnesses or an independent-agent review.

C429’s four Noah-held ladders and companion endpoint cases, C434’s split-source boundary, C287’s17K corners, and C461’s five initial Mirror images remain inherited results. The current contribution is the complete interval grammar, source-family/factorization comparison, full held-family conditions and expanded-path Mirror boundary.

The C476 all-label test retains five companion source inputs, not merely the four matched Flood-close inputs:3899/2841 is the inherited MT Noah-role alias. None has a sourced held middle. C465’s mixed-cycle12→12 is still a vertex-only count; the full anchored count is48→12. C432’s E passage remains corrected to File_46 lines117–133.

The compact kit preserves C478 and C479 in full, all eight preceding reports, selective authenticated C429/C434 references, and the intact C469 baseline evidence ZIP. C479 freezes all nine predecessor data/results/certificates/decisions plus File_18, File_09, File_02, File_46, File_11, the C265 checkpoint/certificate, both declared source registers, C287 rows and the supplemental SKL observation.

Portable replay: within an extracted packet run `python3 evidence/check.py --out replay` and compare DATA.json/RESULTS.json with evidence/. Python3 standard library only. Use C478 for the different arithmetic implementation. The full archive provides every earlier calculation file. Source/graph guards remain unchanged; regular Gears remain Noah/Shem/Flood only.

## Best next bounded step

**C480, proposed and unexecuted:** Reduce the complete51-coordinate/101-label1150 interval inventory already frozen in C470 to disjoint source-role and context templates, retaining aliases separately. Use that grammar to explain the three admitted fixed-E expansions and the failed cases without adding a date, pivot, phase or operator.

The1250 output grammar is complete, while the complete1150 inventory has only been classified for its three admitted E expansions. Its finite source grammar is the remaining direct dependency for explaining the full selection pattern. C480 needs a new instruction and no such classification has been executed.