# Alpha v25 constructive breakthrough-layer closure receipt

The immutable parent is the independently original-kernel-checked 2,008-row
Alpha-v24 edition. Stable remains unchanged at 432 checked theorems.

The additive layer contains **29 complete signed-cofactor-family and
alternating-fold theorems**, **19 exact Taylor/formal-derivative/one-step-Hensel
theorems**, and **24 non-coprime CRT compatibility and gcd/LCM lattice
theorems**. These **72 genuine new proofs** have **210 direct dependencies**;
the resulting edition has **2,080 checked-use entries**, **1,648 Alpha-only
entries**, **6,633 direct proof edges**, and **53 dependency layers**.

The self-contained exact artifact is
`research/arithmetic-library/artifacts/alpha-v25-breakthrough-layer-proof-bundle-v1.json`.
Its dependency cone contains **301 actual theorem bodies**, **29 maximal
endpoints**, and **one unenrolled synthetic conjunction**: **302 original
kernel checks**, **820 actual proof dependencies**, **16,947 structural proof
nodes**, and **1,041,166 bytes**. SHA-256:
`d4532076049be869e4e397d0fcee81b668bd3fd5c7d9173028bb1bdb80b9793a`.

The exact primary signed-minor/fold root is
`signed_matrix_cofactor_family_and_fold_exists`, artifact node **257**,
statement SHA-256
`1f013b934c7540f73e135257094d612345f43f3163b5ee7280dbe97f4f142d2a`.
The full arbitrary determinant/rank/lattice milestone T13 remains **open**.

The exact one-step Hensel root is `beta_horner_hensel_lift_exists`, artifact
node **276**, statement SHA-256
`9cfc4633ea27c492b0deb35a56fe44b25b8dbf50d56fb27f29285f74b6c58a8b`.
The unrestricted canonical prime-power Hensel milestone G095 remains **open**.

The exact arbitrary positive non-coprime canonical merge root is
`crt_merge_compatible_prefix_canonical_exists_unique`, artifact node **288**,
statement SHA-256
`9e3d68192e707b5953b2fd3c9e4716e9fe90317f63be49734bbed00e3492b927`.
The pairwise-compatible dominating-last canonical root is artifact node
**300**. The unrestricted pairwise-compatible finite CRT milestone G011
remains **open**.

The unchanged original kernel independently accepted all **302 ordinary proof
nodes**, and the separately compiled Lean verifier independently returned
`ACCEPT ... nodes=302 root=301` for the exact same artifact.

No historical artifact, Stable entry, proof premise, signature, kernel rule,
or checked-use authority is replaced by a summary, definition alias, executable
example, cryptographic hash, or synthetic packaging root.