# Alpha v24 constructive research-layer closure receipt

The immutable parent is the independently original-kernel-checked
**1,949-theorem Alpha v23** release. Its **432 Stable theorem entries**, every
historical proof certificate, candidate source, first-order signature, and
ordinary intuitionistic arithmetic kernel remain unchanged.

The exact additive inventory comprises **17 arbitrary signed matrix-minor and
four-dimensional determinant proofs**, **15 simultaneous formal polynomial
value/derivative proofs**, and **27 finite CRT and universal-property LCM
proofs**: **59 new original theorems**, **2,008 checked-use Alpha entries**,
**1,576 Alpha-only entries**, and **6,423 checked direct dependencies**.

The actual complete proof artifact is
`research/arithmetic-library/artifacts/alpha-v24-research-layer-proof-bundle-v1.json`.
Its exact dependency cone contains **202 original theorem bodies**, **18
maximal checked theorem endpoints**, and **one unenrolled synthetic packaging
root**. The certificate has **203 independently checked proof nodes**, **502
actual proof-dependency edges**, **11,065 structural proof-body nodes**, and
**738,923 exact bytes**. Its SHA-256 is
`627e39ed29b10db48bf37d5bef8750d48009a7524c822a7c5e7c83e96a8e9cf9`.

Exactly **59 new theorem bodies** and **14 necessary historical parent bodies**
were reconstructed in bounded one-body microbatches. Exact immutable proof
bodies were retained from Alpha-v19 residual closure (**2**), Alpha-v19
frontier (**3**), Alpha v20 (**1**), Alpha v21 (**115**), Alpha v22 (**5**),
and Alpha v23 (**3**).

The exact unrestricted signed-minor root is
`beta_signed_matrix_minor_exists`, artifact node **155**, statement SHA-256
`bf6e9238c2928e4f6525a14015198b673b41022924c6da1944ab87c8df61bba1`.
The exact signed 4×4 determinant-existence root is
`signed_matrix_four_full_determinant_exists`, artifact node **158**, statement
SHA-256
`7ae77d34a56bc459140fcd9afab5bb70cf4792cdb6ebac833c448381adfff848`.
The full arbitrary-dimension determinant/rank/lattice milestone T13 remains
**open**.

The exact unique simultaneous polynomial-value/formal-derivative root is
`beta_horner_derivative_exists_unique`, artifact node **170**, statement
SHA-256
`171b5939376bfb9e9ec9469d3addd98e27584931fa7994dccb4b372c4d9a693f`.
The full prime-power simple-root Hensel milestone G095 remains **open**.

The exact arbitrary-list universal-property LCM root is
`crt_prefix_lcm_exists_unique`, artifact node **190**, statement SHA-256
`09fa610c42ac069677f4fb90f00c6e0780d2b1de843380599e725a9cf19e1175`.
The exact full positive pairwise-coprime finite-list canonical CRT root is
`crt_pairwise_coprime_prefix_canonical_exists_unique`, artifact node **201**,
statement SHA-256
`6d3913cdbd73b6a2662e31aea220a19ab75f0d1995e3fadf0c583c58d270e01f`.
The arbitrary compatible **non-coprime** finite-list CRT milestone G011
remains **open**.

The unchanged original kernel independently accepted all **203** ordinary
proof nodes. The separately compiled Lean verifier independently accepted the
identical self-contained artifact with root node **202**. Neither cryptographic
hashes, synthetic conjunctions, executable examples, nor reviewed definition
expansions are treated as substitutes for an actual constructive proof.

Stable membership, all historical first-admission labels, all frozen Alpha-v23
artifacts, and every previously closed exact milestone are unchanged.