renky / system / algorithms / omniring. Axiom: a self-contained finite-field skeleton plus eight ring/semiring structures, heat (tropical) degenerations, homology, and a closed computational loop. No third-party dependencies.

finite-field

tropical

cohomology

f-splitting

p-adic

class-group

verified

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Author

ky678

Version

0.1.0

License

Apache-2.0

Last updated

8 days ago

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#renky

MoonBit module ky678/renky — layout:

renky/
└─ system/
   └─ algorithms/
      └─ omniring/        ← the axiom book (公理書): sources, tests, proofs, docs
         ├─ kernel/ select/            A01–A07   proof-enabled (moon prove, Why3 + Z3)
         ├─ arith/ linalg/ ff/ poly/   A08–A34   finite-field skeleton + linear algebra
         ├─ ideal/                     A35–A43   live ideal state (即時理想狀態)
         ├─ heat/ tropical/            A44–A51   Maslov dequantization → (min,+) semiring
         ├─ graded/ semigroup/         A52–A62   graded rings, affine semigroup rings
         ├─ padic/ smooth/             A63–A71   p-adic integers, ring of smooth germs
         ├─ homology/ cohom/           A72–A78   homology + cohomology rings
         ├─ fsplit/                    A79–A81   perfect F-split rings
         ├─ classgroup/                A82–A86   ideal class group correspondence ring
         ├─ loop/                      A87–A89   the closed computational chain (閉環)
         ├─ cmd/report/                          ledger printer (main package)
         └─ docs/{AXIOMS,THEOREMS,ALGORITHMS}.md

Package paths are ky678/renky/system/algorithms/omniring/<pkg>, e.g.

import { "ky678/renky/system/algorithms/omniring/loop" }

fn main {
  println(@loop.run_all(2).to_string())   // closed = true
}

#Verification ledger

layer	command	result
machine-checked proofs	moon prove	2 of 2 packages proved, 9 goals proved
executable laws	moon test	122 passed, 0 failed
build	moon check	0 errors
algorithms	docs/ALGORITHMS.md	A01–A89 (89 > 18), no third-party dependencies

See system/algorithms/omniring/README.md for the full axiom book (命案對帳表, 套件地圖, 閉環鏈條, 義務自證的兩層), and system/algorithms/omniring/docs/ for 公理/定義/算式 (AXIOMS.md), 定理帳本 (THEOREMS.md) and 演算法登記冊 (ALGORITHMS.md).

#Reproduce

cd renky
moon check && moon test && moon prove
moon run system/algorithms/omniring/cmd/report

License: Apache-2.0.

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