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Research-Stack/0-Core-Formalism
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allaun ac700c6460 feat(lean): add byte-level gap kernel for cleanMerge_preservesGap 
A boolean is a bit. Eight bins = eight bits = one byte.

mergeCheck_all_256: closed Bool term verified by native_decide over
all 256×256 byte pairs. Zero assumptions, zero free variables, zero sorry.

The kernel proves: for any two bytes where gap(s) ∧ gap(e) ∧ disjoint ∧
crossGap all hold, gap(s OR e) also holds. This is the complete
computational proof of the spectral gap merge property at the bit level.

The remaining sorry is the Q16_16→byte bridge: converting SpectralSignature
bins to/from Nat bytes and showing the predicates correspond. This is
standard list-level reasoning over 8 elements (unzip, map, filter, all).

Build: 3314 jobs, 0 errors (Compiler surface)
2026-06-22 13:48:39 -05:00
..
core fix(adversarial-review): resolve 35 critical coding bugs across 8 subsystems 2026-05-31 23:38:03 -05:00
lean feat(lean): add byte-level gap kernel for cleanMerge_preservesGap 2026-06-22 13:48:39 -05:00
otom fix(lean): complete projectionOrdering proof in GeometricCompressionWorkspace 2026-06-18 15:06:50 -05:00
receipts docs: add bio optical witness living light equations 2026-05-09 20:53:51 -05:00
rust/ftdi_gimbal initial: sovereign research stack (consolidated, weightless, and lfs-optimized) 2026-05-04 18:11:36 -05:00
scripts chore: commit accumulated working tree changes 2026-05-30 00:10:02 -05:00
README.md docs: refresh READMEs, AGENTS.md, and project maps for recent Lean surface 2026-06-20 20:34:09 -05:00

README.md

0-Core-Formalism

Purpose: Formal foundations for the entire Research Stack — Lean modules, bind primitive, Triumvirate consensus, core source.

No external dependencies. All other layers depend on this.

Contents (Target)

Source Destination
0-Core-Formalism/lean/Semantics/ 0-Core-Formalism/lean/Semantics/
core/ 0-Core-Formalism/core/

Concepts

  • bind — State → (State → Action) → State
  • TriumvirateClock — ternary consensus (ADD/PAUSE/SUBTRACT)
  • Builder/Judge/Warden — roles mapped to hardware registers
  • OTOM — Ordered Transformation & Orchestration Model

Build

cd "0-Core-Formalism/lean/Semantics"
lake build

Current baseline: lake build reports 3314 jobs, 0 errors.

Recent Additions

Recently added/blessed Lean/Semantics modules:

  • Semantics.SDPVerify
  • Semantics.GoormaghtighCert
  • Semantics.HachimojiManifoldAxiom / Semantics.HachimojiSubstitution
  • Semantics.GeneticBraidBridge
  • Semantics.SieveLemmas
  • Semantics.InteractionGraphSidon

Fixed-Point Constraint

Core compute paths use Q16_16 fixed-point arithmetic. Float is not allowed in compute paths; ofFloat is only permitted at the external boundary (JSON parsing, sensor input) and must be immediately bracketed to Q16_16.

Dependency Graph / Mathblob Insight

The dependency graph and Gremlin mathblob work serve as documentation and insight tooling for surfacing module relationships and formal-structure context within the Semantics surface.