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The Proofs
Companion to Similes of Symmetry
The formal foundations — definitions, theorems, and constructions — that underpin the witness-structure framework. A self-contained mathematical work.
Structure
The dependency graph of the thirty-one formal anchors. Each node is a definition or construction; each edge, a logical dependency. Hover to trace lineage.
The general reader loses nothing by setting The Proofs aside; the argument is complete without notation. The mathematically curious can follow witness claims into the corresponding formal anchors, or a round trip between the two. The implementer can read The Proofs as a self-contained specification.
Parts
Foundations
Commitment sets, provenance, witness typing, schemas, epistemic status, coherence
- A1Commitment SetsBinding claims to accountable identities
- A2Provenance and Witness TypingWitnessed assertions and witness classes
- A3Schemas and SatisfactionSignatures, models, and the conditions for validity
- A4Epistemic StatusWhat a system knows about what it knows
- A5The Coherence RequirementWhy local truth must compose into global consistency
- A6Sense BoundariesWhere one domain of meaning ends and another begins
Equipment
Group actions, isomorphisms, adjunctions, witnessed sameness, vocabulary operators
Coherence
Covers, sheaves, local theories, logic selection, univalence
Construction
Predicate invention, conservative extension, proposal vs. certification, search, cost
Specification
Context graphs, identity maintenance, predicate packages, query semantics, versioning
Demonstrations
Worked examples: refusal, sense gluing, predicate acceptance, scoped equivalence, n-ary events