The Proofs
Companion to Similes of Symmetry
The trilogy's formal spine: thirty-two anchors that turn witnessed claims, scoped equivalence, gluing obligations, predicate invention, and coherence cost into one inspectable architecture.
Read the canonical introduction →
32 primary anchors·38 named identifiers·6 parts·10 appendices·3 machine-checked·29 prose
Formal Dependency Graph
Thirty-two primary chapters and six named subanchors. Each edge is a logical prerequisite, not an intellectual influence or runtime dependency. Expand the subanchors for the complete 38-identifier registry; hover to trace ancestry and descendants.
Jurisdiction
The formal graph covers
Commitments, witnessed claims, scoped equivalence, restriction, gluing, obstruction, predicate invention, and the formal cost model.
Additional operational layers
Capture, occurrence coverage, independent persistence, authority, grounding, reliance, challenge, and remedy require mechanisms and evidence outside this DAG.
Volume I does not require notation. The Proofs exists for the reader who wants the machinery itself: where witness claims cash out formally, how the anchor dependencies fit together, and what it would mean for a system to reach the Third Mode rather than merely gesture toward it.
Reading Modes
Witness Claim Atlas
Volume I states four witness claims explicitly, all in Ch. 8 Similes of Symmetry. Each can be read as a bridge: historical argument on one side, formal burden on the other.
| Claim | Anchor(s) | Formal burden |
|---|---|---|
| WC-08-01 | A21, A24 | Composition becomes a priced formal obligation: the system must account for the cost of global coherence and specify the package that may travel across contexts. |
| WC-08-02 | A23, A10 | Recourse requires identities that survive transport and equivalences that remain witnessed and scoped rather than merely asserted. |
| WC-08-03 | A1, A2, A10 | Binding means more than attaching a name. Claims must extend a commitment set, carry typed provenance, and specify what kind of sameness they are actually licensed to assert. |
| WC-08-04 | A21 | Stakes become formal only when the system can expose the real cost of composition rather than bury it inside silent failure or political surcharge. |
Read horizontally for the Volume I bridge. Read vertically for the formal burdens that culminate in A32, where proposal, witnessed equivalence, gluing, and coherence accounting become one discipline.
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, third-mode capstone
From Anchors To Research
A12 + A13 + A16
Covers, gluing, and disciplined transport provide the formal local-to-global layer used by Tarski Coherence and SCPI. This layer diagnoses modeled compatibility; it does not certify execution safety.
A1 + A2 + A10 + A23
Commitments, typed witnessing, scoped sameness, and identity maintenance motivate the authority and non-equivocation questions in Compositional Accountability. Persistence and remedy remain additional obligations.
A22 + A23 + A25 + A26
Context graphs, identity, query contracts, and versioning inform Bridge, Seam, and the Glyph/Bulla receipt architecture. The implementation adds coverage, independent retention, typed reliance, and recourse gates.
Historical application record
The coherence-fee and interpretability tracks applied these anchors more broadly. Their falsifications do not delete the anchors; they narrow what those applications may claim. Read the decision dossiers →
Appendices
The appendices sit beside the anchor route rather than inside it. Use them for registries, terminology, interface notes, and background references.
After The Proofs
If you want the historical argument that motivates the anchors, return to Volume I. If you want the living technical program these anchors now support, continue to Research. If you want the capstone itself, end on A32: The Third Mode.