Anchor Registry

The anchors constitute the book's mathematical spine. Later chapters depend on these definitions. The public dependency graph is generated from proofs/content/dependency-graph.json and validated for all 32 primary anchors, all six subanchors, missing endpoints, and cycles. This registry states the same direct dependencies in reader-facing form. It is not the research lineage graph or Bulla's operational architecture.

Status key: formal — a mathematical definition, written statement or construction; the label does not certify proof or implementation. preformal — a requirement awaiting a specified model. engineering — a proposed operational discipline. Appendix K.8 identifies the machine-checked fragment; each result states its own hypotheses and remaining obligations.

Summary Table

ID	Name	Chapter	Status	Dependencies	Core Claim
A1	Commitment Set	Ch. 1	formal	—	Assertions extend a commitment set monotonically while preserving consistency
A2	Provenance Judgement	Ch. 2	formal	A1	Claims carry typed evidence: $(p, \pi)$ not bare $p$
A2b	Witnessed Assertion	Ch. 2	formal	A2	Assertions carry their own verification instructions
A2c	Witness Classes	Ch. 2	formal	A2b	Witnesses typed by verification regime: decidable, probabilistic, attested
A3	Schema as Signature	Ch. 3	formal	—	A schema is a signature $\Sigma = (T, P, I)$; adding a predicate is a language change
A3b	Model & Satisfaction	Ch. 3	formal	A3	Model-theoretic semantics; conservativity concerns consequences in the old language
A4	Epistemic Status	Ch. 4	formal	A3b	Derivability, polarity and absence policy are distinct parts of an epistemic judgement
A5	Coherence Requirement	Ch. 5	preformal	A1–A4	Local extensions must agree on overlaps and preserve invariants
A6	Sense Boundary	Interlude I	preformal	A5	Context-indexed equivalence $\sim_U$; boundaries create equivalence classes
A7	Group Action & Invariant	Ch. 6	formal	A1, A3	An invariant preserves its value under the specified group action
A8	Isomorphism & Witness	Ch. 7	formal	A7	Isomorphism requires inverse maps in the specified category
A9	Adjunction	Ch. 8	formal	A8	An adjunction gives a natural hom-set correspondence with unit and counit laws
A10	Witnessed Sameness	Ch. 9	formal	A2b, A2c, A6, A8, A9	Scoped equivalence records its maps, property footprint and supporting evidence
A11	Vocabulary Operator	Interlude II	formal	A3, A3b, A10	Vocabulary changes expressible distinctions; stabilization requires the declared preservation conditions
A12	Cover & Restriction	Ch. 10	formal	A4, A5, A10	Context is a restriction structure; truth is indexed by view
A12b	Context Site Structure	Ch. 10	formal	A12	A chosen context category and topology form a site when their axioms hold
A13	Sheaf Condition	Ch. 11	formal	A12, A12b	For a sheaf, exact matching on a cover yields a unique amalgamation
A14	Fibration	Ch. 12	formal	A12, A13	A fibration organizes reindexing; descent requires additional structure
A15	Logic Selection	Ch. 13	formal	A4, A12	Different views may operate under different logics; merging requires reconciliation
A16	Transport Discipline	Ch. 14	engineering	A10, A13	Scoped substitution requires the property mapping and evidence specified by its transport contract
A17	Predicate Invention	Ch. 15	formal	A3, A5, A11, A13, A16	Signature extension introducing $q$ under grounding, compatibility and invariant obligations; A13 governs its exact-gluing case
A17b	Conservative Extension	Ch. 16	formal	A1, A3b, A15, A17	Conservativity preserves old-language consequences; query compatibility is a separate obligation
A18	Invariant Set	Ch. 16	formal	A1, A16, A17b	$I = I_{\text{hard}} \cup I_{\text{soft}}$; hard invariants reject, soft constraints penalize
A19	Proposal Operator	Ch. 17	formal	A17, A18	Statistical pattern matching produces hypotheses, not certified truths
A19b	Certification Contract	Ch. 17	formal	A2c, A19	Proposed certification distinguishes success, demonstrated failure and an inconclusive check
A20	Predicate Search Space	Ch. 18	formal	A11, A13, A17–A19	Inventing predicates is searching a constrained hypothesis space
A21	Coherence Cost Model	Ch. 19	formal	A13, A20	Declares verification expenditures and budgets; refinement alone gives no cost ordering
A22	Context-Graph Substrate	Ch. 20	formal	A2c, A13, A17b, A21	Substrate stores locality, witnesses, constraints, and restriction maps
A23	Identity Maintenance	Ch. 21	formal	A10, A22	Evidence supports scoped identifications and their maintenance
A24	Predicate Package	Ch. 22	formal	A17, A17b, A21, A22	A predicate ships with signature, tests, invariants, provenance, scope
A25	Query Semantics	Ch. 23	formal	A19b, A24	Queries are contracts over locality, invariants, and acceptable witnesses
A26	Versioning Rules	Ch. 24	formal	A17b, A21, A24, A25	Versioned compatibility and bounded correction follow actual dependent uses; recorded correction does not complete remedy
A27	Refusal Obligation	Ch. 25	formal	A1, A18, A25	An established inconsistent constraint set can be explained with a checked derivation; an empty query need not be inconsistent
A28	Sense Gluing	Ch. 26	formal	A6, A13, A24	Compatible sense assignments glue in the specified function sheaf; not every disambiguation is such a gluing
A29	Predicate Acceptance	Ch. 27	formal	A17, A24, A26	A proposed admission contract requires scoped tests, invariants and version obligations
A30	Scoped Equivalence	Ch. 28	formal	A10, A12, A23	Equivalence is context-indexed; transport valid only within scope
A31	N-ary Event Object	Ch. 29	formal	A22, A26	Unkeyed role-pair projection can lose event grouping; keyed binary representations can preserve it
A32	The Third Mode	Ch. 30	formal	A10, A12, A12b, A13, A17, A17b, A21, A30	States four design requirements; Appendix I specifies ten operations and their compliance obligations, including correction across reuse

Dependencies and Reading Routes

The graph records the formal dependencies of the constructions as presented. It lets a reader trace a claim back to the definitions and hypotheses it uses. It does not require every receiving operation to invent a predicate, perform exact gluing or implement the whole Third Mode design.

For receiving and reusing evidence, begin with the Part V dossier, then consult Appendix I for the relevant operations. Commitment and witness typing identify what is asserted and how it is checked; A10 and A16 govern scoped substitution; A25 asks what a query requires; A26 follows changes in the grounds consumed. Refusal, unfinished checking and independently supported conclusions remain different outcomes. A fixed vocabulary may suffice for this work. Exact gluing enters when the proposed use depends on the exact local-to-global guarantee and its hypotheses have been established.

For extending the vocabulary, Part IV’s admission problem develops the additional admission problem: proposing a predicate, establishing its grounding, preserving the required old-language consequences and invariants, and accounting for the search and checking work. A24 packages those grounds; A29 states the acceptance obligations. A32 collects the fuller design requirements, and Appendix I supplies the ten-operation manuscript contract. That route adds obligations to reuse; it does not retroactively make every earlier act of reuse a predicate-invention problem.

These are routes through the explanation, not alternative dependency graphs or claims of implementation completeness. A reader assessing a formal result must still inspect its declared prerequisites. A reader using a particular contract must still establish every condition that contract requires.

Normative Correspondence

The 32 anchors constitute the formal apparatus. The following table relates the four formulations of the Codex to relevant formal objects, where supplied.

Equation	Normative Claim	Anchors	What They Formalize
Truth needs witnesses	Claims require evidentiary support adequate to the use made of them	A1–A14	Commitment sets, provenance judgments, witness classes, schemas, epistemic status, the coherence requirement, sense boundaries, group invariants, isomorphism, adjunctions, witnessed sameness, cover structures, the sheaf condition, fibrations
Value needs work	Productive work requires resources; expenditure alone establishes no entitlement to returns	A21	Coherence cost categories, checking regimes and declared budgets; withdrawn refinement ordering
Freedom needs receipts	Power that leaves no trace dominates in darkness; receipts make power legible	A17–A20, A22–A29	Predicate invention, conservative extension, invariant sets, proposal operators, certification contracts, predicate search, context-graph substrate, identity maintenance, predicate packages, query semantics, versioning, refusal obligation, sense gluing, predicate acceptance
Humanity needs mercy	Not formalized	—	No general mercy rule is derived here

These associations identify relevant formal objects, not a deduction of the four formulations or an ordering among them. A21 models declared coherence costs; it does not establish the trilogy's economic or constitutional conclusions. No formal anchor here derives a general rule of mercy. The absence of one records this companion's scope, not an impossibility theorem.

Witness Claim Index

Volume I states five Witness Claims (WC-08-01 through WC-08-05, all in Ch. 8, Similes of Symmetry). Their formal pointers identify related models, where supplied. The table resolves those references without assigning a formal proof to the institutional argument.

WC	Property	Anchor(s)	Related formal object
WC-08-01	composition	A21, A24	Coherence cost model; predicate package
WC-08-02	recourse	A23, A10	Identity maintenance; witnessed sameness
WC-08-03	binding	A1, A2, A10	Commitment set; provenance judgement; witnessed sameness
WC-08-04	verification-cost	A21	Coherence cost model
WC-08-05	temporal-jurisdiction	—	No formal anchor assigned

WC-08-01 makes the effect of portability depend on practicable alternatives and continuing institutional work. WC-08-04 separates technical verification cost from access, interpretation, correction and governance costs. Neither states a universal sequence of concentration and dispersal or makes rent measurable from verification cost alone.

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The chapter anchors supply the statements and citations. proofs/content/dependency-graph.json supplies the declared dependency edges; Appendix K.8 supplies the verification boundary.