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RIME Program Vocabulary

This companion defines the public cross-paper vocabulary used by the RIME program. Owning manuscripts remain authoritative for formal definitions. The purpose here is to prevent neighboring constructions from being collapsed by informal shorthand.

1. Naming Rules

  • Use RIME program, not trilogy, except in an immutable historical title.
  • Use Sectorized Observable Framework (SOF) on first occurrence and SOF thereafter.
  • Treat cross-paper citations as interface references, not hypothesis imports.
  • Use invariant only after declaring an equivalence relation and proving invariance under it.
  • Qualify every count, rate, depth, wall coordinate, and diagnostic by the choices on which it depends.

2. Spectral and Sector Vocabulary

Term Controlled meaning
represented averaging operator a declared operator obtained from a finite-dimensional representation and weighting policy
spectral layer a blockwise or jointly registered spectral component under declared conventions
compatible sectorization a complete marked orthogonal projector family compatible with the stated source data
collision arrangement a fixed declared family of branches together with their equality loci
collision quotient the quotient structure induced by collisions inside that fixed arrangement
Sigma_comm commutativity gate for a declared operator family
Sigma_normal normality gate; it is not implied by commutativity alone
Sigma_spec spectral admissibility domain after the preceding gates
pointwise registration a certified sample at one parameter value, not a coherent moving projector field

Do not use spectral wall for every repeated eigenvalue without identifying the field, chart, multiplicity convention, and wall policy.

3. Static SOF Vocabulary

The static operator core is

F_op = (V, {Q_i}, Y),

where V is a finite-dimensional complex Hilbert space, {Q_i} is a complete marked orthogonal sectorization, and Y = {Y_a} is a labelled observable alphabet. The labels are data and are not recoverable from an aggregate span.

Keep the linear layers distinct:

D_Q       = span{Q_i}
E_Y       = span{I, Y_a, Y_a^*}
S_{Q,Y}   = D_Q + E_Y

Keep the closure layers distinct:

A_Y^+     positive-word algebra
A_Y^*     observable star-closure
A_{Q,Y}^* sector-enriched star-closure

Closure describes eventual generated structure. It does not recover generator labels, route data, word length, or first-hit depth.

4. Accessibility Vocabulary

Operator and word branch

Term Controlled meaning
labelled block Q_i Y_a Q_j for a declared observable label a
R_1[Y] aggregate direct operator support of the labelled family Y
Route_d[Y] routed projected products with declared intermediate sectors
W_d[Y] full associative word support at word length d
D_route[Y] first-hit depth in the routed-product filtration
D_word[Y] first-hit depth in the full-word filtration

Lie/Hall branch

Term Controlled meaning
registered Lie family X independently declared Lie generators
R_1^Lie direct support of the registered Lie generators
R_2^Lie simple-commutator support under the declared convention
Hall filtration H declared formal-expression filtration
D_Lie first-hit depth in that Lie/Hall filtration

The two branches are independent unless an explicit induction or bridge rule is part of the realization. Do not use unqualified R_1, R_2, or D in cross-paper prose.

Depth states

  • exact first hit at d: witness at d plus verified non-hits below d;
  • hit observed by d: a witness exists by d, but minimality is unaudited;
  • UNREACHED_AT_CUTOFF: no hit through the declared finite cutoff;
  • infinity: requires an appropriate closure or saturation certificate.

The retired numeric sentinel 999 never denotes infinity and must not enter statistics.

5. Deformation and Wall Vocabulary

Term Controlled meaning
typed deformation chart a local parameter domain with fixed labels, carrier conventions, comparison maps, and declared continuity
fibre comparison map a typed map placing selected fibrewise data into a fixed comparison space
trajectory a declared one-parameter path in a chart
typed wall a policy-relative local change of a selected typed field under Paper IX admissibility
wall pullback restriction of a chart-level discriminant or wall package to a declared trajectory
response time a trajectory-relative measurement with declared normalization, norm, threshold, and censoring policy

Paper XI records admitted wall data using a sum type:

WallAtom = TrajectoryEvent | LocusSample

A TrajectoryEvent has an orientation, event parameter or interval, sampling rule, and sparse before/after field changes. A LocusSample records incident stratum germs and has no intrinsic before/after order unless a probe path is declared.

Keep these fields independent:

  • realization_kind: strict_sof or diagnostic_analogue;
  • record_role: wall event, locus sample, reference, boundary witness, or another declared role;
  • field_family: spectral, operator, route, word, Lie/Hall, closure, state, proxy, or another typed family.

Wall coordinates are profile-relative diagnostics unless an invariance theorem is separately proved. Multi-label curation tags are not mutually exclusive classification classes.

6. Compilation and Reporting Vocabulary

Term Controlled meaning
Capability Manifest declares which typed capabilities and conventions a source provides
Typed SOF IR records validated typed objects, findings, dependencies, and evidence status
Report Profile declares which supported claims a compiler requests and how they are gated
capability-sound compilation every affirmative emitted claim is supported by the typed IR within its declared scope
Registry capability-aware evidence architecture, not the compiler theorem and not an automatic compiler input
.sofreport one realization-relative report under Paper XII protocol semantics
Audit Profile requested aligned comparison coordinates and their policies
.sofaudit sparse typed comparison of two explicitly aligned reports

Strict SOF and diagnostic analogue are mutually exclusive realization kinds. A diagnostic analogue does not instantiate strict-SOF theorems.

7. SOFAUDIT Comparison States

State Meaning
ALIGNED aligned and equal, or within the declared comparison tolerance
MISMATCH aligned but unequal, or outside the declared comparison tolerance
NOT_DECLARED the source report did not declare a required field
NOT_APPLICABLE the coordinate does not apply under the declared profile
INCOMPARABLE no valid alignment or compatible convention is available
UNRESOLVED the requested comparison has not reached a supported conclusion

ALIGNED names the successful aligned-equality outcome in the current contract; it does not merely mean that an alignment map exists.

8. Action Semantics Vocabulary

Term Controlled meaning
ActionContext independently admitted actor, scope, objective, constraints, time, authority, and uncertainty input; it is not derived from an audit
PolicyProfile the sole normative rule input of the current Paper XIV contract, with closed predicate, uncertainty, exception, and precedence semantics
InterpretationRecord context- and policy-relative interpretation of retained Paper XIII coordinates; it does not rewrite the audit
CandidateActionSet bounded set of policy-supported candidate records; it is not a selected or executed plan
.sofaction Paper XIV artifact binding the immutable audit projection, admitted context and policy, interpretations, and disposition result
NoDisposition no legal disposition was formed, including failed context or policy admission
UnresolvedDisposition admitted inputs remain insufficient for a supported disposition
NoActionDisposition an explicit applicable-policy result; it is not an empty candidate set by default

The current .sofaction contract stops at bounded candidates. Selected plans, authorization receipts, post-action observations, and independently validated effects require separate downstream contracts. A missing context, policy, or capability is never promoted into NoAction.

9. Claim and Evidence Vocabulary

Use exactly four reader-facing levels:

Level Meaning
Theorem exact statement proved from declared hypotheses
Computational Certificate reproducible finite computation tied to declared inputs
Computational Observation bounded numerical pattern without theorem promotion
Research Program open problem, conjectural bridge, or proposed extension

Use conditional when a conclusion depends on an unverified registration or bridge. Use proxy when the measured field is not the claimed strict field. Use sampled or truncated when the conclusion is bounded by a grid, interval, or cutoff.

Certificate class is a separate contract axis from reader-facing evidence level. A class identifies what a machine certificate checks; it does not by itself promote the associated claim to a Theorem or establish scientific adequacy.

Certificate class Serialized value or record class Controlled scope
Protocol Conformance Certificate protocol_conformance contract, validator, artifact, and receipt closure only
Object Certificate object independently checkable source- or object-level recomputation under the declared basis
Migration/Assembly Certificate migration_assembly source identity and declared migration or faithful-assembly preservation
Comparison Audit Certificate comparison_audit alignment-relative comparison under the declared profile and basis
Policy Conformance Certificate policy_conformance_certificate admitted context/policy execution under the closed SOFAction contract
Decision Trace Certificate decision_trace_certificate deterministic interpretation and bounded disposition trace; not selection or authorization

The first four values occur in SOFRS or SOFAUDIT claim records as permitted by their owning schema. The final two are SOFAction record classes. Their scopes are not interchangeable, and none overrides the four evidence levels above.

10. Deprecated or Restricted Shorthand

Avoid the following as active cross-paper vocabulary:

Avoid Use instead
observable invariant without a theorem profile-relative observable coordinate or diagnostic
accessibility determines behavior the declared carrier records or constrains the selected behavior
universal Sigma_access a named typed discriminant or declared wall package
unqualified R_1, R_2, D carrier-qualified support or depth notation
graph path as route witness graph diagnostic unless a projected-product certificate exists
word support as commutator support W_d[Y] or R_2^Lie, whichever was computed
capability becomes present along a chart typed field witness or reachability state becomes present
NOT_RECORDED as a result state record-field presence marker only
999 UNREACHED_AT_CUTOFF with an explicit cutoff
Type I--IV as universal wall/accessibility classes named mechanism such as commutator cancellation or image--kernel incidence
ADE as universal wall taxonomy ADE candidate local model after a declared eligibility gate

11. Numerical and Release Discipline

Public numerical values belong to versioned result records and passing validators. Public release identity belongs to Zenodo records, accepted release manifests, and the root Public Release table. Vocabulary documents must not become parallel numerical or release ledgers.