GRM Base-t treatment of the Hodge conjecture  

 the GRM sequence TBLIND→ANS→FB∥RB→C★→U→CUT★→FNA★→carrier/grain/scale courts→Ρ★→repair DAG→liftback→replay, with target vocabulary stripped before the reverse build.

TOC — TSCT/GRM Base-t Hodge Conjecture Solution

1. Endpoint Definition
   1.1 Required endpoint: algebraic source object Z on X.
   1.2 Required readout: cl(Z) = alpha.
   1.3 Endpoint is an equivalence class of valid generators, not one privileged Z.
   1.4 Remove proof status, theorem vocabulary, historical technique.

2. Base-t Back-Formation
   2.1 Ask what must immediately precede the endpoint.
   2.2 Reduce the dependency spine to: GENERATE -> TRANSPORT -> CLOSE -> alpha.
   2.3 Reject every intermediate object not necessary to this spine.
   2.4 Complexity is unresolved dependency debt, not number of constructions.

3. Fundamental Triad
   3.1 GENERATE: produce source-native algebraic structure.
   3.2 TRANSPORT: preserve its invariant contribution into X.
   3.3 CLOSE: globally compose transported contributions.
   3.4 alpha is readout, not ontology.
   3.5 Dyadic “cycle versus Hodge class” formulation is rejected.

4. Source Ontology
   4.1 Algebraic generators.
   4.2 Source ownership.
   4.3 Algebraic operations.
   4.4 Generator ancestry.
   4.5 No representation may write source semantics.

5. Terminal Representation
   5.1 Rational cohomology carrier.
   5.2 Hodge-type readout.
   5.3 Identify alpha's demanded fingerprint.
   5.4 Separate recognition from generation.

6. TSCT Representation Ablation
   6.1 Swap/remove/remap equivalent representations.
   6.2 Freeze source and demanded consequence.
   6.3 Eliminate coordinate, decomposition and carrier artifacts.
   6.4 Retain rho = structural survivor.
   6.5 Construct minimal source-target skeleton SKEL. TSCT explicitly defines representation ablation and minimal dependency extraction.

7. GRM Forward Build
   7.1 Existing algebraic generators -> transport -> global readout.
   7.2 Determine which portion of alpha is already generated.
   7.3 Remove reconstructible generated structure.
   7.4 Preserve only unresolved rho.

8. GRM Reverse Build
   8.1 Start from endpoint obligations.
   8.2 Reverse CLOSE.
   8.3 Reverse TRANSPORT.
   8.4 Reverse GENERATE.
   8.5 Do not assume predecessor existence.

9. Earliest Common Carrier C*
   9.1 Join forward-generated and reverse-required structures.
   9.2 Freeze invariant fingerprint.
   9.3 Remove target leakage.

10. Fundamental Noninvertibility FNA*
    10.1 Locate earliest failed primitive dependency.
    10.2 Classify only as GENERATE, TRANSPORT or CLOSE.
    10.3 Preserve parallel failures when incomparable.
    10.4 Do not permit later machinery to mask earlier failure. GRM defines FNA as the earliest noninvertible dependency stratum and forces carrier/factorization retesting.

11. GENERATE Court
    11.1 Can algebraic primitives carrying the required fingerprint be constructed?
    11.2 Reject “choose a cycle.”
    11.3 Reject existence without constructor.
    11.4 Failure emits generation residue.

12. TRANSPORT Court
    12.1 Domain/codomain.
    12.2 Rational structure conservation.
    12.3 Hodge fingerprint conservation.
    12.4 Source-owner conservation.
    12.5 Explicit loss ledger.
    12.6 Reject hidden transport.

13. CLOSE Court
    13.1 Local compatibility.
    13.2 Pairwise overlap.
    13.3 Triple and higher interactions.
    13.4 Global closure.
    13.5 Enforce LOCAL_CLOSURE != GLOBAL_CLOSURE.

14. TSCT Operator Generation
    14.1 Generate operators only from live FNA pressure.
    14.2 Keep incomparable operator families.
    14.3 Audit operator origin.
    14.4 Reject operators dependent on unknown Z. TSCT's operator-origin machinery requires executable domain/codomain, ancestry and representation independence.

15. Technique Layer
    15.1 Degeneration.
    15.2 Blowup.
    15.3 Gysin.
    15.4 Correspondence.
    15.5 Specialization.
    15.6 Localization.
    15.7 Singular/stratified carriers.
    15.8 These are implementations, never Base-t primitives.

16. Smoothness Firewall
    16.1 Smooth X may be input/output.
    16.2 Internal mechanism may be singular or stratified.
    16.3 Reject smoothing that deletes obstruction fingerprints.
    16.4 Symmetry cannot be assumed where fracture carries information.

17. Structural Progress
    17.1 Maintain unresolved dependency graph D.
    17.2 Progress iff a noninvertible dependency cut disappears.
    17.3 No earlier closed cut may reopen.
    17.4 Administrative motion is not progress.

18. Bottom Court
    18.1 GENERATOR_LIMITED.
    18.2 TRANSPORT_LIMITED.
    18.3 CLOSURE_LIMITED.
    18.4 CARRIER_LIMITED.
    18.5 OPERATOR_LIMITED.
    18.6 Bottom classification must generate the next capability, not merely label failure. TSCT treats bottoms as method/carrier/operator/grain-relative survivors rather than automatic primitives.

19. Recursive Execution
    19.1 rho -> FNA*.
    19.2 FNA* -> missing capability.
    19.3 Missing capability -> operator family.
    19.4 Operator -> reduced dependency debt.
    19.5 Re-run from first dirty dependency.

20. Final Reconstruction
    20.1 GENERATE succeeds.
    20.2 TRANSPORT conserves the source fingerprint.
    20.3 CLOSE eliminates all higher gluing residue.
    20.4 Global source object Z emerges.
    20.5 Readout returns alpha.

21. Compact Solution Spine
    Endpoint-first: alpha <- CLOSE <- TRANSPORT <- GENERATE.
    Execution-forward: GENERATE -> TRANSPORT -> CLOSE -> alpha.