{ "schema": "physica.theorem-dag.v1", "revision": "R26", "nodes": [ { "id": "EXT-WILSON-RG", "label": "Wilson renormalization-group scale flow", "lane": "external", "status": "ESTABLISHED_EXTERNAL_RESULT", "source_id": "SRC-WILSON-RG-1971" }, { "id": "EXT-OS", "label": "Osterwalder\u2013Schrader reconstruction conditions", "lane": "external", "status": "ESTABLISHED_EXTERNAL_MATHEMATICAL_PHYSICS", "source_id": "SRC-OS-1973" }, { "id": "EXT-JSV-TRACE", "label": "Traced monoidal categories", "lane": "external", "status": "ESTABLISHED_EXTERNAL_MATHEMATICS", "source_id": "SRC-JSV-1996" }, { "id": "EXT-NOETHER", "label": "Noether symmetry/conservation theorem", "lane": "external", "status": "ESTABLISHED_EXTERNAL_THEOREM", "source_id": "SRC-NOETHER-1918" }, { "id": "EXT-GKSL", "label": "GKSL quantum dynamical semigroup generators", "lane": "external", "status": "ESTABLISHED_EXTERNAL_RESULT", "source_id": "SRC-GKS-1976" }, { "id": "EXT-PROCESS-TENSOR", "label": "Finite-dimensional operational 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"theorem_target", "status": "OPEN_THEOREM_TARGET", "statement": "", "assumptions": [], "dependencies": [ "GFTM-T01" ], "correspondence_obligation": null, "observable": null, "falsifier": "Reduced/arbitrary basis reproduces the same declared outputs", "source_refs": [] }, { "id": "GFTM-T03", "label": "Irreducible theorem/observable output", "programme": "GFTM", "lane": "physical", "kind": "target", "status": "PHYSICAL_OR_MATHEMATICAL_TARGET_OPEN", "statement": "", "assumptions": [], "dependencies": [ "GFTM-T02" ], "correspondence_obligation": null, "observable": null, "falsifier": "Output does not depend irreducibly on 72/144 structure", "source_refs": [] }, { "id": "OM-THM-01", "label": "Affine Record-Law Representation", "programme": "Observer Monad", "lane": "physical", "kind": "internal_result", "status": "MATHEMATICAL_PROOF_CLOSED_MACHINE_CHECK_PENDING", "statement": "Finite-dimensional affine positive normalized record law has POVM representation", "assumptions": [], 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applicable: source construction exactly reproduces registered law under standard baseline", "source_refs": [ "00_ATI.HM_AGENT.md:L4696-L4760" ] }, { "id": "SNAT-01", "label": "Structural Non-Absorbability Admission Theorem", "programme": "Observer Monad", "lane": "physical", "kind": "working_theorem", "status": "ADMISSION_CRITERION_A6_CIRCULAR_FOR_REPRESENTATION", "statement": "Source admission router; not an independent representation theorem because A6 assumes standard process contraction.", "assumptions": [], "dependencies": [ "OM-PTL-001-NOGO", "EXT-PROCESS-TENSOR", "EXT-COMB" ], "correspondence_obligation": null, "observable": null, "falsifier": null, "source_refs": [ "00_ATI.HM_AGENT.md:L4788-L4888" ] }, { "id": "CEM-009", "label": "Radial certified GE3 theta separator", "programme": "Observer Monad", "lane": "physical", "kind": "internal_result", "status": "CERTIFIED_INTERNAL_MATHEMATICAL_SEPARATION", "statement": "", "assumptions": [], "dependencies": [ "SNAT-01", "EXT-KS" ], "correspondence_obligation": null, "observable": null, "falsifier": "Only the declared GE1-3 vs theta statement is certified; arbitrary-copy or physics interpretation is not", "source_refs": [ "00_ATI.HM_AGENT.md:L7169-L7281" ] }, { "id": "CEM-010", "label": "Four-copy global exclusivity bound", "programme": "Observer Monad", "lane": "physical", "kind": "computational_bound", "status": "UNRESOLVED_TIME_LIMIT", "statement": "", "assumptions": [], "dependencies": [ "CEM-009" ], "correspondence_obligation": null, "observable": null, "falsifier": "Resolve by tightening bounds until GE4 threshold interval lies wholly on one side of theta-dual threshold", "source_refs": [ "00_ATI.HM_AGENT.md:L7372-L7433" ] }, { "id": "OM-PHYS-ADMISSION", "label": "Observer physical admission", "programme": "Observer Monad", "lane": "physical", "kind": "empirical_target", "status": "PHYSICAL_TARGET_NOT_ADMITTED", "statement": "", "assumptions": [], "dependencies": [ "CEM-010" ], "correspondence_obligation": "Consistent generalized theory outside admissible standard-process class", "observable": "Distinct predeclared operational prediction", "falsifier": "Absorption, inconsistency, null hardware result, or failed independent replication", "source_refs": [] }, { "id": "FQFT-D00", "label": "Metric-measure / Dirichlet analytic carrier", "programme": "FQFT", "lane": "physical", "kind": "definition", "status": "PROVISIONAL_TYPED_DEFINITION", "statement": "Specify (X,d,mu,E,D,Delta) or an equivalent analytic carrier supporting the declared field theory objects.", "assumptions": [], "dependencies": [ "EXT-FRACTAL-ANALYSIS" ], "correspondence_obligation": null, "observable": null, "falsifier": "Declared gradient/Laplacian/action objects are undefined on the chosen carrier", "source_refs": [ "SFRFULL:L1543:8f49bb7640" ] }, { "id": "OM-NOGO-02B", "label": "Full conditioned-update instrument equivalence", "programme": "Observer Monad", "lane": "physical", "kind": "theorem_target", "status": "FORMALIZATION_TARGET", "statement": "Match the candidate conditioned state-update law to a standard CP instrument, not only its POVM statistics.", "assumptions": [], "dependencies": [ "OM-NOGO-02", "OM-THM-02" ], "correspondence_obligation": null, "observable": null, "falsifier": "Post-measurement conditional states distinguish the candidate from every admissible standard instrument", "source_refs": [ "00_ATI.HM_AGENT.md:L1893-L1910" ] }, { "id": "SNAT-T01", "label": "Process representation from operational axioms without A6", "programme": "Observer Monad", "lane": "physical", "kind": "theorem_target", "status": "COUNTEREXAMPLE_BREAK_AS_TYPED", "statement": "A1-A5+A7 with the source local-CP wording do not suffice to force a positive higher-order process operator.", "assumptions": [ "finite-dimensional or finite operator-span operational domain" ], "dependencies": [ "SNAT-01", "EXT-PROCESS-TENSOR", "EXT-COMB" ], "correspondence_obligation": null, "observable": null, "falsifier": "Explicit normalized swap/block-positive counterexample W=F/d.", "source_refs": [ "00_ATI.HM_AGENT.md:L4788-L4940" ] }, { "id": "EXT-FRACTAL-ANALYSIS", "label": "Dirichlet/Laplacian analysis on fractals", "programme": "External baseline", "lane": "external", "kind": "external_result", "status": "ESTABLISHED_EXTERNAL", "statement": "Fractal analysis requires specified energy/Dirichlet-form structures to define Laplacian-type operators on important self-similar classes.", "assumptions": [], "dependencies": [], "correspondence_obligation": null, "observable": null, "falsifier": null, "source_refs": [ "SRC-KIGAMI-1993", "SRC-AKKERMANS-2013" ] }, { "id": "SNAT-T01R", "label": "Repaired higher-order CP process representation", "programme": "Observer Monad", "lane": "physical", "kind": "representation_theorem_target", "status": "MATHEMATICAL_PROOF_CLOSED_STANDARD_BASELINE_MACHINE_CHECK_PENDING", "statement": "Finite-dimensional multilinearity + higher-order complete positivity + causal normalization yield a positive causally normalized comb/process representation; closed by reduction to standard quantum-network representation results.", "assumptions": [ "A2", "A5", "A3* higher-order complete positivity", "A4 causal normalization", "A7 label encodability" ], "dependencies": [ "SNAT-T01", "EXT-PROCESS-TENSOR", "EXT-COMB" ], "correspondence_obligation": null, "observable": null, "falsifier": "counterexample satisfying higher-order CP and causal normalization without a positive normalized process operator", "source_refs": [ "00_ATI.HM_AGENT.md#115-Structural-Non-Absorbability-Theorem" ] }, { "id": "FQFT-DIM-01", "label": "Typed dimension-flow object", "programme": "FQFT", "lane": "physical", "kind": "definition_and_relation_target", "status": "PARTIALLY_CLOSED_OPEN_MODEL_CHOICE", "statement": "Carry Hausdorff, spectral, walk and topological dimensions separately; relate them only by carrier-specific theorems.", "assumptions": [], "dependencies": [ "FQFT-D00" ], "correspondence_obligation": "Declare which dimension controls measure, spectral/kinetic flow and the four-dimensional recovery limit.", "observable": "Heat-kernel/return scaling for Ds; volume scaling for DH where defined.", "falsifier": "single scalar dimension is used inconsistently across inequivalent roles", "source_refs": [] }, { "id": "FQFT-DIM-02", "label": "G5 Kesten\u2013McKay heat-kernel dimension test", "programme": "FQFT", "lane": "physical", "kind": "analytic_computational_result", "status": "CLOSED_NEGATIVE_FOR_FIXED_G5_DIMENSION_DERIVATION", "statement": "For the q=5 Kesten\u2013McKay Laplacian density on [1,9], raw Ds(t)->infinity because of the spectral gap; gap-subtracted edge Ds->3; finite connected graph IR Ds->0. The source DH*=27.6 is not derived by this standard heat-kernel dimension.", "assumptions": [ "q=5 Kesten\u2013McKay limiting density", "standard heat-trace spectral-dimension definition" ], "dependencies": [ "FQFT-DIM-01", "EXT-FRACTAL-ANALYSIS" ], "correspondence_obligation": "Provide a separate beta/fixed-point derivation for DH*=27.6 and define a scale-dependent carrier if a Ds flow to 4 is claimed.", "observable": "P(t)=Tr exp(-t Delta) and Ds(t)=-2 d ln P/d ln t", "falsifier": "fixed-G5 numerical/analytic heat trace exhibits a stable plateau at the claimed dimension under the same unmodified generator", "source_refs": [ "SFRFULL:L1543:8f49bb7640" ] }, { "id": "FQFT-SPEC-01", "label": "Three-band partition from G5 spectrum", "programme": "FQFT", "lane": "physical", "kind": "retired_hypothesis_branch", "status": "SUPERSEDED_RETIRED_BY_SPECTRAL_AUDIT", "statement": "The historical q=5 Kesten\u2013McKay three-band generation assignment is retired by the later spectral audit. It remains preserved as a historical authorial calibrated model, not an active derived generation theorem.", "assumptions": [ "q=5 Kesten\u2013McKay density" ], "dependencies": [ "FQFT-DIM-02" ], "correspondence_obligation": "Do not reactivate the KM triplet without a new non-arbitrary derivation that survives the existing spectral audit.", "observable": "band edges/centroids and perturbation sensitivity", "falsifier": "A new source-level theorem establishes a canonical robust three-band decomposition of the declared q=5 carrier and restores the branch.", "source_refs": [ "SFRFULL:L1587-L1655" ] }, { "id": "FQFT-FP-03", "label": "Fixed-point reconstruction audit", "programme": "FQFT", "lane": "physical", "kind": "reproducibility_gate", "status": "UNRESOLVED_SOURCE_DERIVATION_MISSING", "statement": "The source reports DH*=27.6\u00b10.3 and simultaneous beta_D/beta_G/zeta_net zero conditions, but the accessible corpus does not define those functions and numerical uncertainty pipeline sufficiently to independently reconstruct the reported value.", "assumptions": [ "current accessible FQFT source corpus" ], "dependencies": [ "FQFT-DIM-02" ], "correspondence_obligation": "Publish the explicit beta/zeta system, couplings, numerical root procedure and uncertainty propagation.", "observable": "independent numerical reproduction of DH* and its uncertainty", "falsifier": "the complete frozen equations already present in the accessible source reproduce the value independently", "source_refs": [ "SFRFULL:L1543:8f49bb7640" ] }, { "id": "FQFT-FP-04", "label": "Two-exponent UV fixed-point completeness", "programme": "FQFT", "lane": "physical", "kind": "current_research_requirement", "status": "OPEN_COMPLETION_REQUIREMENT", "statement": "A scalar Hausdorff fixed point alone does not determine kinetic propagation; a minimally complete geometric scaling fixed point must also specify an independent diffusion/spectral/resistance exponent.", "assumptions": [ "typed distinction DH != Ds != Dw unless proved", "scale-dependent geometric carrier" ], "dependencies": [ "FQFT-DIM-01", "FQFT-FP-03" ], "correspondence_obligation": "Derive one of zeta_R*, Dw*, or Ds* from the same carrier/fixed-point construction as DH*.", "observable": "heat-kernel/diffusion scaling and volume/resistance scaling", "falsifier": "the declared FQFT carrier proves that DH alone uniquely determines all kinetic scaling data", "source_refs": [ "SFRFULL:L1543:8f49bb7640" ] }, { "id": "FQFT-FP-05", "label": "Fixed-point pushforward theorem", "programme": "FQFT", "lane": "mathematical", "kind": "bridge_theorem", "status": "MATHEMATICAL_PROOF_CLOSED", "statement": "For differentiable h=H(s), beta_h=DH(s) beta_s. Therefore every source fixed point pushes forward to a hidden/effective fixed point provided the hidden couplings are derived by H.", "assumptions": [ "H differentiable", "hidden running has no independent term beyond pushforward" ], "dependencies": [ "FQFT-FP-03" ], "correspondence_obligation": "Derive the physical reduction map H before applying the theorem to threshold/flavor variables.", "observable": "none \u2014 mathematical bridge", "falsifier": "counterexample to the chain-rule pushforward under the stated assumptions", "source_refs": [ "SFRFULL:L1543:8f49bb7640" ] }, { "id": "FQFT-FP-06", "label": "Source-to-hidden fixed-point map obligation", "programme": "FQFT", "lane": "physical", "kind": "formalization_physics_target", "status": "OPEN_REDUCTION_MAP_REQUIRED", "statement": "Derive H:(DH,GN,zeta_net,...) -> (tau,g_Gamma,ZD/ZV,MF,...) so the hidden threshold/flavor sector is an actual consequence of source FQFT rather than an independent extension.", "assumptions": [ "source and hidden variable sets are explicitly typed" ], "dependencies": [ "FQFT-FP-05" ], "correspondence_obligation": "Construct H from a declared action/operator and verify dimensions, symmetries and RG covariance.", "observable": "threshold/matching parameters predicted from upstream FQFT data", "falsifier": "no source-consistent reduction map exists or multiple inequivalent maps fit equally without discriminators", "source_refs": [ "SFRFULL:L1543:8f49bb7640" ] }, { "id": "FQFT-SCALE-01", "label": "Universal parent scale obligation", "programme": "FQFT", "lane": "physical", "kind": "physical_scale_target", "status": "OPEN_NO_UNIVERSAL_PARENT_SCALE_DERIVED", "statement": "Seek Lambda_* such that Lambda_sigma,f=c_f Lambda_* and MF=c_F Lambda_*; the accessible source presently supplies sector-dependent Lambda_sigma but not this universal parent-scale derivation.", "assumptions": [ "a common parent scale is part of the candidate completion" ], "dependencies": [ "FQFT-FP-06" ], "correspondence_obligation": "derive Lambda_* and coefficients from the fixed-point/action sector rather than fit them by flavor sector", "observable": "absolute threshold and sector-scale relations", "falsifier": "no universal scale relation survives multi-sector matching", "source_refs": [ "SFRFULL:L1543:8f49bb7640" ] }, { "id": "FQFT-SPEC-02", "label": "Current flavor threshold/matching branch", "programme": "FQFT", "lane": "physical", "kind": "replacement_research_branch", "status": "ACTIVE_OPEN_REPLACEMENT_BRANCH", "statement": "After retirement of the intrinsic KM-band mass branch, active flavor work is organized as FQFT hidden phase -> threshold/orientation data -> Y_f(MF) boundary -> ordinary SM RG -> observables.", "assumptions": [ "historical KM band branch retired", "threshold geometry treated as candidate until dynamics derived" ], "dependencies": [ "FQFT-SPEC-01", "FQFT-FP-06" ], "correspondence_obligation": "derive threshold dynamics, matching purity and multi-sector observables without sector-by-sector refit", "observable": "charged-lepton/up/down Yukawa shapes and mixing after standard RG", "falsifier": "the branch requires independent untracked flavor textures or arbitrary threshold corrections", "source_refs": [ "SFRFULL:L1543:8f49bb7640" ] }, { "id": "FQFT-H-04", "label": "Seven-stage FQFT reduction-map factorization", "programme": "FQFT", "lane": "physical", "kind": "reduction_architecture", "status": "PARTIAL_CONDITIONAL_FACTORIZATION", "statement": "Factor the source-to-hidden map into analytic carrier, physical finite-carrier embedding, representation bridge, physical dynamics, phase/orientation, absolute-scale generation, and matching stages; only selected middle representation maps are presently mathematically closed conditionally.", "assumptions": [ "source and hidden variable sets explicitly typed", "later incidence mathematics treated as continuation work, not retroactive source content" ], "dependencies": [ "FQFT-FP-06" ], "correspondence_obligation": "derive H0,H1,H3,H5 and H6 from a declared source action/operator and verify the RG reduction equation", "observable": "upstream-predicted threshold and matching parameters", "falsifier": "full H is claimed source-derived while required stages remain assumptions", "source_refs": [ "SFRFULL:L1543:8f49bb7640" ] }, { "id": "FQFT-H-T01", "label": "Critical-exponent intertwining under reduction", "programme": "FQFT", "lane": "mathematical", "kind": "conditional_bridge_theorem", "status": "MATHEMATICAL_PROOF_CLOSED_CONDITIONAL", "statement": "If h=H(s) satisfies beta_h(H(s))=DH(s) beta_s(s), then at a source fixed point the linearizations satisfy B_h DH = DH B_s; critical directions in the image of DH inherit the corresponding reduced critical exponents.", "assumptions": [ "H differentiable", "RG reduction equation holds", "evaluation at a source fixed point" ], "dependencies": [ "FQFT-FP-05", "FQFT-H-04" ], "correspondence_obligation": "construct the physical H before using the theorem to infer hidden critical behavior", "observable": "none \u2014 conditional mathematical audit criterion", "falsifier": "a proposed physical H violates the intertwining relation under its declared beta functions", "source_refs": [ "SFRFULL:L1543:8f49bb7640" ] }, { "id": "FQFT-H-NG01", "label": "Current-corpus reduction underdetermination", "programme": "FQFT", "lane": "methodological", "kind": "derivation_no_go", "status": "CORPUS_DERIVATION_NO_GO", "statement": "Without complete source and hidden beta vectors, physical carrier typing, and boundary/normalization data, the RG reduction equations do not uniquely determine the project-specific map H from the current corpus.", "assumptions": [ "audit limited to currently accessible canonical source and continuation records" ], "dependencies": [ "FQFT-H-04" ], "correspondence_obligation": "supply the missing beta systems and selection data or declare a new axiom packet", "observable": "none \u2014 source-closure audit", "falsifier": "a frozen source artifact supplies all missing equations and boundary data and independently reconstructs a unique H", "source_refs": [ "SFRFULL:L1543:8f49bb7640" ] }, { "id": "FQFT-H-NG02", "label": "Absolute threshold scale nonclosure", "programme": "FQFT", "lane": "physical", "kind": "scale_no_go", "status": "PHYSICAL_SCALE_NONCLOSURE", "statement": "The source-reported sector-dependent Lambda_sigma and fixed-point labels do not by themselves determine one universal absolute threshold MF; an RG-invariant scale, boundary condition, symmetry-breaking law, or transmutation mechanism is required.", "assumptions": [ "candidate completion requires a common MF" ], "dependencies": [ "FQFT-SCALE-01", "FQFT-H-04" ], "correspondence_obligation": "derive Lambda_* and MF from source dynamics independently of flavor data", "observable": "absolute threshold scale and sector-scale ratios", "falsifier": "source-derived dynamics uniquely produce MF and required universal ratios without downstream calibration", "source_refs": [ "SFRFULL:L1543:8f49bb7640" ] }, { "id": "FQFT-H-NG03", "label": "Levi Gaussian / dark-nine pole non-equivalence", "programme": "FQFT", "lane": "mathematical", "kind": "internal_no_go", "status": "INTERNAL_MATHEMATICAL_NO_GO", "statement": "In the audited conditional 21-state model, the full Levi Gaussian response has R=2738/2375>1, whereas the corresponding pure positive-mass tree-mediator cone obeys R<=1; therefore the full Levi determinant cannot be identified with the isolated D9 tree-threshold coefficient matrix.", "assumptions": [ "conditional Levi carrier and internal coefficient definitions of the continuation model" ], "dependencies": [ "FQFT-H-05" ], "correspondence_obligation": "separate tree pole, loop and contact terms in any physical matching construction", "observable": "matching coefficient identities if the carrier is physically realized", "falsifier": "a corrected derivation within the same declared model removes the invariant ratio mismatch", "source_refs": [ "SFRFULL:L1543:8f49bb7640" ] }, { "id": "FQFT-H-05", "label": "Conditional 21-state incidence carrier bridge", "programme": "FQFT", "lane": "mathematical", "kind": "conditional_representation_bridge", "status": "MATHEMATICAL_BRIDGE_CLOSED_CONDITIONAL_ON_PHYSICAL_EMBEDDING", "statement": "Assuming a 21-state Levi/incidence carrier, its representation decomposition and selected V5->D9->edge intertwiners are mathematically fixed, including conditional dimensionless normalization; FQFT has not yet derived the physical embedding into that carrier.", "assumptions": [ "21-state carrier admitted", "declared S6/incidence action and inner products" ], "dependencies": [ "FQFT-H-04" ], "correspondence_obligation": "derive Phi_FQFT -> (X_F,z_M), physical kinetic metric, and mode-selection rule from the FQFT analytic carrier", "observable": "none until physical embedding and readout are supplied", "falsifier": "the conditional representation identities fail under their declared finite-carrier definitions", "source_refs": [ "SFRFULL:L1543:8f49bb7640" ] }, { "id": "FQFT-CARRIER-NG01", "label": "Global truncation / internal-fiber no-go", "programme": "FQFT", "lane": "mathematical", "kind": "projection_no_go", "status": "MATHEMATICAL_NO_GO", "statement": "A 21-dimensional global Galerkin truncation yields 21 amplitudes, not 21 fields over 4D spacetime, unless an external/internal fiber or projection structure is independently supplied.", "assumptions": [ "finite-dimensional global mode truncation", "no declared base/fiber decomposition" ], "dependencies": [ "FQFT-D00", "FQFT-H-04" ], "correspondence_obligation": "derive an explicit observable base and internal fiber/projection map", "observable": "none \u2014 projection typing result", "falsifier": "construct 21 4D fields from global coefficients without any equivalent external/internal projection structure", "source_refs": [ "SFRFULL:L1543:8f49bb7640" ] }, { "id": "FQFT-CARRIER-T01", "label": "S6 equivariant quadratic-form parameter count", "programme": "FQFT", "lane": "mathematical", "kind": "commutant_result", "status": "MATHEMATICAL_RESULT_CLOSED", "statement": "On the declared 2\u00b71 \u2295 2\u00b7V5 \u2295 D9 real 21-carrier, an S6-equivariant symmetric quadratic form retains seven real parameters; conservation of the constant mode still leaves five.", "assumptions": [ "declared real S6 representation decomposition" ], "dependencies": [ "FQFT-H-05" ], "correspondence_obligation": "do not infer physical Levi locality from symmetry alone", "observable": "none", "falsifier": "representation/commutant recount gives a different dimension under the same carrier and reality assumptions", "source_refs": [ "SFRFULL:L1543:8f49bb7640" ] }, { "id": "FQFT-CARRIER-T02", "label": "Incidence-orbit locality implies Levi stiffness", "programme": "FQFT", "lane": "mathematical", "kind": "conditional_uniqueness_theorem", "status": "MATHEMATICAL_PROOF_CLOSED_CONDITIONAL", "statement": "If a conservative positive S6-equivariant coarse Dirichlet form has support on exactly the single 30-incidence orbit between six factorization and fifteen pair nodes, then K21=\u03ba L_Levi for \u03ba>0.", "assumptions": [ "S6 transitivity", "conservativity", "positivity", "exact incidence-orbit locality" ], "dependencies": [ "FQFT-CARRIER-T01" ], "correspondence_obligation": "derive incidence-orbit locality from the physical FQFT carrier", "observable": "conditional coarse kinetic operator", "falsifier": "a second independent conservative S6-equivariant positive stiffness with the same exact support exists", "source_refs": [ "SFRFULL:L1543:8f49bb7640" ] }, { "id": "FQFT-CARRIER-T03", "label": "Master harmonic projection equality", "programme": "FQFT", "lane": "physical", "kind": "formalization_physics_target", "status": "FORMALIZATION_TARGET", "statement": "Seek C21 such that inf_{Phi:C21 Phi=q} E[Phi]=(\u03ba/2)\u03a3_{F_i~M_e}(q_Fi-q_Me)^2.", "assumptions": [ "source-level closed symmetric Dirichlet form", "declared 21-observable coarse map" ], "dependencies": [ "FQFT-CARRIER-T02" ], "correspondence_obligation": "construct C21 and prove the equality from the actual FQFT/HDFT carrier", "observable": "Levi coarse kinetic matrix if realized", "falsifier": "every source-admissible C21 generates extra couplings or fails positivity/locality", "source_refs": [ "SFRFULL:L1543:8f49bb7640" ] }, { "id": "FQFT-CARRIER-T04", "label": "21-observable Dirichlet-nerve existence theorem", "programme": "FQFT", "lane": "mathematical", "kind": "conditional_existence_theorem", "status": "MATHEMATICAL_EXISTENCE_CLOSED_CONDITIONAL", "statement": "A parent metric-measure Dirichlet space with six factorization terminals, fifteen pair terminals, thirty equivalent two-terminal conservative channels and S6 transitivity has coarse stiffness K21=\u03ba L_Levi.", "assumptions": [ "six terminal orbit", "fifteen pair terminals", "thirty two-terminal channels", "positive conservative harmonic trace", "S6 transitivity" ], "dependencies": [ "FQFT-CARRIER-T02" ], "correspondence_obligation": "show that actual FQFT supplies such a nerve rather than merely that one can be constructed", "observable": "none until physical identification", "falsifier": "counterexample satisfying all stated hypotheses but producing non-Levi coarse stiffness", "source_refs": [ "SFRFULL:L1543:8f49bb7640" ] }, { "id": "FQFT-CARRIER-P01", "label": "Actual FQFT 21-channel realization", "programme": "FQFT", "lane": "physical", "kind": "physical_projection_target", "status": "OPEN_PHYSICAL_PROJECTION", "statement": "Derive the six terminals, fifteen pair terminals, thirty channels, coarse measure and harmonic trace directly from the FQFT analytic carrier.", "assumptions": [ "FQFT analytic carrier exists as typed in D00" ], "dependencies": [ "FQFT-CARRIER-T03", "FQFT-CARRIER-T04" ], "correspondence_obligation": "provide explicit coarse observables and physical locality mechanism", "observable": "source-derived 21-component effective carrier", "falsifier": "the required coarse nerve cannot arise from the admitted FQFT carrier without new independent postulates", "source_refs": [ "SFRFULL:L1543:8f49bb7640" ] }, { "id": "FQFT-COVER-T01", "label": "Equitable six-fiber / K6-cover equivalence", "programme": "FQFT", "lane": "mathematical", "kind": "graph_cover_theorem", "status": "MATHEMATICAL_PROOF_CLOSED", "statement": "For a connected 5-regular graph partitioned into six fibers, the condition that every vertex has exactly one neighbor in every other fiber is equivalent to a graph covering p:G\u2192K6.", "assumptions": [ "connected 5-regular graph", "six nonempty fibers" ], "dependencies": [ "FQFT-CARRIER-P01" ], "correspondence_obligation": "derive the six-fiber condition physically if the cover branch is adopted", "observable": "none", "falsifier": "counterexample to the local covering equivalence under stated assumptions", "source_refs": [ "SFRFULL:L1543:8f49bb7640" ] }, { "id": "FQFT-COVER-T02", "label": "Exact old/new spectral decomposition for K6 covers", "programme": "FQFT", "lane": "mathematical", "kind": "spectral_cover_theorem", "status": "MATHEMATICAL_PROOF_CLOSED", "statement": "For a finite K6 cover, the fiber-constant subspace is reducing and carries the exact K6 spectrum 5,-1\u00d75 (equivalently Laplacian 0,6\u00d75), with all remaining modes in the orthogonal new sector.", "assumptions": [ "finite undirected K6 graph cover" ], "dependencies": [ "FQFT-COVER-T01" ], "correspondence_obligation": "show the physical FQFT operator respects this graph-cover adjacency/Laplacian sector", "observable": "conditional quotient spectral sector", "falsifier": "a valid undirected cover fails to contain the base quotient spectrum in the fiber-constant subspace", "source_refs": [ "SFRFULL:L1543:8f49bb7640" ] }, { "id": "FQFT-COVER-T03", "label": "Ramanujan / K6-cover spectral compatibility", "programme": "FQFT", "lane": "mathematical", "kind": "compatibility_result", "status": "MATHEMATICAL_RESULT_CLOSED_CONDITIONAL", "statement": "A non-bipartite 5-regular Ramanujan K6 cover can contain the old quotient Laplacian eigenvalue 6 while all genuinely new nontrivial Laplacian eigenvalues remain in [1,9].", "assumptions": [ "5-regular non-bipartite Ramanujan cover", "standard Ramanujan bound" ], "dependencies": [ "FQFT-COVER-T02", "FQFT-DIM-02" ], "correspondence_obligation": "select or derive an actual cover family from FQFT", "observable": "conditional micro/quotient spectral compatibility", "falsifier": "spectral contradiction under the declared cover and Ramanujan hypotheses", "source_refs": [ "SFRFULL:L1543:8f49bb7640" ] }, { "id": "FQFT-COVER-NG01", "label": "Cover / Kesten\u2013McKay separation", "programme": "FQFT", "lane": "methodological", "kind": "spectral_separation_no_go", "status": "MATHEMATICAL_SEPARATION_NO_GO", "statement": "q=5, Ramanujanity and the Kesten\u2013McKay universal-cover law do not uniquely select a finite K6 quotient, and a single finite cover does not have an exactly continuous KM empirical spectrum.", "assumptions": [ "standard graph-cover/universal-cover interpretation" ], "dependencies": [ "FQFT-COVER-T03", "FQFT-SPEC-01" ], "correspondence_obligation": "supply an independent physical quotient-selection principle and asymptotic/local-convergence condition if needed", "observable": "none \u2014 selection boundary", "falsifier": "prove unique K6 selection from only q=5+Ramanujan+KM data", "source_refs": [ "SFRFULL:L1543:8f49bb7640" ] }, { "id": "FQFT-COVER-T04", "label": "Degree-measure derivation of the 5:2 quotient measure", "programme": "FQFT", "lane": "mathematical", "kind": "conditional_measure_theorem", "status": "MATHEMATICAL_PROOF_CLOSED_CONDITIONAL", "statement": "In the subdivision of an n-sheet K6 cover, the reversible degree measure assigns total weights 5n to each old-fiber quotient node and 2n to each edge-bundle quotient node, yielding wF:wM=5:2.", "assumptions": [ "subdivision graph", "reversible degree measure", "equal sheet size n" ], "dependencies": [ "FQFT-COVER-T01" ], "correspondence_obligation": "justify why FQFT kinetic measure descends to this reversible degree measure", "observable": "conditional quotient mass/measure matrix", "falsifier": "degree-measure quotient count differs under the same subdivision construction", "source_refs": [ "SFRFULL:L1543:8f49bb7640" ] }, { "id": "FQFT-COVER-T05", "label": "Normalized Levi quotient spectrum from a K6-cover subdivision", "programme": "FQFT", "lane": "mathematical", "kind": "conditional_spectrum_theorem", "status": "MATHEMATICAL_PROOF_CLOSED_CONDITIONAL", "statement": "With the degree-normalized 6+15 quotient of a K6-cover subdivision, the normalized Laplacian spectrum is 0,2,1\u00d79,(1\u00b1sqrt(2/5))\u00d75.", "assumptions": [ "K6 cover", "subdivision", "degree-normalized quotient" ], "dependencies": [ "FQFT-COVER-T04", "FQFT-COVER-T02" ], "correspondence_obligation": "show the physical coarse kinetic operator uses this normalization", "observable": "conditional finite quotient spectrum", "falsifier": "exact matrix calculation under the declared construction yields a different spectrum", "source_refs": [ "SFRFULL:L1543:8f49bb7640" ] }, { "id": "FQFT-SEL-NG01", "label": "Current FQFT source does not select K6/21 carrier", "programme": "FQFT", "lane": "physical", "kind": "corpus_provenance_no_go", "status": "CORPUS_PROVENANCE_NO_GO", "statement": "Current source data do not specify a quotient-selection law, K6 cover, six-fiber partition, or 21-terminal nerve.", "assumptions": [], "dependencies": [ "FQFT-COVER-NG01" ], "correspondence_obligation": null, "observable": null, "falsifier": "A source-level selector is produced with derivation and provenance", "source_refs": [] }, { "id": "FQFT-ALG-D01", "label": "Five-involution master algebra candidate", "programme": "FQFT", "lane": "mathematical", "kind": "candidate_revision_definition", "status": "CANDIDATE_REVISION_DEFINITION", "statement": "W5=C2^{*5}, A5=sum s_a with s_a^2=1.", "assumptions": [ "candidate extension, not historical FQFT source" ], "dependencies": [], "correspondence_obligation": "derive physical representation/state selection", "observable": null, "falsifier": null, "source_refs": [] }, { "id": "FQFT-ALG-T01", "label": "Regular representation gives 5-regular tree radial sector", "programme": "FQFT", "lane": "mathematical", "kind": "mathematical_result", "status": "MATHEMATICAL_RESULT_CLOSED", "statement": "The Cayley graph of C2^{*5} with its involutive generators is the 5-regular tree; the radial recurrence is A R_n=R_{n+1}+4R_{n-1} for n>=2.", "assumptions": [ "regular representation" ], "dependencies": [ "FQFT-ALG-D01" ], "correspondence_obligation": null, "observable": null, "falsifier": null, "source_refs": [] }, { "id": "FQFT-ALG-T02", "label": "Minimal simple transitive realization is K6", "programme": "FQFT", "lane": "mathematical", "kind": "theorem", "status": "MATHEMATICAL_PROOF_CLOSED", "statement": "For five fixed-point-free involutions with five distinct neighbours on a finite transitive simple realization, |X|>=6 and equality forces K6.", "assumptions": [ "finite transitive action", "fixed-point-free generators", "five distinct neighbours", "simple realization" ], "dependencies": [ "FQFT-ALG-D01" ], "correspondence_obligation": "a physical minimum-cardinality principle would still be needed to select it", "observable": null, "falsifier": null, "source_refs": [] }, { "id": "FQFT-ALG-NG01", "label": "q=5/KM/Ramanujan data do not uniquely select K6", "programme": "FQFT", "lane": "mathematical_or_physical", "kind": "no_go", "status": "MATHEMATICAL_SEPARATION_NO_GO", "statement": "Regular-tree/KM spectral information does not uniquely determine the finite quotient representation.", "assumptions": [], "dependencies": [ "FQFT-ALG-T01", "FQFT-COVER-NG01" ], "correspondence_obligation": null, "observable": null, "falsifier": null, "source_refs": [] }, { "id": "FQFT-ALG-NG02", "label": "Scalar K6 adjacency functional cannot yield three vertex-sector amplitudes", "programme": "FQFT", "lane": "mathematical", "kind": "no_go", "status": "MATHEMATICAL_NO_GO", "statement": "Because Spec(A_K6)={5,-1}, scalar functional calculus f(A_K6) has at most two spectral values on the six-vertex representation.", "assumptions": [ "ordinary scalar functional calculus on K6 vertex adjacency" ], "dependencies": [ "FQFT-ALG-T02" ], "correspondence_obligation": "non-radial/multiplicity-space operator required for any three-way finite-sector structure", "observable": null, "falsifier": null, "source_refs": [] }, { "id": "FQFT-REV-G01", "label": "FQFT v2 substrate revision promotion gate", "programme": "FQFT", "lane": "physical", "kind": "promotion_gate", "status": "HOLD_NEW_PHYSICAL_SELECTION_PRINCIPLE", "statement": "W5/K6/21 completion cannot enter canonical FQFT until physical substrate, representation, quotient, non-radial dynamics, carrier, scale and observable gates close.", "assumptions": [], "dependencies": [ "FQFT-SEL-NG01", "FQFT-ALG-T02", "FQFT-ALG-NG01", "FQFT-ALG-NG02", "FQFT-CARRIER-P01" ], "correspondence_obligation": "full source-derived physical chain", "observable": "nondegenerate falsifiable observable", "falsifier": "promotion occurs while selection remains postulated", "source_refs": [] }, { "id": "FQFT-ALG-NG03", "label": "No nonzero bounded regular-to-finite quotient intertwiner", "lane": "fqft", "status": "MATHEMATICAL_NO_GO" }, { "id": "FQFT-ALG-D02", "label": "Shared full group-algebra / representation-evaluation carrier", "lane": "fqft", "status": "CANDIDATE_REVISION_DEFINITION" }, { "id": "FQFT-ALG-NG06", "label": "Reduced-only group C*-carrier cannot host the six-point representation", "lane": "fqft", "status": "MATHEMATICAL_NO_GO" }, { "id": "FQFT-ALG-D03", "label": "Finite-cover quotient intertwiner AS=SB", "lane": "fqft", "status": "MATHEMATICAL_DEFINITION_CONDITIONAL" }, { "id": "FQFT-ALG-T03", "label": "Symmetric-square 21-carrier theorem", "lane": "fqft", "status": "MATHEMATICAL_PROOF_CLOSED" }, { "id": "FQFT-ALG-T04", "label": "Johnson J(6,2) three-sector spectrum 1+5+9", "lane": "fqft", "status": "MATHEMATICAL_PROOF_CLOSED" }, { "id": "FQFT-ALG-NG04", "label": "Linear incidence transfer cannot populate D9", "lane": "fqft", "status": "MATHEMATICAL_NO_GO" }, { "id": "FQFT-ALG-T05", "label": "Quadratic symmetric-square lift can populate D9", "lane": "fqft", "status": "MATHEMATICAL_PROOF_CLOSED" }, { "id": "FQFT-ALG-T06", "label": "Induced pair representation retains non-radial generator-color information", "lane": "fqft", "status": "EXACT_FINITE_MATRIX_RESULT_CLOSED" }, { "id": "FQFT-ALG-G02", "label": "Physical representation and observable selection gate", "lane": "fqft", "status": "OPEN_PHYSICAL_SELECTION_GATE" }, { "id": "EXT-CJT-1974", "label": "Composite-operator / 2PI effective-action formalism", "lane": "external", "status": "ESTABLISHED_EXTERNAL_QFT", "source_id": "SRC-CJT-1974" }, { "id": "EXT-BETHE-SALPETER-1951", "label": "Two-body bound-state integral-equation framework", "lane": "external", "status": "ESTABLISHED_EXTERNAL_QFT", "source_id": "SRC-BETHE-SALPETER-1951" }, { "id": "EXT-HUBBARD-1959", "label": "Auxiliary-field interaction decoupling", "lane": "external", "status": "ESTABLISHED_EXTERNAL_METHOD", "source_id": "SRC-HUBBARD-1959" }, { "id": "FQFT-REP-NG01", "label": "Present source action does not select pi6 or Sym2(pi6)", "lane": "fqft", "status": "CORPUS_TYPING_NO_GO" }, { "id": "FQFT-REP-NG02", "label": "Pure Gaussian truncation has no interaction-generated composite kernel", "lane": "fqft", "status": "MATHEMATICAL_NO_GO_CONDITIONAL_GAUSSIAN" }, { "id": "FQFT-REP-D01", "label": "2PI / bilocal dynamic selector definition", "lane": "fqft", "status": "CANDIDATE_REVISION_DEFINITION" }, { "id": "FQFT-REP-T01", "label": "Diagonal elimination preserves S6-equivariance by Schur complement", "lane": "fqft", "status": "MATHEMATICAL_PROOF_CLOSED_CONDITIONAL" }, { "id": "FQFT-REP-T02", "label": "Multiplicity-free pair kernel has 1+5+9 three-channel form", "lane": "fqft", "status": "MATHEMATICAL_PROOF_CLOSED" }, { "id": "FQFT-REP-G01", "label": "Dynamic bilocal/composite selection from explicit FQFT interaction", "lane": "fqft", "status": "OPEN_PHYSICAL_SELECTION_GATE" }, { "id": "FQFT-REP-G02", "label": "Physical observable / generation interpretation of pair sectors", "lane": "fqft", "status": "OPEN_PHYSICAL_CORRESPONDENCE_GATE" }, { "id": "EXT-EICHMANN-ETAL-2024", "label": "Interacting scalar phi4 bound-state calculation with Bethe-Salpeter equation", "lane": "external", "status": "ESTABLISHED_EXTERNAL_QFT", "source_id": "SRC-EICHMANN-ETAL-2024" }, { "id": "FQFT-INT-NG01", "label": "Current source leaves V(Phi) insufficiently specified for a unique four-point kernel", "lane": "fqft", "status": "CORPUS_INTERACTION_UNDERSPECIFIED" }, { "id": "FQFT-INT-D01", "label": "Minimal S6-invariant Z2-even quartic on selected V5 carrier", "lane": "fqft", "status": "CANDIDATE_REVISION_DEFINITION" }, { "id": "FQFT-INT-T01", "label": "Minimal quartic pair-channel eigenvalues kappa1,kappa5,kappa9", "lane": "fqft", "status": "MATHEMATICAL_PROOF_CLOSED_CONDITIONAL" }, { "id": "FQFT-INT-T02", "label": "Quartic channel sum rule 4 kappa1 = 5 kappa5 + 9 kappa9", "lane": "fqft", "status": "MATHEMATICAL_PROOF_CLOSED_CONDITIONAL" }, { "id": "FQFT-INT-T03", "label": "Stable minimal quartic implies nonnegative singlet bare channel", "lane": "fqft", "status": "MATHEMATICAL_PROOF_CLOSED_CONDITIONAL" }, { "id": "FQFT-INT-T04", "label": "Stable minimal quartic admits selective V5 or D9 sign-separated regions", "lane": "fqft", "status": "MATHEMATICAL_PROOF_CLOSED_CONDITIONAL" }, { "id": "FQFT-INT-P01", "label": "Singlet composite Bethe-Salpeter pole target", "lane": "fqft", "status": "OPEN_PHYSICAL_POLE_TARGET" }, { "id": "FQFT-INT-P05", "label": "V5 composite 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"SNAT-T01", "target": "SNAT-T01R", "relation": "REPAIRED_BY" }, { "source": "FQFT-DIM-01", "target": "FQFT-DIM-02", "relation": "TESTED_BY" }, { "source": "FQFT-DIM-02", "target": "FQFT-SPEC-01", "relation": "EXPOSES" }, { "source": "FQFT-DIM-02", "target": "FQFT-FP-03", "relation": "FORCES_SEPARATE_FIXED_POINT_RECONSTRUCTION" }, { "source": "FQFT-FP-03", "target": "FQFT-FP-04", "relation": "REQUIRES_COMPLETION" }, { "source": "FQFT-FP-03", "target": "FQFT-FP-05", "relation": "SUPPLIES_SOURCE_FIXED_POINT_DOMAIN" }, { "source": "FQFT-FP-05", "target": "FQFT-FP-06", "relation": "BLOCKED_BY_MISSING_MAP" }, { "source": "FQFT-FP-06", "target": "FQFT-SCALE-01", "relation": "MUST_DERIVE_SCALE" }, { "source": "FQFT-SPEC-01", "target": "FQFT-SPEC-02", "relation": "SUPERSEDED_BY" }, { "source": "FQFT-FP-06", "target": "FQFT-SPEC-02", "relation": "MUST_GROUND" }, { "source": "FQFT-SCALE-01", "target": "FQFT-SPEC-02", "relation": "SETS_THRESHOLD_SCALE" }, { "source": "FQFT-FP-04", "target": "FQFT-FP-06", "relation": "CONSTRAINS_REDUCTION" }, { "source": "FQFT-DIM-01", "target": "FQFT-FP-04", "relation": "MOTIVATES" }, { "source": "FQFT-FP-06", "target": "FQFT-H-04", "relation": "FACTORED_BY" }, { "source": "FQFT-H-04", "target": "FQFT-H-05", "relation": "CONTAINS_CONDITIONAL_STAGE" }, { "source": "FQFT-H-04", "target": "FQFT-H-NG01", "relation": "LIMITED_BY" }, { "source": "FQFT-H-04", "target": "FQFT-H-NG02", "relation": "LIMITED_BY" }, { "source": "FQFT-H-04", "target": "FQFT-H-T01", "relation": "SUPPORTS_CONDITIONAL_THEOREM" }, { "source": "FQFT-H-05", "target": "FQFT-H-NG03", "relation": "CONSTRAINED_BY" }, { "source": "FQFT-H-NG02", "target": "FQFT-SCALE-01", "relation": "SHARPENS" }, { "source": "FQFT-H-04", "target": "FQFT-SPEC-02", "relation": "MUST_GROUND" }, { "source": "FQFT-H-05", "target": "FQFT-SPEC-02", "relation": "CONSTRAINS" }, { "source": "FQFT-H-NG03", "target": "FQFT-SPEC-02", "relation": "BLOCKS_SHORTCUT" }, { "source": "FQFT-H-04", "target": "FQFT-CARRIER-NG01", "relation": "MOTIVATES" }, { "source": "FQFT-H-05", "target": "FQFT-CARRIER-T01", "relation": "DECOMPOSES" }, { "source": "FQFT-CARRIER-T01", "target": "FQFT-CARRIER-T02", "relation": "SHARPENED_BY_LOCALITY" }, { "source": "FQFT-CARRIER-T02", "target": "FQFT-CARRIER-T03", "relation": "FORMULATES" }, { "source": "FQFT-CARRIER-T02", "target": "FQFT-CARRIER-T04", "relation": "SUPPORTS_EXISTENCE" }, { "source": "FQFT-CARRIER-T03", "target": "FQFT-CARRIER-P01", "relation": "MUST_BE_REALIZED_BY" }, { "source": "FQFT-CARRIER-T04", "target": "FQFT-CARRIER-P01", "relation": "MATH_EXISTENCE_DOES_NOT_CLOSE_PHYSICS" }, { "source": "FQFT-CARRIER-P01", "target": "FQFT-COVER-T01", "relation": "HAS_CANDIDATE_REALIZATION" }, { "source": "FQFT-COVER-T01", "target": "FQFT-COVER-T02", "relation": "IMPLIES" }, { "source": "FQFT-COVER-T02", "target": "FQFT-COVER-T03", "relation": "COMPATIBLE_WITH" }, { "source": "FQFT-COVER-T03", "target": "FQFT-COVER-NG01", "relation": "DOES_NOT_SELECT" }, { "source": "FQFT-COVER-T01", "target": "FQFT-COVER-T04", "relation": "SUBDIVISION_MEASURE" }, { "source": "FQFT-COVER-T02", "target": "FQFT-COVER-T05", "relation": "SUPPORTS" }, { "source": "FQFT-COVER-T04", "target": "FQFT-COVER-T05", "relation": "NORMALIZES" }, { "source": "FQFT-COVER-NG01", "target": "FQFT-SPEC-02", "relation": "ENFORCES_REVISION_BOUNDARY" }, { "source": "FQFT-SPEC-01", "target": "FQFT-COVER-NG01", "relation": "NOT_RESCUED_BY" }, { "source": "FQFT-COVER-T05", "target": "FQFT-H-05", "relation": "PROVIDES_CONDITIONAL_CARRIER" }, { "source": "FQFT-CARRIER-P01", "target": "FQFT-H-04", "relation": "WOULD_CLOSE_H1" }, { "source": "FQFT-COVER-NG01", "target": "FQFT-SEL-NG01", "relation": "REQUIRES" }, { "source": "FQFT-ALG-D01", "target": "FQFT-ALG-T01", "relation": "REQUIRES" }, { "source": "FQFT-ALG-D01", "target": "FQFT-ALG-T02", "relation": "REQUIRES" }, { "source": "FQFT-ALG-T01", "target": "FQFT-ALG-NG01", "relation": "REQUIRES" }, { "source": "FQFT-COVER-NG01", "target": "FQFT-ALG-NG01", "relation": "REQUIRES" }, { "source": "FQFT-ALG-T02", "target": "FQFT-ALG-NG02", "relation": "REQUIRES" }, { "source": "FQFT-SEL-NG01", "target": "FQFT-REV-G01", "relation": "REQUIRES" }, { "source": "FQFT-ALG-T02", "target": "FQFT-REV-G01", "relation": "REQUIRES" }, { "source": "FQFT-ALG-NG01", "target": "FQFT-REV-G01", "relation": "REQUIRES" }, { "source": "FQFT-ALG-NG02", "target": "FQFT-REV-G01", "relation": "REQUIRES" }, { "source": "FQFT-CARRIER-P01", "target": "FQFT-REV-G01", "relation": "REQUIRES" }, { "source": "FQFT-REV-G01", "target": "FQFT-H-04", "relation": "GATES_PHYSICAL_PROMOTION" }, { "source": "FQFT-ALG-D01", "relation": "ENABLES_OR_PRECEDES", "target": "FQFT-ALG-D02" }, { "source": "FQFT-ALG-D02", "relation": "CONSTRAINED_BY", "target": "FQFT-ALG-NG03" }, { "source": "FQFT-ALG-D02", "relation": "CONSTRAINED_BY", "target": "FQFT-ALG-NG06" }, { "source": "FQFT-COVER-T01", "relation": "ENABLES_OR_PRECEDES", "target": "FQFT-ALG-D03" }, { "source": "FQFT-ALG-T02", "relation": "ENABLES_OR_PRECEDES", "target": "FQFT-ALG-T03" }, { "source": "FQFT-ALG-T03", "relation": "DECOMPOSES_TO", "target": "FQFT-ALG-T04" }, { "source": "FQFT-ALG-T03", "relation": "CONSTRAINED_BY", "target": "FQFT-ALG-NG04" }, { "source": "FQFT-ALG-NG04", "relation": "MOTIVATES", "target": "FQFT-ALG-T05" }, { "source": "FQFT-ALG-T03", "relation": "ENABLES_OR_PRECEDES", "target": "FQFT-ALG-T06" }, { "source": "FQFT-ALG-D03", "relation": "ENABLES_OR_PRECEDES", "target": "FQFT-ALG-G02" }, { "source": "FQFT-ALG-T04", "relation": "DOES_NOT_ESTABLISH", "target": "FQFT-ALG-G02" }, { "source": "FQFT-ALG-T05", "relation": "DOES_NOT_ESTABLISH", "target": "FQFT-ALG-G02" }, { "source": "FQFT-ALG-T06", "relation": "DOES_NOT_ESTABLISH", "target": "FQFT-ALG-G02" }, { "source": "FQFT-SEL-NG01", "relation": "REQUIRES_REVISION_BEFORE", "target": "FQFT-ALG-G02" }, { "source": "FQFT-ALG-G02", "relation": "ENABLES_OR_PRECEDES", "target": "FQFT-REV-G01" }, { "source": "FQFT-ALG-NG02", "relation": "MOTIVATES", "target": "FQFT-ALG-T03" }, { "source": "FQFT-CARRIER-T04", "relation": "CORRESPONDS_TO", "target": "FQFT-ALG-T03" }, { "source": "FQFT-H-05", "relation": "CORRESPONDS_TO", "target": "FQFT-ALG-T03" }, { "source": "EXT-CJT-1974", "relation": "GROUNDS_STANDARD_METHOD", "target": "FQFT-REP-D01" }, { "source": "EXT-HUBBARD-1959", "relation": "GROUNDS_AUXILIARY_FIELD_ROUTE", "target": "FQFT-REP-D01" }, { "source": "EXT-BETHE-SALPETER-1951", "relation": "GROUNDS_BOUND_STATE_CRITERION", "target": "FQFT-REP-G01" }, { "source": "FQFT-D02", "relation": "AUDITED_BY", "target": "FQFT-REP-NG01" }, { "source": "FQFT-ALG-T03", "relation": "ENABLES", "target": "FQFT-REP-D01" }, { "source": "FQFT-ALG-T03", "relation": "ENABLES", "target": "FQFT-REP-T01" }, { "source": "FQFT-REP-NG01", "relation": "CONSTRAINS", "target": "FQFT-REP-G01" }, { "source": "FQFT-REP-NG02", "relation": "CONSTRAINS", "target": "FQFT-REP-G01" }, { "source": "FQFT-REP-D01", "relation": "ENABLES_OR_PRECEDES", "target": "FQFT-REP-G01" }, { "source": "FQFT-REP-T01", "relation": "ENABLES_OR_PRECEDES", "target": "FQFT-REP-T02" }, { "source": "FQFT-REP-T02", "relation": "ENABLES_OR_PRECEDES", "target": "FQFT-REP-G02" }, { "source": "FQFT-REP-G01", "relation": "ENABLES_OR_PRECEDES", "target": "FQFT-REP-G02" }, { "source": "FQFT-ALG-G02", "relation": "REFINED_BY", "target": "FQFT-REP-G01" }, { "source": "FQFT-CARRIER-P01", "relation": "UPSTREAM_REQUIREMENT_FOR", "target": "FQFT-REP-G01" }, { "source": "FQFT-REP-G02", "relation": "REQUIRES_CORRESPONDENCE_TEST", "target": "FQFT-T03" }, { "source": "FQFT-D02", "relation": "AUDITED_BY", "target": "FQFT-INT-NG01" }, { "source": "FQFT-REP-G01", "relation": "REFINED_BY", "target": "FQFT-INT-G01" }, { "source": "FQFT-INT-NG01", "relation": "MOTIVATES_CONDITIONAL_CANDIDATE", "target": "FQFT-INT-D01" }, { "source": "FQFT-REP-T02", "relation": "SUPPLIES_CHANNEL_DECOMPOSITION", "target": "FQFT-INT-T01" }, { "source": "FQFT-INT-D01", "relation": "YIELDS", "target": "FQFT-INT-T01" }, { "source": "FQFT-INT-T01", "relation": "IMPLIES", "target": "FQFT-INT-T02" }, { "source": "FQFT-INT-D01", "relation": "WITH_STABILITY_IMPLIES", "target": "FQFT-INT-T03" }, { "source": "FQFT-INT-T01", "relation": "WITH_STABILITY_IMPLIES", "target": "FQFT-INT-T04" }, { "source": "EXT-CJT-1974", "relation": "GROUNDS_STANDARD_METHOD", "target": "FQFT-INT-G01" }, { "source": "EXT-BETHE-SALPETER-1951", "relation": "GROUNDS_POLE_CRITERION", "target": "FQFT-INT-P01" }, { "source": "EXT-BETHE-SALPETER-1951", "relation": "GROUNDS_POLE_CRITERION", "target": "FQFT-INT-P05" }, { "source": "EXT-BETHE-SALPETER-1951", "relation": "GROUNDS_POLE_CRITERION", "target": "FQFT-INT-P09" }, { "source": "EXT-EICHMANN-ETAL-2024", "relation": "SUPPORTS_SCALAR_BOUND_STATE_PRECEDENT", "target": "FQFT-INT-G01" }, { "source": "FQFT-INT-T01", "relation": "PARAMETERIZES_BARE_CHANNEL", "target": "FQFT-INT-P01" }, { "source": "FQFT-INT-T01", "relation": "PARAMETERIZES_BARE_CHANNEL", "target": "FQFT-INT-P05" }, { "source": "FQFT-INT-T01", "relation": "PARAMETERIZES_BARE_CHANNEL", "target": "FQFT-INT-P09" }, { "source": "FQFT-INT-P01", "relation": "REQUIRES_SOURCE_DYNAMICS", "target": "FQFT-INT-G01" }, { "source": "FQFT-INT-P05", "relation": "REQUIRES_SOURCE_DYNAMICS", "target": "FQFT-INT-G01" }, { "source": "FQFT-INT-P09", "relation": "REQUIRES_SOURCE_DYNAMICS", "target": "FQFT-INT-G01" }, { "source": "FQFT-INT-G01", "relation": "PRECEDES", "target": "FQFT-REP-G02" }, { "source": "FQFT-INT-NG01", "relation": "REFINED_BY", "target": "FQFT-INT-NG02" }, { "source": "FQFT-INT-NG02", "relation": "EXPOSES", "target": "FQFT-INT-NG03" }, { "source": "FQFT-INT-NG02", "relation": "EXPOSES", "target": "FQFT-INT-NG04" }, { "source": "FQFT-INT-D01", "relation": "HAS_COMPARATOR_FLOW", "target": "FQFT-INT-T05" }, { "source": "FQFT-INT-T05", "relation": "HAS_FIXED_POINT", "target": "FQFT-INT-FP00" }, { "source": "FQFT-INT-T05", "relation": "HAS_FIXED_POINT", "target": "FQFT-INT-FP05" }, { "source": "FQFT-INT-T05", "relation": "HAS_FIXED_POINT", "target": "FQFT-INT-FP06" }, { "source": "FQFT-INT-FP06", "relation": "HAS_ONE_LOOP_PROPERTY", "target": "FQFT-INT-T06" }, { "source": "FQFT-INT-FP05", "relation": "CONSTRAINS", "target": "FQFT-INT-NG05" }, { "source": "FQFT-INT-FP06", "relation": "CONSTRAINS", "target": "FQFT-INT-NG05" }, { "source": "FQFT-INT-NG03", "relation": "REQUIRES", "target": "FQFT-INT-G02" }, { "source": "FQFT-INT-NG04", "relation": "REQUIRES", "target": "FQFT-INT-G02" }, { "source": "FQFT-INT-T06", "relation": "REQUIRES", "target": "FQFT-INT-G02" }, { "source": "FQFT-INT-NG05", "relation": "PRECEDES", "target": "FQFT-INT-G02" }, { "source": "FQFT-INT-G02", "relation": "PRECEDES", "target": "FQFT-INT-P01" }, { "source": "FQFT-INT-G02", "relation": "PRECEDES", "target": "FQFT-INT-P05" }, { "source": "FQFT-INT-G02", "relation": "PRECEDES", "target": "FQFT-INT-P09" }, { "source": "EXT-S6-TWOLOOP", "relation": "GROUNDS", "target": "FQFT-INT-T07" }, { "source": "FQFT-INT-T05", "relation": "IDENTIFIED_WITH_EXTERNAL_MODEL_BY", "target": "FQFT-INT-T07" }, { "source": "FQFT-INT-T07", "relation": "TRANSLATES", "target": "FQFT-INT-T08" }, { "source": "FQFT-INT-T08", "relation": "SUPERSEDES_REAL_INTERPRETATION_OF", "target": "FQFT-INT-FP06" }, { "source": "FQFT-INT-T08", "relation": "IMPLIES", "target": "FQFT-INT-NG06" }, { "source": "FQFT-INT-NG06", "relation": "REFINES", "target": "FQFT-INT-T09" }, { "source": "FQFT-INT-NG03", "relation": "REFINED_BY", "target": "FQFT-INT-NG07" }, { "source": "EXT-S6-TWOLOOP", "relation": "CLARIFIES_PARITY_ROLE", "target": "FQFT-INT-NG07" }, { "source": "FQFT-INT-NG07", "relation": "IMPLIES_COMPARATOR_LIMIT", "target": "FQFT-INT-NG08" }, { "source": "FQFT-INT-NG06", "relation": "IMPLIES", "target": "FQFT-INT-NG09" }, { "source": "FQFT-INT-NG08", "relation": "CONSTRAINS", "target": "FQFT-INT-G03" }, { "source": "FQFT-INT-NG09", "relation": "CONSTRAINS", "target": "FQFT-INT-G03" }, { "source": "FQFT-INT-NG04", "relation": "CONSTRAINS", "target": "FQFT-INT-G03" }, { "source": "FQFT-INT-G03", "relation": "PRECEDES", "target": "FQFT-INT-P01" }, { "source": "FQFT-INT-G03", "relation": "PRECEDES", "target": "FQFT-INT-P05" }, { "source": "FQFT-INT-G03", "relation": "PRECEDES", "target": "FQFT-INT-P09" }, { "source": "FQFT-D00", "relation": "ENABLES_OR_PRECEDES", "target": "FQFT-ACRG-D01" }, { "source": "FQFT-DIM-01", "relation": "CONSTRAINS", "target": "FQFT-ACRG-D01" }, { "source": "EXT-FRACTAL-QFT-2012", "relation": "GROUNDS_COMPARATOR", "target": "FQFT-ACRG-D01" }, { "source": "FQFT-ACRG-D01", "relation": "ENABLES_OR_PRECEDES", "target": "FQFT-ACRG-T01" }, { "source": "EXT-LR-MULTISCALAR-2020", "relation": "GROUNDS_COMPARATOR", "target": "FQFT-ACRG-T01" }, { "source": "FQFT-ACRG-T01", "relation": "ENABLES_OR_PRECEDES", "target": "FQFT-ACRG-T02" }, { "source": "FQFT-ACRG-T01", "relation": "ENABLES_OR_PRECEDES", "target": "FQFT-ACRG-T03" }, { "source": "FQFT-DIM-02", "relation": "SUPPORTS_NO_GO", "target": "FQFT-ACRG-NG02" }, { "source": "FQFT-ACRG-NG02", "relation": "REQUIRES_REPAIR", "target": "FQFT-ACRG-D01" }, { "source": "FQFT-ACRG-NG01", "relation": "REQUIRES_REPAIR", "target": "FQFT-ACRG-G01" }, { "source": "FQFT-ACRG-G01", "relation": "ENABLES_OR_PRECEDES", "target": "FQFT-ACRG-T03" }, { "source": "FQFT-INT-NG07", "relation": "STRENGTHENED_BY", "target": "FQFT-ACRG-T02" }, { "source": "FQFT-INT-G03", "relation": "REFINED_TO", "target": "FQFT-NP-G01" }, { "source": "EXT-FRG-WETTERICH-1993", "relation": "ENABLES_OR_PRECEDES", "target": "FQFT-NP-D01" }, { "source": "FQFT-ACRG-D01", "relation": "ENABLES_OR_PRECEDES", "target": "FQFT-NP-D01" }, { "source": "FQFT-ACRG-G01", "relation": "CONSTRAINS", "target": "FQFT-NP-D01" }, { "source": "EXT-FRACTAL-COMPLEX-2009", "relation": "SUPPORTS_CONDITIONAL_TARGET", "target": "FQFT-NP-C01" }, { "source": "FQFT-NP-D01", "relation": "ENABLES_OR_PRECEDES", "target": "FQFT-NP-C01" }, { "source": "FQFT-NP-D01", "relation": "ENABLES_OR_PRECEDES", "target": "FQFT-NP-G01" }, { "source": "FQFT-ACRG-T03", "relation": "CONSTRAINS", "target": "FQFT-NP-G01" }, { "source": "FQFT-INT-NG09", "relation": "MOTIVATES", "target": "FQFT-NP-G01" }, { "source": "FQFT-NP-G01", "relation": "ENABLES_OR_PRECEDES", "target": "FQFT-INT-P01" }, { "source": "FQFT-NP-G01", "relation": "ENABLES_OR_PRECEDES", "target": "FQFT-INT-P05" }, { "source": "FQFT-NP-G01", "relation": "ENABLES_OR_PRECEDES", "target": "FQFT-INT-P09" }, { "source": "FQFT-D00", "relation": "ENABLES_OR_PRECEDES", "target": "FQFT-AN-D01" }, { "source": "FQFT-ACRG-NG02", "relation": "MOTIVATES", "target": "FQFT-AN-D01" }, { "source": "EXT-POST-SIMMER-2018", "relation": "GROUNDS_COMPARATOR", "target": "FQFT-AN-T01" }, { "source": "EXT-HAMBLY-KUMAGAI-1999", "relation": "GROUNDS_COMPARATOR", "target": "FQFT-AN-T01" }, { "source": "FQFT-AN-D01", "relation": "ENABLES_OR_PRECEDES", "target": "FQFT-AN-T01" }, { "source": "FQFT-AN-T01", "relation": "ENABLES_OR_PRECEDES", "target": "FQFT-AN-T02" }, { "source": "FQFT-AN-T01", "relation": "ENABLES_OR_PRECEDES", "target": "FQFT-AN-T03" }, { "source": "FQFT-AN-NG02", "relation": "REQUIRES_REPAIR", "target": "FQFT-AN-T02" }, { "source": "FQFT-ACRG-NG01", "relation": "REFINED_TO", "target": "FQFT-AN-NG02" }, { "source": "FQFT-AN-T02", "relation": "ENABLES_OR_PRECEDES", "target": "FQFT-ACRG-G01" }, { "source": "FQFT-AN-T03", "relation": "ENABLES_OR_PRECEDES", "target": "FQFT-ACRG-G01" }, { "source": "FQFT-AN-NG01", "relation": "REQUIRES_REPAIR", "target": "FQFT-AN-G01" }, { "source": "FQFT-AN-G01", "relation": "ENABLES_OR_PRECEDES", "target": "FQFT-AN-D01" }, { "source": "FQFT-AN-P01", "relation": "SUPPORTS_COMPARATOR", "target": "FQFT-AN-T03" }, { "source": "FQFT-AN-G01", "relation": "ENABLES_OR_PRECEDES", "target": "FQFT-NP-G01" }, { "source": "FQFT-AN-NG01", "relation": "SHARPENED_BY", "target": "FQFT-MIC-NG01" }, { "source": "FQFT-MIC-NG01", "relation": "REQUIRES_REPAIR", "target": "FQFT-MIC-D01" }, { "source": "EXT-RAMANUJAN", "relation": "SUPPORTS_BASELINE", "target": "FQFT-MIC-T01" }, { "source": "FQFT-MIC-D01", "relation": "TESTED_BY", "target": "FQFT-MIC-T01" }, { "source": "FQFT-MIC-T01", "relation": "MOTIVATES_CANDIDATE", "target": "FQFT-MIC-D02" }, { "source": "FQFT-MIC-D02", "relation": "ENABLES_OR_PRECEDES", "target": "FQFT-MIC-T02" }, { "source": "FQFT-MIC-T02", "relation": "ENABLES_OR_PRECEDES", "target": "FQFT-MIC-T03" }, { "source": "FQFT-MIC-T02", "relation": "LIMITED_BY", "target": "FQFT-MIC-NG02" }, { "source": "FQFT-MIC-T01", "relation": "MOTIVATES_CANDIDATE", "target": "FQFT-MIC-D03" }, { "source": "FQFT-MIC-D03", "relation": "ENABLES_OR_PRECEDES", "target": "FQFT-MIC-G02" }, { "source": "FQFT-MIC-T03", "relation": "ENABLES_OR_PRECEDES", "target": "FQFT-MIC-G03" }, { "source": "FQFT-MIC-D01", "relation": "ENABLES_OR_PRECEDES", "target": "FQFT-MIC-G01" }, { "source": "FQFT-MIC-G01", "relation": "ENABLES_OR_PRECEDES", "target": "FQFT-AN-D01" }, { "source": "FQFT-MIC-G01", "relation": "GOVERNED_BY", "target": "FQFT-MIC-REV01" }, { "source": "FQFT-MIC-D03", "relation": "GOVERNED_BY", "target": "FQFT-MIC-REV01" }, { "source": "FQFT-MIC-D02", "relation": "GOVERNED_BY", "target": "FQFT-MIC-REV01" }, { "source": "FQFT-MIC-D03", "relation": "REFINED_BY", "target": "FQFT-MIC-D04" }, { "source": "FQFT-MIC-D04", "relation": "ENABLES_OR_PRECEDES", "target": "FQFT-MIC-T04" }, { "source": "FQFT-MIC-D04", "relation": "ENABLES_OR_PRECEDES", "target": "FQFT-MIC-T05" }, { "source": "FQFT-MIC-D04", "relation": "ENABLES_OR_PRECEDES", "target": "FQFT-MIC-T06" }, { "source": "FQFT-MIC-D04", "relation": "ADMITS_PROFILE", "target": "FQFT-MIC-C04" }, { "source": "FQFT-MIC-D04", "relation": "ADMITS_PROFILE", "target": "FQFT-MIC-C05" }, { "source": "FQFT-MIC-C04", "relation": "INSTANTIATES", "target": "FQFT-MIC-T05" }, { "source": "FQFT-MIC-C05", "relation": "ENABLES_OR_PRECEDES", "target": "FQFT-MIC-T07" }, { "source": "FQFT-MIC-C05", "relation": "GOVERNED_BY", "target": "FQFT-MIC-NG04" }, { "source": "FQFT-MIC-T05", "relation": "GOVERNED_BY", "target": "FQFT-MIC-NG03" }, { "source": "FQFT-MIC-T04", "relation": "SUPPORTS", "target": "FQFT-AN-D01" }, { "source": "FQFT-MIC-T04", "relation": "SUPPORTS", "target": "FQFT-AN-T01" }, { "source": "FQFT-MIC-D04", "relation": "ENABLES_OR_PRECEDES", "target": "FQFT-MIC-G04" }, { "source": "FQFT-MIC-D04", "relation": "ENABLES_OR_PRECEDES", "target": "FQFT-MIC-G05" }, { "source": "FQFT-MIC-NG03", "relation": "REQUIRES", "target": "FQFT-MIC-G05" }, { "source": "FQFT-MIC-G04", "relation": "GOVERNED_BY", "target": "FQFT-MIC-REV02" }, { "source": "FQFT-MIC-G05", "relation": "GOVERNED_BY", "target": "FQFT-MIC-REV02" }, { "source": "FQFT-MIC-D04", "relation": "GOVERNED_BY", "target": "FQFT-MIC-REV02" } ], "firewalls": [ "proof != physical truth", "correspondence != novelty", "detectability != nonabsorbability", "internal certified result != external validation", "formal systems theorem != physical law", "source-reported fixed point != independently reconstructed fixed point", "retired mechanism != refuted entire FQFT programme", "mathematical fixed-point pushforward != physical reduction map", "parallel representations of one algebra != bounded direct Hilbert-space transfer", "1+5+9 representation sectors != three physical generations", "functorial symmetric-square carrier != physical bilocal-sector selection" ] }