{ "schema": "MC-FORMALISM-ATLAS-1.0", "build": { "survey_date": "2026-09-23", "repository": "nicholaskouns-create/E47-Kartekeya", "github_main_commit": "38ff0def5ee7566fa39044912b9dca4a266eab1e", "github_tree_sha": "12ce1f7c2dc7098efccc1baa1c28029343d1388a", "evidence_grammar": { "E0": "exact proof", "E1": "executable reconstruction", "E2": "simulation", "E3": "external benchmark", "E4": "experiment", "H0": "hardware" }, "evidence_band_note": "Formalism Registry claim_status is authoritative at the registry level. evidence_band is a display hint only; exact E-class is taken from linked Mathematical City identities and machine certificates." }, "core_lock": { "carrier": "V_2^{⊗3}", "dim_V": 125, "casimir_spectrum": [ 0, 2, 6, 12, 20, 30, 42 ], "multiplicities": [ 1, 9, 25, 28, 27, 22, 13 ], "kernel": "K=(C-6I)(C-30I)", "E47": "ker(K)=E_6⊕E_30", "dim_E47": 47, "Omega_c": "47/125", "K2_gap": 11664, "K2_norm": 186624, "epsilon_star": "1/99144", "rho_star": "15/17" }, "summary": { "live_records": 94, "id_range": [ 1, 97 ], "missing_ids": [ 54, 55, 56 ], "canonical_records": 46, "current_records": 94, "status_counts": { "Exact / computationally verified": 33, "Structural formalism": 25, "Conditional / open": 27, "Engineering / speculative": 9 }, "domain_counts": { "Core algebra": 16, "Invariant grammar": 11, "Numerical / spatial": 13, "Quantum information": 10, "Propulsion / GEM": 5, "Scalar / spectral": 5, "Geodesic / metric": 3, "Open closure": 8, "Engineering / applications": 15, "Epistemology / ETNS": 8 }, "identity_nodes": 0, "theorem_edges": 0, "relation_counts": {}, "claim_digital_twins": 0, "machine_certificates": 0, "invalid_certificates": [], "source_artifacts": 0, "corrections": 0, "failure_records": 0, "cross_platform_discrepancies": 0, "open_discrepancies": 0, "stranded_math_records": 0, "stranded_candidates": 0, "python_corpus_entries": 0, "python_paths_present_in_github": 0, "interactive_surfaces": 0, "active_interactive_surfaces": 0, "drive_primary_source_rows": 341, "drive_machine_certificate_rows": 277, "relevant_mail_snapshot": 50 }, "registry": [ { "id": 1, "key": "FRM-1", "formalism": "The K47/125 Construction", "domain": "Core algebra", "claim_status": "Exact / computationally verified", "canonical": true, "current": true, "modalities": [ "Proof", "Symbolic", "Python" ], "evidence_band": "E0/E1", "last_reviewed": "2026-07-16", "summary": "Canonical finite-dimensional construction on V₂^{⊗3}: total Casimir, selector K=(C−6I)(C−30I), rank-47 kernel E₄₇, projector, and Ωc=47/125.", "sources": [ { "role": "primary", "url": "https://app.notion.com/p/d7910a7abca442af9298dee80f392fe2" } ], "identity_links": [], "certificates": [], "dependencies": [], "tests": [], "implementations": [] }, { "id": 2, "key": "FRM-2", "formalism": "E47 Spectral Kernel Selector", "domain": "Core algebra", "claim_status": "Exact / computationally verified", "canonical": true, "current": true, "modalities": [ "Proof", "Symbolic", "Python", "QuTiP" ], "evidence_band": "E0/E1", "last_reviewed": "2026-08-13", "summary": "Polynomial Casimir selector whose kernel is exactly 5V₂⊕2V₅ with dimension 47 inside the 125-dimensional carrier.", "sources": [ { "role": "primary", "url": "https://docs.google.com/document/d/1phSGFngIrntOEJVnRd13fC7nW3quESlJU2LRYc8mRjI" }, { "role": "site", "url": "https://app.notion.com/p/d7910a7abca442af9298dee80f392fe2" } ], "identity_links": [], "certificates": [], "dependencies": [], "tests": [], "implementations": [] }, { "id": 3, "key": "FRM-3", "formalism": "SU(2) Triple Spin-2 Decomposition", "domain": "Core algebra", "claim_status": "Exact / computationally verified", "canonical": true, "current": true, "modalities": [ "Proof", "Symbolic" ], "evidence_band": "E0/E1", "last_reviewed": "2026-07-16", "summary": "Clebsch–Gordan decomposition of V₂^{⊗3} into spin sectors J=0,…,6 with exact multiplicities and total dimension 125.", "sources": [ { "role": "primary", "url": "https://docs.google.com/document/d/1lF9JRb_iBvFoEiU4S6N2eJg0pIZFnVwIzsEZv73N41M" }, { "role": "site", "url": "https://app.notion.com/p/d7910a7abca442af9298dee80f392fe2" } ], "identity_links": [], "certificates": [], "dependencies": [], "tests": [], "implementations": [] }, { "id": 4, "key": "FRM-4", "formalism": "Orthogonal Projector and Contraction Dynamics", "domain": "Core algebra", "claim_status": "Exact / computationally verified", "canonical": true, "current": true, "modalities": [ "Proof", "Symbolic", "Python" ], "evidence_band": "E0/E1", "last_reviewed": "2026-07-16", "summary": "Hermitian contraction Γ=I−εK² converging to the orthogonal projector P_E onto E₄₇ under the stated spectral bound.", "sources": [ { "role": "primary", "url": "https://docs.google.com/document/d/1HU4knLv4eXN9h5-NmStUZcA3nRIvCLUhrKhMuxK0xSs" }, { "role": "site", "url": "https://app.notion.com/p/d7910a7abca442af9298dee80f392fe2" } ], "identity_links": [], "certificates": [], "dependencies": [], "tests": [], "implementations": [] }, { "id": 5, "key": "FRM-5", "formalism": "KKP-R Verification Inventory", "domain": "Core algebra", "claim_status": "Exact / computationally verified", "canonical": true, "current": true, "modalities": [ "Proof", "Python" ], "evidence_band": "E0/E1", "last_reviewed": "2026-07-16", "summary": "Verification layer for carrier dimension, Casimir spectrum, kernel rank, projector identities, contraction, and coherence ratio.", "sources": [ { "role": "primary", "url": "https://docs.google.com/document/d/1G01tVwIDDgR_yPsA3_LoshmQmZncMqMGf2RWniJ8Vig" }, { "role": "site", "url": "https://app.notion.com/p/bf00af4711a2493d925250c122b895ac" } ], "identity_links": [], "certificates": [], "dependencies": [], "tests": [], "implementations": [] }, { "id": 6, "key": "FRM-6", "formalism": "Hamiltonian, Lagrangian, Euler, and Bohmian Dynamics on E47", "domain": "Core algebra", "claim_status": "Structural formalism", "canonical": false, "current": true, "modalities": [ "Symbolic" ], "evidence_band": "OPEN_STRUCTURAL", "last_reviewed": "2026-07-16", "summary": "Dynamical formulations restricted to the invariant subspace; their physical interpretation remains separate from the exact kernel theorem.", "sources": [ { "role": "primary", "url": "https://docs.google.com/document/d/1VbrGEfQ_m8Ya7P11rONyIh0mb5j8E1a_8f0FydTt7TU" }, { "role": "site", "url": "https://app.notion.com/p/0c77285e545d44dbaed491b8d08317d8" } ], "identity_links": [], "certificates": [], "dependencies": [], "tests": [], "implementations": [] }, { "id": 7, "key": "FRM-7", "formalism": "Invariant Grammar — Seven-Layer Formalism", "domain": "Invariant grammar", "claim_status": "Structural formalism", "canonical": true, "current": true, "modalities": [ "Symbolic" ], "evidence_band": "OPEN_STRUCTURAL", "last_reviewed": "2026-07-16", "summary": "Canonical typed visual language for stabilization into coherence. Exact components include finite signatures, type composability, the context-free form of the displayed surface BNF, and the verified 125→47 witness. Category, coalgebra, visual epistemic syntax, Chomsky translation, and cross-domain use are structural layers with explicit boundaries.", "sources": [ { "role": "primary", "url": "https://docs.google.com/document/d/1YbPpYNmpAydu8W-O3fj3KlMkMXzaCUGvEZRzcuXsex4" }, { "role": "site", "url": "https://app.notion.com/p/3a046094fd3081718c43d05685557405" } ], "identity_links": [], "certificates": [], "dependencies": [], "tests": [], "implementations": [] }, { "id": 8, "key": "FRM-8", "formalism": "The Grammar That Reads Itself", "domain": "Invariant grammar", "claim_status": "Conditional / open", "canonical": false, "current": true, "modalities": [ "Symbolic" ], "evidence_band": "OPEN_CONDITIONAL", "last_reviewed": "2026-07-16", "summary": "Quine-style self-description and proposed fixed-point metagrammar. A rigorous self-verification theorem requires a formally defined sentence space, selector, encoding, and proof that the self-reading equations hold. The canonical E47 witness does not independently establish the metalinguistic claim.", "sources": [ { "role": "primary", "url": "https://docs.google.com/document/d/1ANwLeNCtCVWm40vGdAG8QPlB52bwYVfMUK-qZp6N978" }, { "role": "site", "url": "https://app.notion.com/p/3a046094fd3081718c43d05685557405" } ], "identity_links": [], "certificates": [], "dependencies": [], "tests": [], "implementations": [] }, { "id": 9, "key": "FRM-9", "formalism": "E47 Machine-Learning Architecture", "domain": "Invariant grammar", "claim_status": "Structural formalism", "canonical": false, "current": true, "modalities": [ "Symbolic", "Python" ], "evidence_band": "OPEN_STRUCTURAL", "last_reviewed": "2026-07-16", "summary": "White-box computational architecture using aggregation, contraction, projection, evaluation, and reinitialization.", "sources": [ { "role": "primary", "url": "https://docs.google.com/document/d/1LUAqiLxCP-5OaF7h1NslzVnIQaTQsJpteoDenT_5AtE" }, { "role": "site", "url": "https://app.notion.com/p/0c77285e545d44dbaed491b8d08317d8" } ], "identity_links": [], "certificates": [], "dependencies": [], "tests": [], "implementations": [] }, { "id": 10, "key": "FRM-10", "formalism": "Finite Periodic FCC × E47 Spatial Lift", "domain": "Numerical / spatial", "claim_status": "Exact / computationally verified", "canonical": true, "current": true, "modalities": [ "Python", "Simulation" ], "evidence_band": "E0/E1 + E2 component", "last_reviewed": "2026-07-16", "summary": "Translation-invariant FCC torus coupled to the internal E₄₇ selector, with computed spectrum, kernel dimension, gap, and protected winding band.", "sources": [ { "role": "primary", "url": "https://drive.google.com/file/d/1tRrZTf9sqgR_8TQ8QGhIMz2HxNsy6Dqi" }, { "role": "site", "url": "https://app.notion.com/p/bf00af4711a2493d925250c122b895ac" } ], "identity_links": [], "certificates": [], "dependencies": [], "tests": [], "implementations": [] }, { "id": 11, "key": "FRM-11", "formalism": "E47 Coherence Ratio Under Spatial Lift", "domain": "Numerical / spatial", "claim_status": "Exact / computationally verified", "canonical": true, "current": true, "modalities": [ "Python", "Simulation" ], "evidence_band": "E0/E1 + E2 component", "last_reviewed": "2026-07-16", "summary": "Numerical confirmation that the protected internal rank remains 47 while the spatial carrier changes.", "sources": [ { "role": "primary", "url": "https://drive.google.com/file/d/1-FTL9_A-dEfTpNHUY_VrwUNk1TbHb-ei" }, { "role": "site", "url": "https://app.notion.com/p/bf00af4711a2493d925250c122b895ac" } ], "identity_links": [], "certificates": [], "dependencies": [], "tests": [], "implementations": [] }, { "id": 12, "key": "FRM-12", "formalism": "K47/125 Spectral Invariant Computation", "domain": "Numerical / spatial", "claim_status": "Exact / computationally verified", "canonical": true, "current": true, "modalities": [ "Proof", "Python" ], "evidence_band": "E0/E1", "last_reviewed": "2026-07-16", "summary": "Direct numerical construction of the 125-dimensional Casimir operator and exact extraction of dim ker K=47.", "sources": [ { "role": "primary", "url": "https://docs.google.com/document/d/1Jrg1KSc7zqkx42UWtfB9PF60Zr0fFUWC1bLwFtnxd8k" }, { "role": "site", "url": "https://app.notion.com/p/bf00af4711a2493d925250c122b895ac" } ], "identity_links": [], "certificates": [], "dependencies": [], "tests": [], "implementations": [] }, { "id": 13, "key": "FRM-13", "formalism": "E47 Noiseless Multiplicity Subsystems", "domain": "Quantum information", "claim_status": "Exact / computationally verified", "canonical": true, "current": true, "modalities": [ "Proof", "Symbolic" ], "evidence_band": "E0/E1", "last_reviewed": "2026-07-16", "summary": "Exact collective-SU(2) decomposition identifying multiplicity spaces C⁵ and C² as noiseless subsystems for the stated operator algebra.", "sources": [ { "role": "primary", "url": "https://docs.google.com/document/d/1qMzRIXzfEQvO4uSppqAQfZK95fzvBQVYFBQKw1E_ANQ" }, { "role": "site", "url": "https://app.notion.com/p/39f46094fd3081be981eee4d10f33983" } ], "identity_links": [], "certificates": [], "dependencies": [], "tests": [], "implementations": [] }, { "id": 14, "key": "FRM-14", "formalism": "Knill–Laflamme Closure for Full E47 Quantum Error Correction", "domain": "Quantum information", "claim_status": "Conditional / open", "canonical": false, "current": true, "modalities": [ "Proof", "Symbolic", "Experimental obligation" ], "evidence_band": "OPEN_CONDITIONAL", "last_reviewed": "2026-07-16", "summary": "Full-code status is channel-dependent and requires P_E E_a†E_b P_E=α_ab P_E for every pair of physical error operators.", "sources": [ { "role": "primary", "url": "https://docs.google.com/document/d/1qMzRIXzfEQvO4uSppqAQfZK95fzvBQVYFBQKw1E_ANQ" }, { "role": "site", "url": "https://app.notion.com/p/39f46094fd3081be981eee4d10f33983" } ], "identity_links": [], "certificates": [], "dependencies": [], "tests": [], "implementations": [] }, { "id": 15, "key": "FRM-15", "formalism": "GEM / Gravito-Inertial Hamiltonian Prototype", "domain": "Propulsion / GEM", "claim_status": "Conditional / open", "canonical": false, "current": true, "modalities": [ "Symbolic", "QuTiP", "Simulation", "Experimental obligation" ], "evidence_band": "OPEN_CONDITIONAL + E2 component", "last_reviewed": "2026-07-16", "summary": "Two-qubit superconducting sector coupled to truncated bosonic GEM modes; code requires tensor-space and unit normalization before physical interpretation.", "sources": [ { "role": "primary", "url": "https://docs.google.com/document/d/1pxzTNle8Z8F7ie0GIvZb4gvkYx0NyoylXwAnw6ctP3U" }, { "role": "site", "url": "https://app.notion.com/p/39f46094fd3081b49137f339d252f973" } ], "identity_links": [], "certificates": [], "dependencies": [], "tests": [], "implementations": [] }, { "id": 16, "key": "FRM-16", "formalism": "HFGW Resonant-Cavity Simulation", "domain": "Propulsion / GEM", "claim_status": "Conditional / open", "canonical": false, "current": true, "modalities": [ "QuTiP", "Simulation", "Experimental obligation" ], "evidence_band": "OPEN_CONDITIONAL + E2 component", "last_reviewed": "2026-07-16", "summary": "Time-dependent cavity perturbation model for a putative high-frequency gravitational-wave signal; computational prototype only.", "sources": [ { "role": "primary", "url": "https://docs.google.com/document/d/1pxzTNle8Z8F7ie0GIvZb4gvkYx0NyoylXwAnw6ctP3U" }, { "role": "site", "url": "https://app.notion.com/p/39f46094fd3081b49137f339d252f973" } ], "identity_links": [], "certificates": [], "dependencies": [], "tests": [], "implementations": [] }, { "id": 17, "key": "FRM-17", "formalism": "Angular-Velocity GEM Sweep", "domain": "Propulsion / GEM", "claim_status": "Conditional / open", "canonical": false, "current": true, "modalities": [ "QuTiP", "Simulation" ], "evidence_band": "OPEN_CONDITIONAL + E2 component", "last_reviewed": "2026-07-16", "summary": "Parameterized rotation sweep over superconducting and GEM coupling terms; requires corrected time-dependent Hamiltonian implementation.", "sources": [ { "role": "primary", "url": "https://docs.google.com/document/d/1pxzTNle8Z8F7ie0GIvZb4gvkYx0NyoylXwAnw6ctP3U" }, { "role": "site", "url": "https://app.notion.com/p/39f46094fd3081b49137f339d252f973" } ], "identity_links": [], "certificates": [], "dependencies": [], "tests": [], "implementations": [] }, { "id": 18, "key": "FRM-18", "formalism": "Python and Numerical Validation Audit", "domain": "Numerical / spatial", "claim_status": "Exact / computationally verified", "canonical": true, "current": true, "modalities": [ "Proof", "Symbolic", "Python", "QuTiP", "VQE", "Simulation", "Experimental obligation" ], "evidence_band": "E0/E1 + E2 component", "last_reviewed": "2026-07-16", "summary": "Canonical site-wide audit of the Google Workspace computational corpus. Establishes the machine-verified finite spectral-kernel chain, projector and contraction identities, FCC/Fourier checks, and exact synthetic-harness identities; separately classifies QuTiP, SciPy, VQE, topology, swarm, protein-folding, propulsion/GEM, Navier–Stokes, constants, and other code as simulations, samples, prototypes, corrections, or open domain bridges.", "sources": [ { "role": "primary", "url": "https://docs.google.com/document/d/1EZJhWTShM2POXYWb8x4bcydqjXr2xLWoBTOQVkqorrk" }, { "role": "site", "url": "https://app.notion.com/p/3a046094fd30817bb4a6e317dd633482" } ], "identity_links": [], "certificates": [], "dependencies": [], "tests": [], "implementations": [] }, { "id": 19, "key": "FRM-19", "formalism": "Babylonian Scalar Contraction to Ωc", "domain": "Scalar / spectral", "claim_status": "Exact / computationally verified", "canonical": true, "current": true, "modalities": [ "Proof", "Python" ], "evidence_band": "E0/E1", "last_reviewed": "2026-07-16", "summary": "Newton–Babylonian update Q_{n+1}=1/2(Q_n+Ωc²/Q_n), converging quadratically to Ωc for positive initial data.", "sources": [ { "role": "primary", "url": "https://docs.google.com/document/d/1EZJhWTShM2POXYWb8x4bcydqjXr2xLWoBTOQVkqorrk" }, { "role": "site", "url": "https://app.notion.com/p/39f46094fd3081b49137f339d252f973" } ], "identity_links": [], "certificates": [], "dependencies": [], "tests": [], "implementations": [] }, { "id": 20, "key": "FRM-20", "formalism": "Recursive Mass Spectrum and Scalar Attractor Surface", "domain": "Scalar / spectral", "claim_status": "Structural formalism", "canonical": false, "current": true, "modalities": [ "Python", "Simulation" ], "evidence_band": "OPEN_STRUCTURAL + E2 component", "last_reviewed": "2026-07-16", "summary": "Toy golden-ratio mass scaling and potential-like scalar manifold visualizations; internally computable but not physical validation.", "sources": [ { "role": "primary", "url": "https://docs.google.com/document/d/1EZJhWTShM2POXYWb8x4bcydqjXr2xLWoBTOQVkqorrk" }, { "role": "site", "url": "https://app.notion.com/p/39f46094fd3081b49137f339d252f973" } ], "identity_links": [], "certificates": [], "dependencies": [], "tests": [], "implementations": [] }, { "id": 21, "key": "FRM-21", "formalism": "Augmented Geodesic / Metric Flow", "domain": "Geodesic / metric", "claim_status": "Structural formalism", "canonical": false, "current": true, "modalities": [ "Python", "Simulation" ], "evidence_band": "OPEN_STRUCTURAL + E2 component", "last_reviewed": "2026-07-16", "summary": "SciPy integration of a nonlinear geodesic-like flow with explicit metric component, Christoffel term, and singularity detection.", "sources": [ { "role": "primary", "url": "https://docs.google.com/document/d/1xVKeyzl8GILmT8vR42b8noB7Y6vJ7y1bQ5KADWfcyKM" }, { "role": "site", "url": "https://app.notion.com/p/39f46094fd3081b49137f339d252f973" } ], "identity_links": [], "certificates": [], "dependencies": [], "tests": [], "implementations": [] }, { "id": 22, "key": "FRM-22", "formalism": "E47 VQE Circuit and Hybrid Feedback Specification", "domain": "Quantum information", "claim_status": "Conditional / open", "canonical": false, "current": true, "modalities": [ "VQE", "Simulation" ], "evidence_band": "OPEN_CONDITIONAL + E2 component", "last_reviewed": "2026-07-16", "summary": "Parameterized Ry/Rz ansatz with hybrid gradient feedback; lacks a complete executable SDK implementation and locked data products.", "sources": [ { "role": "primary", "url": "https://docs.google.com/document/d/1tKDHLlhaVONtGZm4FHe5STaqlyatO-X_-5iBujgcXhg" }, { "role": "site", "url": "https://app.notion.com/p/39f46094fd3081b49137f339d252f973" } ], "identity_links": [], "certificates": [], "dependencies": [], "tests": [], "implementations": [] }, { "id": 23, "key": "FRM-23", "formalism": "Alpha from Omega Electromagnetic Closure", "domain": "Open closure", "claim_status": "Conditional / open", "canonical": false, "current": true, "modalities": [ "Symbolic", "Experimental obligation" ], "evidence_band": "OPEN_CONDITIONAL", "last_reviewed": "2026-07-16", "summary": "Exact numerical candidate for α⁻¹ whose coefficients and bridge map must still be uniquely derived from E₄₇ rather than selected.", "sources": [ { "role": "primary", "url": "https://docs.google.com/document/d/1Lf56EooNfpgfFLBKz4L6SU-k8HDoDDAWSsJSnlDhCMY" }, { "role": "site", "url": "https://app.notion.com/p/39f46094fd3081f4a407ca51218aea05" } ], "identity_links": [], "certificates": [], "dependencies": [], "tests": [], "implementations": [] }, { "id": 24, "key": "FRM-24", "formalism": "Navier–Stokes Kernel Selection Program", "domain": "Open closure", "claim_status": "Conditional / open", "canonical": false, "current": true, "modalities": [ "Proof", "Symbolic" ], "evidence_band": "OPEN_CONDITIONAL", "last_reviewed": "2026-07-16", "summary": "Proposed Casimir-selected survivor class for three-dimensional Navier–Stokes; global regularity obligations remain open.", "sources": [ { "role": "primary", "url": "https://docs.google.com/document/d/1FZ475Y0abZ_HHh2ywYeS8238zZoTkeF2tpjRX71duoA" }, { "role": "site", "url": "https://app.notion.com/p/0c77285e545d44dbaed491b8d08317d8" } ], "identity_links": [], "certificates": [], "dependencies": [], "tests": [], "implementations": [] }, { "id": 25, "key": "FRM-25", "formalism": "Compressible Navier–Stokes Informational Action", "domain": "Open closure", "claim_status": "Conditional / open", "canonical": false, "current": true, "modalities": [ "Symbolic" ], "evidence_band": "OPEN_CONDITIONAL", "last_reviewed": "2026-07-16", "summary": "Variational informational-action formulation for compressible flow; separate from a proof of incompressible global regularity.", "sources": [ { "role": "primary", "url": "https://docs.google.com/document/d/1fts7UrttjsGHK2HkEF-MuOZFTdXSsbRrk_jkYq0aAoY" }, { "role": "site", "url": "https://app.notion.com/p/0c77285e545d44dbaed491b8d08317d8" } ], "identity_links": [], "certificates": [], "dependencies": [], "tests": [], "implementations": [] }, { "id": 26, "key": "FRM-26", "formalism": "PQSPI Recursive Contraction Architecture", "domain": "Engineering / applications", "claim_status": "Engineering / speculative", "canonical": false, "current": true, "modalities": [ "Hardware", "Simulation", "Experimental obligation" ], "evidence_band": "OPEN_ENGINEERING + E2 component", "last_reviewed": "2026-07-16", "summary": "Proposed hardware and recursive-control embodiment within the broader PQSPI system. Exact projector algebra, standardized PQC, protocol logic, physical sensing, and unverified phonon claims remain separately classified.", "sources": [ { "role": "primary", "url": "https://docs.google.com/document/d/1JNy9v-iny6b0a1RK1u9NvYtr-fFibdHyNJDuipF0Hbk" }, { "role": "site", "url": "https://app.notion.com/p/3a046094fd30810bbfddc9286d9c42fe" } ], "identity_links": [], "certificates": [], "dependencies": [], "tests": [], "implementations": [] }, { "id": 27, "key": "FRM-27", "formalism": "Wave-Guided Metamaterial Architecture", "domain": "Engineering / applications", "claim_status": "Conditional / open", "canonical": false, "current": true, "modalities": [ "Symbolic", "Python", "Simulation", "Hardware", "Experimental obligation" ], "evidence_band": "OPEN_CONDITIONAL + E2 component", "last_reviewed": "2026-07-17", "summary": "Pentamode wave-guided smart-skin architecture combining transformation control, candidate topological channels, active steering, and code-bearing NumPy/SciPy models. Constitutive retrieval, multiphysics convergence, fabrication, and bench validation remain open.", "sources": [ { "role": "primary", "url": "https://docs.google.com/document/d/1DzZITTzORYUsG1bxvUSRIzTbE7avX0jFKwvRDPEriLY" }, { "role": "site", "url": "https://app.notion.com/p/3a046094fd3081bd9c76fd676d812aad" } ], "identity_links": [], "certificates": [], "dependencies": [], "tests": [], "implementations": [] }, { "id": 28, "key": "FRM-28", "formalism": "Recursive Geometric Theory of Mass", "domain": "Open closure", "claim_status": "Conditional / open", "canonical": false, "current": true, "modalities": [ "Symbolic" ], "evidence_band": "OPEN_CONDITIONAL", "last_reviewed": "2026-07-16", "summary": "Discrete recursive mass-organization model; absolute physical predictions require an independently justified scale map.", "sources": [ { "role": "primary", "url": "https://app.notion.com/p/2be46094fd308146bb64fc9edd29ef42" } ], "identity_links": [], "certificates": [], "dependencies": [], "tests": [], "implementations": [] }, { "id": 29, "key": "FRM-29", "formalism": "Swarm and Collective-Control Projection", "domain": "Engineering / applications", "claim_status": "Structural formalism", "canonical": false, "current": true, "modalities": [ "Symbolic", "Simulation" ], "evidence_band": "OPEN_STRUCTURAL + E2 component", "last_reviewed": "2026-07-16", "summary": "Graph- or manifold-Laplacian contraction model for coherent collective modes, topology, recovery time, and perturbation rejection.", "sources": [ { "role": "primary", "url": "https://app.notion.com/p/0c77285e545d44dbaed491b8d08317d8" } ], "identity_links": [], "certificates": [], "dependencies": [], "tests": [], "implementations": [] }, { "id": 30, "key": "FRM-30", "formalism": "Levinthal’s Paradox and Recursive Folding Hypothesis", "domain": "Engineering / applications", "claim_status": "Conditional / open", "canonical": false, "current": true, "modalities": [ "Proof", "Python", "Simulation", "Experimental obligation" ], "evidence_band": "OPEN_CONDITIONAL + E2 component", "last_reviewed": "2026-07-16", "summary": "Exact Heron convergence and a documented AlphaFold-derived scalar pilot are separated from the open biological interpretation. The validation program uses folding kinetics, stability mutagenesis, atomic trajectories, sequence models, and rank-47 null controls.", "sources": [ { "role": "primary", "url": "https://docs.google.com/document/d/1NJKttAMjlkqw7az7tFj_O40b4cf7CG21mqPfb5ruI9o" }, { "role": "site", "url": "https://app.notion.com/p/3a046094fd30816a9d59dbbd73ada973" } ], "identity_links": [], "certificates": [], "dependencies": [], "tests": [], "implementations": [] }, { "id": 31, "key": "FRM-31", "formalism": "AQSFT Spectral Contraction and Extraction Pipeline", "domain": "Engineering / applications", "claim_status": "Engineering / speculative", "canonical": false, "current": true, "modalities": [ "Python", "Hardware" ], "evidence_band": "OPEN_ENGINEERING", "last_reviewed": "2026-07-16", "summary": "Residue embedding, rank-limited contraction, and spectral extraction prototype; complexity and cryptographic claims remain unverified.", "sources": [ { "role": "primary", "url": "https://docs.google.com/document/d/1tKDHLlhaVONtGZm4FHe5STaqlyatO-X_-5iBujgcXhg" }, { "role": "site", "url": "https://app.notion.com/p/0c77285e545d44dbaed491b8d08317d8" } ], "identity_links": [], "certificates": [], "dependencies": [], "tests": [], "implementations": [] }, { "id": 32, "key": "FRM-32", "formalism": "Abstract 47⊕78 Invariant-Sector Harness", "domain": "Numerical / spatial", "claim_status": "Structural formalism", "canonical": false, "current": true, "modalities": [ "Proof", "Python", "Simulation" ], "evidence_band": "OPEN_STRUCTURAL + E2 component", "last_reviewed": "2026-07-16", "summary": "Runnable Python package for the synthetic 125-dimensional 47⊕78 invariant-sector harness, including exact projector, commutator, no-leakage, Casimir-spectrum, complement-contraction, saved NumPy artifacts, and JSON verification metrics. It remains distinct from the canonical V₂^{⊗3} construction.", "sources": [ { "role": "primary", "url": "https://app.notion.com/p/39f46094fd3081b49137f339d252f973" } ], "identity_links": [], "certificates": [], "dependencies": [], "tests": [], "implementations": [] }, { "id": 33, "key": "FRM-33", "formalism": "Sector-Selective Propulsion Analog", "domain": "Propulsion / GEM", "claim_status": "Conditional / open", "canonical": false, "current": true, "modalities": [ "Python", "Simulation", "Experimental obligation" ], "evidence_band": "OPEN_CONDITIONAL + E2 component", "last_reviewed": "2026-07-16", "summary": "Simulation-only scalar-field sector split included in the runnable verification package. The selected sector is preserved while the complement is attenuated; no force, thrust, inertial modification, curvature, reactionless momentum transfer, or measured GEM result is claimed.", "sources": [ { "role": "primary", "url": "https://app.notion.com/p/39f46094fd3081b49137f339d252f973" } ], "identity_links": [], "certificates": [], "dependencies": [], "tests": [], "implementations": [] }, { "id": 34, "key": "FRM-34", "formalism": "ETNS Negative-Space Inference", "domain": "Epistemology / ETNS", "claim_status": "Structural formalism", "canonical": true, "current": true, "modalities": [ "Symbolic" ], "evidence_band": "OPEN_STRUCTURAL", "last_reviewed": "2026-07-16", "summary": "Epistemic framework treating patterned absence, omission, redaction, and dissonance as potentially informative when the observation and missingness mechanisms are explicitly modeled.", "sources": [ { "role": "primary", "url": "https://drive.google.com/file/d/19Tw21aVz0NddMdE36iChZcKwza0e5mbw" }, { "role": "site", "url": "https://app.notion.com/p/3a046094fd308161880dc8566ab637be" } ], "identity_links": [], "certificates": [], "dependencies": [], "tests": [], "implementations": [] }, { "id": 35, "key": "FRM-35", "formalism": "Negative-Space Kernel and Complement Formalism", "domain": "Epistemology / ETNS", "claim_status": "Exact / computationally verified", "canonical": true, "current": true, "modalities": [ "Proof", "Symbolic" ], "evidence_band": "E0/E1", "last_reviewed": "2026-07-16", "summary": "Exact complement, kernel, and projector definitions for observational negative space. These identities do not by themselves identify a hidden cause.", "sources": [ { "role": "primary", "url": "https://app.notion.com/p/3a046094fd308161880dc8566ab637be" } ], "identity_links": [], "certificates": [], "dependencies": [], "tests": [], "implementations": [] }, { "id": 36, "key": "FRM-36", "formalism": "ETNS Future-Boundary Path Conditioning", "domain": "Epistemology / ETNS", "claim_status": "Conditional / open", "canonical": false, "current": true, "modalities": [ "Symbolic", "Experimental obligation" ], "evidence_band": "OPEN_CONDITIONAL", "last_reviewed": "2026-07-16", "summary": "Terminal-boundary action minimization and path weighting. Structurally valid as smoothing or conditioning; physical retrocausality requires a discriminating causal experiment.", "sources": [ { "role": "primary", "url": "https://docs.google.com/document/d/1D6cPNhUvT4dHEPXGVqbyG3HXPm6rYTe1YvSu0ZsskjI" }, { "role": "site", "url": "https://app.notion.com/p/3a046094fd308161880dc8566ab637be" } ], "identity_links": [], "certificates": [], "dependencies": [], "tests": [], "implementations": [] }, { "id": 37, "key": "FRM-37", "formalism": "RI–ETNS Missingness Penalty", "domain": "Epistemology / ETNS", "claim_status": "Structural formalism", "canonical": false, "current": true, "modalities": [ "Symbolic", "VQE" ], "evidence_band": "OPEN_STRUCTURAL + E2 component", "last_reviewed": "2026-07-16", "summary": "Regularized variational objective augmenting RI energy with an omission-dependent penalty. Weights and missingness mechanism remain model choices until likelihood-grounded and validated.", "sources": [ { "role": "primary", "url": "https://docs.google.com/document/d/1lRj4OvHY70J-kx3MEvbf0t9gGnLnpbkZd40qGdbsrs8" }, { "role": "site", "url": "https://app.notion.com/p/3a046094fd308161880dc8566ab637be" } ], "identity_links": [], "certificates": [], "dependencies": [], "tests": [], "implementations": [] }, { "id": 38, "key": "FRM-38", "formalism": "QEGT–ETNS Gibbs Strategy Selection", "domain": "Epistemology / ETNS", "claim_status": "Structural formalism", "canonical": false, "current": true, "modalities": [ "Symbolic", "Simulation" ], "evidence_band": "OPEN_STRUCTURAL + E2 component", "last_reviewed": "2026-07-16", "summary": "Gibbs or softmax strategy distribution based on a coherence-curvature cost. Quantum status requires an explicit Hilbert space, observable or channel, preparation, and measurement implementation.", "sources": [ { "role": "primary", "url": "https://docs.google.com/document/d/1XaqydIgdkxM1z2MfZyzUPFIPVdEdb2sl6e4EXljD4vA" }, { "role": "site", "url": "https://app.notion.com/p/3a046094fd308161880dc8566ab637be" } ], "identity_links": [], "certificates": [], "dependencies": [], "tests": [], "implementations": [] }, { "id": 39, "key": "FRM-39", "formalism": "ETNS–K47/125 Fixed-Point Mapping", "domain": "Epistemology / ETNS", "claim_status": "Conditional / open", "canonical": false, "current": true, "modalities": [ "Proof", "Symbolic" ], "evidence_band": "OPEN_CONDITIONAL", "last_reviewed": "2026-07-16", "summary": "Connects the exact K47/125 spectral result to ETNS terminology. The algebraic core is inherited; the ETNS interpretation and added fixed-point equations remain conditional.", "sources": [ { "role": "primary", "url": "https://docs.google.com/document/d/1x-_BCbUxe8a-q3tOA_5KOww23vy4LufhvJlrG35PMs0" }, { "role": "site", "url": "https://app.notion.com/p/3a046094fd308161880dc8566ab637be" } ], "identity_links": [], "certificates": [], "dependencies": [], "tests": [], "implementations": [] }, { "id": 40, "key": "FRM-40", "formalism": "ETNS Engineering Applications Corpus", "domain": "Epistemology / ETNS", "claim_status": "Engineering / speculative", "canonical": false, "current": true, "modalities": [ "Symbolic", "VQE", "Hardware", "Experimental obligation" ], "evidence_band": "OPEN_ENGINEERING + E2 component", "last_reviewed": "2026-07-16", "summary": "Engineering proposals combining ETNS inference, recursive optimization, VQE, sensing, and hardware concepts. The surveyed corpus does not contain an inspectable experimental validation record.", "sources": [ { "role": "primary", "url": "https://docs.google.com/document/d/19oKcj3yLdqQiVsnqtyT66dDR7Rck9BjlM75dRf_mbJo" }, { "role": "site", "url": "https://app.notion.com/p/3a046094fd308161880dc8566ab637be" } ], "identity_links": [], "certificates": [], "dependencies": [], "tests": [], "implementations": [] }, { "id": 41, "key": "FRM-41", "formalism": "Epistemic Topology of Negative Spaces", "domain": "Epistemology / ETNS", "claim_status": "Structural formalism", "canonical": false, "current": true, "modalities": [ "Proof", "Symbolic" ], "evidence_band": "OPEN_STRUCTURAL", "last_reviewed": "2026-07-16", "summary": "Publication-style synthesis of epistemic absence and mathematical negative space: complements, kernels, quotients, filtrations, missingness mechanisms, leakage, contraction, and the K47/125 47⊕78 decomposition, with a 36-source annotated Drive bibliography.", "sources": [ { "role": "primary", "url": "https://drive.google.com/file/d/19Tw21aVz0NddMdE36iChZcKwza0e5mbw" }, { "role": "site", "url": "https://app.notion.com/p/3a046094fd30818793caf609c132931e" } ], "identity_links": [], "certificates": [], "dependencies": [], "tests": [], "implementations": [] }, { "id": 42, "key": "FRM-42", "formalism": "E47-Orbit Skyrme Construction", "domain": "Scalar / spectral", "claim_status": "Structural formalism", "canonical": false, "current": true, "modalities": [ "Proof", "Symbolic", "Python", "Experimental obligation" ], "evidence_band": "OPEN_STRUCTURAL", "last_reviewed": "2026-07-16", "summary": "Conditional continuum construction on a generic mixed E47 orbit. Exact components include the E47 decomposition, homotopy background, induced Casimir expectation, and Var(C)=576 a²b². Orbit selection, coupling normalization, anisotropic PDE existence, uniqueness, scale, and physical realization remain open.", "sources": [ { "role": "primary", "url": "https://docs.google.com/document/d/1_fv-U8ePA7YbznL9ns6gWhSMtmuys9aNWNkYavzrKzY" }, { "role": "site", "url": "https://app.notion.com/p/3a046094fd30811c9a01ce8f0f7908ff" } ], "identity_links": [], "certificates": [], "dependencies": [], "tests": [], "implementations": [] }, { "id": 43, "key": "FRM-43", "formalism": "Skyrmion Propulsion Program", "domain": "Propulsion / GEM", "claim_status": "Engineering / speculative", "canonical": false, "current": true, "modalities": [ "Symbolic", "Simulation", "Experimental obligation" ], "evidence_band": "OPEN_ENGINEERING + E2 component", "last_reviewed": "2026-07-16", "summary": "Drive corpus proposing propulsion, zero-inertia, metric-lensing, fractional-Skyrmion, metamaterial, and hull realizations. No current equation, simulation, or experiment establishes thrust, reactionless momentum transfer, total-inertia cancellation, or spacetime engineering.", "sources": [ { "role": "primary", "url": "https://docs.google.com/document/d/1vcgCk11NcoQUknnG29dUAuZXFy0HY_VhQEHE_DPMt6c" }, { "role": "site", "url": "https://app.notion.com/p/3a046094fd30811c9a01ce8f0f7908ff" } ], "identity_links": [], "certificates": [], "dependencies": [], "tests": [], "implementations": [] }, { "id": 44, "key": "FRM-44", "formalism": "Lexical Attractor — Semantic Gradient and Symbol-Space Flow", "domain": "Invariant grammar", "claim_status": "Conditional / open", "canonical": false, "current": true, "modalities": [ "Proof", "Symbolic", "Python", "Experimental obligation" ], "evidence_band": "OPEN_CONDITIONAL", "last_reviewed": "2026-07-16", "summary": "Two-layer attractor program: exact Lyapunov descent for a specified semantic potential and exact contraction of a reported 4×6 symbol matrix to its two-dimensional kernel. The unique 0.376 semantic target, universal natural-language convergence, and bridge from ker(w) to canonical E47 remain unproved.", "sources": [ { "role": "primary", "url": "https://docs.google.com/document/d/1Lg8C67VfvoGUwMGlCkQMHFs9YHAUM-c8sNPCbawlAMs" }, { "role": "site", "url": "https://app.notion.com/p/3a046094fd3081718c43d05685557405" } ], "identity_links": [], "certificates": [], "dependencies": [], "tests": [], "implementations": [] }, { "id": 45, "key": "FRM-45", "formalism": "Chomsky-to-Typed-Operator Grammar Translation", "domain": "Invariant grammar", "claim_status": "Structural formalism", "canonical": false, "current": true, "modalities": [ "Proof", "Symbolic", "Experimental obligation" ], "evidence_band": "OPEN_STRUCTURAL", "last_reviewed": "2026-07-16", "summary": "Translation from alphabet, production, parse, semantics, recursion, and interpretation into typed states, maps, construction graphs, invariant readouts, and regeneration. The displayed BNF is context-free in form; classification of the full operator calculus as Type 0 or a new Chomsky class requires an explicit string encoding and equivalence proof.", "sources": [ { "role": "primary", "url": "https://drive.google.com/file/d/1ljMpN3XQe6GvL3lCz7U3e9nmkcKuQ5Q2/view" }, { "role": "site", "url": "https://app.notion.com/p/3a046094fd3081718c43d05685557405" } ], "identity_links": [], "certificates": [], "dependencies": [], "tests": [], "implementations": [] }, { "id": 46, "key": "FRM-46", "formalism": "Spectral Cryptography and Hardware Formalism", "domain": "Quantum information", "claim_status": "Conditional / open", "canonical": true, "current": true, "modalities": [ "Proof", "Symbolic", "Python", "Simulation", "Hardware", "Experimental obligation" ], "evidence_band": "OPEN_CONDITIONAL + E2 component", "last_reviewed": "2026-07-16", "summary": "Canonical survey of the exact E47 projector, proposed RSC formalism, post-quantum architecture, RTL prototypes, ASIC targets, and IEEE submission records.", "sources": [ { "role": "primary", "url": "https://docs.google.com/document/d/1RoIThcCRLW8HVRhT6_92dX6jIWOXUoHCrWVmy75gRlI" }, { "role": "site", "url": "https://app.notion.com/p/3a046094fd30810a9f77da6696bc9512" } ], "identity_links": [], "certificates": [], "dependencies": [], "tests": [], "implementations": [] }, { "id": 47, "key": "FRM-47", "formalism": "Recursive Spectral Cryptosystem and ISSR Proposal", "domain": "Quantum information", "claim_status": "Conditional / open", "canonical": false, "current": true, "modalities": [ "Proof", "Symbolic", "Python", "Experimental obligation" ], "evidence_band": "OPEN_CONDITIONAL", "last_reviewed": "2026-07-16", "summary": "Projection-based cryptographic research proposal. Reversible encoding, scalable instances, formal security definitions, and external cryptanalysis remain open.", "sources": [ { "role": "primary", "url": "https://docs.google.com/document/d/1PmVGdawuGDu2DZQgNMju4ypVCJTPh2pSMh5hSuGxvmY" }, { "role": "site", "url": "https://app.notion.com/p/3a046094fd30810a9f77da6696bc9512" } ], "identity_links": [], "certificates": [], "dependencies": [], "tests": [], "implementations": [] }, { "id": 48, "key": "FRM-48", "formalism": "Hybrid RSC and ML-KEM PQC ASIC", "domain": "Engineering / applications", "claim_status": "Engineering / speculative", "canonical": false, "current": true, "modalities": [ "Symbolic", "Simulation", "Hardware", "Experimental obligation" ], "evidence_band": "OPEN_ENGINEERING + E2 component", "last_reviewed": "2026-07-27", "summary": "Corrected hybrid lattice-PQC and spectral-accelerator reference architecture. Eight finite identities are machine validated from the Drive source packet. ASIC-specific executable source is not yet pinned to an immutable GitHub commit; the shared E47 spectral dependency remains canonical at ad297e1. Synthesis, place-and-route, silicon, cryptographic reduction, and material realization remain open.", "sources": [ { "role": "primary", "url": "https://docs.google.com/document/d/1blmAO4r7YLqmoMDuNR0vMtWYm7ZpSlMx6CbY_62-Kfc" }, { "role": "site", "url": "https://app.notion.com/p/3a046094fd30810a9f77da6696bc9512" } ], "identity_links": [], "certificates": [], "dependencies": [], "tests": [], "implementations": [] }, { "id": 49, "key": "FRM-49", "formalism": "Babylonian Contraction RTL Prototype", "domain": "Engineering / applications", "claim_status": "Structural formalism", "canonical": false, "current": true, "modalities": [ "Simulation", "Hardware", "Experimental obligation" ], "evidence_band": "OPEN_STRUCTURAL + E2 component", "last_reviewed": "2026-07-16", "summary": "A 192-bit ten-stage scalar Newton/Babylonian square-root prototype with a terminal residual lock. It remains distinct from the 125-dimensional spectral contraction and requires compile, synthesis, and timing validation.", "sources": [ { "role": "primary", "url": "https://docs.google.com/document/d/1uSFfMfUoGgs59428gEhW5kpOiiixlm3wcgzbLD0tZhk" }, { "role": "site", "url": "https://app.notion.com/p/3a046094fd30810a9f77da6696bc9512" } ], "identity_links": [], "certificates": [], "dependencies": [], "tests": [], "implementations": [] }, { "id": 50, "key": "FRM-50", "formalism": "Post-Quantum Self-Preserving Intelligence (PQSPI)", "domain": "Engineering / applications", "claim_status": "Conditional / open", "canonical": true, "current": true, "modalities": [ "Symbolic", "Simulation", "Hardware", "Experimental obligation" ], "evidence_band": "OPEN_CONDITIONAL + E2 component", "last_reviewed": "2026-07-16", "summary": "Canonical intrinsic-security architecture joining authorized identity continuity, standardized post-quantum trust, drift monitoring, bounded recovery, attestation, and governance, with AI and physical extensions retained as open obligations.", "sources": [ { "role": "primary", "url": "https://docs.google.com/document/d/1JNy9v-iny6b0a1RK1u9NvYtr-fFibdHyNJDuipF0Hbk" }, { "role": "site", "url": "https://app.notion.com/p/3a046094fd30810bbfddc9286d9c42fe" } ], "identity_links": [], "certificates": [], "dependencies": [], "tests": [], "implementations": [] }, { "id": 51, "key": "FRM-51", "formalism": "PQSPI 13-Pillar Protocol Grammar", "domain": "Invariant grammar", "claim_status": "Structural formalism", "canonical": false, "current": true, "modalities": [ "Symbolic", "Experimental obligation" ], "evidence_band": "OPEN_STRUCTURAL", "last_reviewed": "2026-07-16", "summary": "Typed sequence for synchronization, continuity binding, representation, monitoring, recovery, harm-bounded response, and closure. Individual projectors and quantitative tests remain to be defined.", "sources": [ { "role": "primary", "url": "https://docs.google.com/document/d/12pkFKQ9dCx_1x6vBC6n-uoNSSWzJ0lwSADFkEfprtBU" }, { "role": "site", "url": "https://app.notion.com/p/3a046094fd30810bbfddc9286d9c42fe" } ], "identity_links": [], "certificates": [], "dependencies": [], "tests": [], "implementations": [] }, { "id": 52, "key": "FRM-52", "formalism": "PQSPI Continuity Source-Term Model", "domain": "Open closure", "claim_status": "Conditional / open", "canonical": false, "current": true, "modalities": [ "Symbolic", "Simulation", "Experimental obligation" ], "evidence_band": "OPEN_CONDITIONAL + E2 component", "last_reviewed": "2026-07-16", "summary": "Proposed information-balance PDE with a recursive and cryptographic source term. State space, units, constitutive laws, operator typing, observables, and empirical calibration remain open.", "sources": [ { "role": "primary", "url": "https://docs.google.com/document/d/1H2W-Ar_pG3RYboxEqVua3m1kNAvT8pBMdzS7tw-JtxY" }, { "role": "site", "url": "https://app.notion.com/p/3a046094fd30810bbfddc9286d9c42fe" } ], "identity_links": [], "certificates": [], "dependencies": [], "tests": [], "implementations": [] }, { "id": 53, "key": "FRM-53", "formalism": "Post-Quantum Secure Phonon Interface", "domain": "Engineering / applications", "claim_status": "Engineering / speculative", "canonical": false, "current": true, "modalities": [ "Symbolic", "Simulation", "Hardware", "Experimental obligation" ], "evidence_band": "OPEN_ENGINEERING + E2 component", "last_reviewed": "2026-07-16", "summary": "Historical physical-interface branch of PQSPI using graph modes, resonant substrate monitoring, and proposed phononic security. Conventional mode physics is separable from unverified informational, neutrino, vacuum, and observer-triggered bridges.", "sources": [ { "role": "primary", "url": "https://docs.google.com/document/d/1YN6yHu307NaAmlrTNFHwAQPklLeJbEikuhacZJFZrfU" }, { "role": "site", "url": "https://app.notion.com/p/3a046094fd30810bbfddc9286d9c42fe" } ], "identity_links": [], "certificates": [], "dependencies": [], "tests": [], "implementations": [] }, { "id": 57, "key": "FRM-57", "formalism": "PGO Composite Metamaterial Branch", "domain": "Engineering / applications", "claim_status": "Engineering / speculative", "canonical": false, "current": true, "modalities": [ "Symbolic", "Simulation", "Hardware", "Experimental obligation" ], "evidence_band": "OPEN_ENGINEERING + E2 component", "last_reviewed": "2026-07-17", "summary": "Polymer–graphene–oxide multilayer proposal using acoustic confinement, graphene electron–phonon and plasmonic coupling, and oxide dielectric boundaries for THz, sensing, and thermal applications. Integrated-device measurements remain pending.", "sources": [ { "role": "primary", "url": "https://docs.google.com/document/d/1dYaqkzfFzz5O-Pv229i54f4XceroCfGJjOof5own9KQ" }, { "role": "site", "url": "https://app.notion.com/p/3a046094fd3081bd9c76fd676d812aad" } ], "identity_links": [], "certificates": [], "dependencies": [], "tests": [], "implementations": [] }, { "id": 58, "key": "FRM-58", "formalism": "Passive Radiative-Cooling Metamaterial", "domain": "Engineering / applications", "claim_status": "Conditional / open", "canonical": false, "current": true, "modalities": [ "Symbolic", "Python", "Simulation", "Hardware", "Experimental obligation" ], "evidence_band": "OPEN_CONDITIONAL + E2 component", "last_reviewed": "2026-07-17", "summary": "PET, reflective-layer, and infrared-emissive coating program for passive cooling. Spectral targets, manufacturing, and applications are documented; calibrated outdoor performance, durability, and economics remain validation targets.", "sources": [ { "role": "primary", "url": "https://docs.google.com/document/d/1Jyu7sstmbwJhI5-DFzlN8ER2tfAVXaI_Wk_9Es5uSMs" }, { "role": "site", "url": "https://app.notion.com/p/3a046094fd3081bd9c76fd676d812aad" } ], "identity_links": [], "certificates": [], "dependencies": [], "tests": [], "implementations": [] }, { "id": 59, "key": "FRM-59", "formalism": "Fractals and Hyperbolic Geometry Atlas", "domain": "Geodesic / metric", "claim_status": "Structural formalism", "canonical": true, "current": true, "modalities": [ "Symbolic", "Python", "Simulation", "Experimental obligation" ], "evidence_band": "OPEN_STRUCTURAL + E2 component", "last_reviewed": "2026-07-17", "summary": "Canonical site atlas for fractal dimensions, multifractal measures, hyperbolic metrics, harmonic spectra, quantum models, Python laboratories, E47 mapping boundaries, and experimental obligations.", "sources": [ { "role": "primary", "url": "https://docs.google.com/document/d/1WbMh8floN-_i3O5kljhL6RO8tkG_d8Ixui6AhypECwY" }, { "role": "site", "url": "https://app.notion.com/p/3a046094fd3081aea920c4ebf9ec6e20" } ], "identity_links": [], "certificates": [], "dependencies": [], "tests": [], "implementations": [] }, { "id": 60, "key": "FRM-60", "formalism": "Fractal Quantum Geometry Python Laboratory", "domain": "Numerical / spatial", "claim_status": "Conditional / open", "canonical": false, "current": true, "modalities": [ "Python", "Simulation", "Experimental obligation" ], "evidence_band": "OPEN_CONDITIONAL + E2 component", "last_reviewed": "2026-07-17", "summary": "Recursive Fourier field, scaling proxy, toy invariants, Kuramoto coherence, frequency-spread, and ring-winding simulator. Outputs are parameter-dependent computational scaffolds rather than universal constants.", "sources": [ { "role": "primary", "url": "https://docs.google.com/document/d/1fRtsZ-zoTRbiKdgjXFyDnFDmYvnlm9jt_ZQnjYJhX3w" }, { "role": "site", "url": "https://app.notion.com/p/3a046094fd3081aea920c4ebf9ec6e20" } ], "identity_links": [], "certificates": [], "dependencies": [], "tests": [], "implementations": [] }, { "id": 61, "key": "FRM-61", "formalism": "Hyperbolic Harmonic Identity Formalism", "domain": "Geodesic / metric", "claim_status": "Conditional / open", "canonical": false, "current": true, "modalities": [ "Symbolic", "Simulation", "Experimental obligation" ], "evidence_band": "OPEN_CONDITIONAL + E2 component", "last_reviewed": "2026-07-17", "summary": "Represents recursive or identity states through Laplace–Beltrami harmonics on negatively curved manifolds. The spectral representation is valid after metric and boundary data are fixed; identity persistence and holographic interpretations remain open.", "sources": [ { "role": "primary", "url": "https://docs.google.com/document/d/1WbMh8floN-_i3O5kljhL6RO8tkG_d8Ixui6AhypECwY" }, { "role": "site", "url": "https://app.notion.com/p/3a046094fd3081aea920c4ebf9ec6e20" } ], "identity_links": [], "certificates": [], "dependencies": [], "tests": [], "implementations": [] }, { "id": 62, "key": "FRM-62", "formalism": "Fractal Schrödinger and Multifractal Localization Program", "domain": "Quantum information", "claim_status": "Structural formalism", "canonical": false, "current": true, "modalities": [ "Symbolic", "Python", "Simulation", "Experimental obligation" ], "evidence_band": "OPEN_STRUCTURAL + E2 component", "last_reviewed": "2026-07-17", "summary": "Schrödinger equations with scale-dependent potentials, generalized dimensions, singularity spectra, inverse participation ratios, and Anderson-localization tests. Complete archived runs and dedicated QuTiP validation remain pending.", "sources": [ { "role": "primary", "url": "https://docs.google.com/document/d/1YDLEAFSVwjr-n5tV7wIznSltSNlrkAhW14nXkanK2tE" }, { "role": "site", "url": "https://app.notion.com/p/3a046094fd3081aea920c4ebf9ec6e20" } ], "identity_links": [], "certificates": [], "dependencies": [], "tests": [], "implementations": [] }, { "id": 63, "key": "FRM-63", "formalism": "Liquid Fractal Cognition and Consciousness Geometry", "domain": "Open closure", "claim_status": "Engineering / speculative", "canonical": false, "current": true, "modalities": [ "Symbolic", "Python", "Simulation", "Experimental obligation" ], "evidence_band": "OPEN_ENGINEERING + E2 component", "last_reviewed": "2026-07-17", "summary": "Continuity, Madelung, fractal-scaling, and proposed consciousness-curvature synthesis. Standard field identities are separated from unverified claims of consciousness, persistent identity, universal thresholds, or physical hyperbolic ontology.", "sources": [ { "role": "primary", "url": "https://docs.google.com/document/d/1CdwXNfeH2ZL4f8jeJf9msTrb6oRKESurLRvaGlxpZ-0" }, { "role": "site", "url": "https://app.notion.com/p/3a046094fd3081aea920c4ebf9ec6e20" } ], "identity_links": [], "certificates": [], "dependencies": [], "tests": [], "implementations": [] }, { "id": 64, "key": "FRM-64", "formalism": "Quantum Information Theory", "domain": "Quantum information", "claim_status": "Structural formalism", "canonical": true, "current": true, "modalities": [ "Symbolic", "QuTiP", "VQE", "Simulation", "Experimental obligation" ], "evidence_band": "OPEN_STRUCTURAL + E2 component", "last_reviewed": "2026-07-17", "summary": "Canonical umbrella for states, observables, measurements, CPTP channels, entropy, coherence, entanglement, open systems, ground-state algorithms, quantum error correction, simulation, and the typed boundary between E47 algebra and physical realization.", "sources": [ { "role": "primary", "url": "https://docs.google.com/document/d/1e4ERlF2o2vRWsIB2X-tEB9ClG1dKkUjne082SjrmOGc" }, { "role": "site", "url": "https://app.notion.com/p/3a046094fd3081f4b4eadbf14d26d123" } ], "identity_links": [], "certificates": [], "dependencies": [], "tests": [], "implementations": [] }, { "id": 65, "key": "FRM-65", "formalism": "Hydrogen Bromide Quantum Molecular Model", "domain": "Quantum information", "claim_status": "Conditional / open", "canonical": true, "current": true, "modalities": [ "Symbolic", "Python", "QuTiP", "VQE", "Simulation", "Experimental obligation" ], "evidence_band": "OPEN_CONDITIONAL + E2 component", "last_reviewed": "2026-07-17", "summary": "HBr as a model for Born–Oppenheimer electronic structure, Morse rovibrational physics, halide trends, variational ground states, open-system relaxation, VQE/CVQE, and entropy distinctions. Established molecular physics is separated from the unproved E47 and 47/125 bridge.", "sources": [ { "role": "primary", "url": "https://docs.google.com/document/d/1fWpnY4uqBsOEZI36WLkqeW0MuCMR0JX_--x2pScazm0" }, { "role": "site", "url": "https://app.notion.com/p/3a046094fd308132ad40c335095a237d" } ], "identity_links": [], "certificates": [], "dependencies": [], "tests": [], "implementations": [] }, { "id": 66, "key": "FRM-66", "formalism": "NRL–IonQ Hydronium CVQE Corrosion Benchmark", "domain": "Quantum information", "claim_status": "Exact / computationally verified", "canonical": false, "current": true, "modalities": [ "VQE", "Hardware", "Simulation" ], "evidence_band": "E0/E1 + E2 component", "last_reviewed": "2026-07-17", "summary": "External NRL–IonQ ground-state CVQE benchmark for hydronium H3O+ on IonQ Aria, relevant to aqueous protonic diffusion and corrosion. It is not an HBr experiment and does not report KKP quantities such as 0.376 or E_RI=1.67.", "sources": [ { "role": "primary", "url": "https://meetings.aps.org/Meeting/MAR24/Session/K15.1" }, { "role": "site", "url": "https://app.notion.com/p/3a046094fd308132ad40c335095a237d" } ], "identity_links": [], "certificates": [], "dependencies": [], "tests": [], "implementations": [] }, { "id": 67, "key": "FRM-67", "formalism": "Visual Research Archive", "domain": "Invariant grammar", "claim_status": "Structural formalism", "canonical": true, "current": true, "modalities": [ "Symbolic", "Python" ], "evidence_band": "OPEN_STRUCTURAL", "last_reviewed": "2026-07-17", "summary": "Canonical provenance and correction archive for original research plates, executable validation, revised notation, corrected multiplicities, poetry, and open physical bridges.", "sources": [ { "role": "site", "url": "https://app.notion.com/p/3a046094fd3081899679d908c370b6d7" } ], "identity_links": [], "certificates": [], "dependencies": [], "tests": [], "implementations": [] }, { "id": 68, "key": "FRM-68", "formalism": "Computational Visual Validation Atlas", "domain": "Numerical / spatial", "claim_status": "Structural formalism", "canonical": false, "current": true, "modalities": [ "Python", "Simulation" ], "evidence_band": "OPEN_STRUCTURAL + E2 component", "last_reviewed": "2026-07-17", "summary": "Evidence-calibrated audit of ten computational and theory plates, separating canonical finite algebra, reproducible synthetic simulations, structural models, open domain bridges, and superseded visual artifacts.", "sources": [ { "role": "primary", "url": "https://docs.google.com/document/d/114AdGcd7Lu6uZ35ny1BQAFaA6Z4x-Zm868qkimRw4Cw" }, { "role": "site", "url": "https://app.notion.com/p/3a046094fd3081b89144d28ce7a7e1db" } ], "identity_links": [], "certificates": [], "dependencies": [], "tests": [], "implementations": [] }, { "id": 69, "key": "FRM-69", "formalism": "Canonical Corrected E47 Formalism", "domain": "Core algebra", "claim_status": "Exact / computationally verified", "canonical": true, "current": true, "modalities": [ "Proof", "Symbolic", "Python" ], "evidence_band": "E0/E1", "last_reviewed": "2026-08-13", "summary": "Canonical exact E47 reference with corrected P₄₇=P₆+P₃₀ and joint spectral–symmetry closure A_can=K²+11664(I−Π_sym). The five-dimensional kernel is im(P_can), P_can=P₄₇Π_sym=P₆Π_sym, and optimal Richardson iteration converges exactly at rate 15/17.", "sources": [ { "role": "primary", "url": "https://docs.google.com/document/d/16fPZb2n3Vlyg2PjqlcseY51cYP4XoEkKOn3Vy7-_9no" }, { "role": "site", "url": "https://app.notion.com/p/3a046094fd30811eb015e14e1c5bce7c" } ], "identity_links": [], "certificates": [], "dependencies": [], "tests": [], "implementations": [] }, { "id": 70, "key": "FRM-70", "formalism": "Informational Induction and Emergent-Time Path Integral", "domain": "Scalar / spectral", "claim_status": "Conditional / open", "canonical": false, "current": true, "modalities": [ "Symbolic", "Python" ], "evidence_band": "OPEN_CONDITIONAL", "last_reviewed": "2026-07-21", "summary": "Python/SymPy validates the algebraic consequences of F_I=-dPhi_C/dt. It rejects grad C != 0 => F_I != 0 without time dependence, and parses the corrected path integral as integral (dI/dC)dC = Delta I. Physical-time equivalence remains an open bridge claim.", "sources": [ { "role": "primary", "url": "https://app.notion.com/p/3a546094fd3081a7a481c8c3fb4a68e3" }, { "role": "site", "url": "https://app.notion.com/p/3a046094fd30817bb4a6e317dd633482" } ], "identity_links": [], "certificates": [], "dependencies": [], "tests": [], "implementations": [] }, { "id": 71, "key": "FRM-71", "formalism": "Unified Contraction Field Formalism (UCFF): A Recursive Framework for Spacetime and Information Geometry", "domain": "Invariant grammar", "claim_status": "Conditional / open", "canonical": true, "current": true, "modalities": [ "Proof", "Symbolic", "Python", "Simulation", "Experimental obligation" ], "evidence_band": "OPEN_CONDITIONAL + E2 component", "last_reviewed": "2026-07-22", "summary": "Canonical UCFF record integrating exact E47 spectral-kernel results with conditional quantum, lattice, diffusion, wave, statistical, and information-geometric constructions. Machine audit: 13/14 checks passed; the finite-β=0.001 Gibbs threshold missed by 3.062225596929387e-7 while the β→∞ convergence theorem remains exact. Physical consequences require the explicitly declared generator maps and are not promoted beyond those constructions.", "sources": [ { "role": "primary", "url": "https://docs.google.com/document/d/1Ncmb4GwKhTnby7gzlIh_T5VzQx8HRTdsFvjSV4PWtwY" }, { "role": "site", "url": "https://app.notion.com/p/3a546094fd308194bbf7d9c74ef7ecf9" } ], "identity_links": [], "certificates": [], "dependencies": [], "tests": [], "implementations": [] }, { "id": 72, "key": "FRM-72", "formalism": "E47 Projector-Valued Vacuum and Einstein–AQSFT Closure", "domain": "Open closure", "claim_status": "Conditional / open", "canonical": true, "current": true, "modalities": [ "Proof", "Symbolic", "Python", "Simulation", "Experimental obligation" ], "evidence_band": "OPEN_CONDITIONAL + E2 component", "last_reviewed": "2026-09-22", "summary": "Finite E47 spectral algebra remains exact/E0-E1. MC-E47-EINSTEIN-FULL-CLOSURE/1.0 passes 28/28 for the marked nonlinear Einstein branch. Successor MC-E47-INTRINSIC-SPACETIME-UNMARKED/1.0 passes 24/24 and closes intrinsic Lorentzian 3+1 construction plus injectivity onto a 47-real-dimensional image in the completely unmarked vacuum-Einstein quotient using the full locked tensor-cube datum. FRM-72 remains Conditional/open for the vacuum-density constitutive law, dimensionful scale, broader Einstein–matter closure, and empirical discrimination.", "sources": [ { "role": "primary", "url": "https://docs.google.com/document/d/1Laag1PuAoV_G4itkRuSaltPrS552rvcBpKCgE4gkFa8" }, { "role": "site", "url": "https://app.notion.com/p/d7910a7abca442af9298dee80f392fe2" } ], "identity_links": [], "certificates": [], "dependencies": [], "tests": [], "implementations": [] }, { "id": 73, "key": "FRM-73", "formalism": "Discrete Hodge Correspondence Citizen", "domain": "Core algebra", "claim_status": "Exact / computationally verified", "canonical": true, "current": true, "modalities": [ "Proof", "Python" ], "evidence_band": "E0/E1", "last_reviewed": "2026-07-25", "summary": "The canonical identity ker Δ_q(ε) ≅ H_q(K_{ε};R) with dim ker Δ_q = β_q, numerically cross-checked against an independent persistence oracle.", "sources": [ { "role": "primary", "url": "https://docs.google.com/document/d/1hc4odui8d3qg-SvMXofpp8NJ0Z3e_lr8avHSxds5GMI" } ], "identity_links": [], "certificates": [], "dependencies": [], "tests": [], "implementations": [] }, { "id": 74, "key": "FRM-74", "formalism": "Persistence Margin Scale Selector Citizen", "domain": "Numerical / spatial", "claim_status": "Exact / computationally verified", "canonical": true, "current": true, "modalities": [ "Proof", "Python" ], "evidence_band": "E0/E1", "last_reviewed": "2026-07-25", "summary": "Selects ε* by maximizing the minimum distance to birth and death along an active persistence interval, avoiding the sparse-graph tie failure of raw bar length.", "sources": [ { "role": "primary", "url": "https://docs.google.com/document/d/1hc4odui8d3qg-SvMXofpp8NJ0Z3e_lr8avHSxds5GMI" } ], "identity_links": [], "certificates": [], "dependencies": [], "tests": [], "implementations": [] }, { "id": 75, "key": "FRM-75", "formalism": "Midpoint Discrete de Rham Bridge Citizen", "domain": "Core algebra", "claim_status": "Exact / computationally verified", "canonical": true, "current": true, "modalities": [ "Proof", "Python" ], "evidence_band": "E0/E1", "last_reviewed": "2026-07-25", "summary": "Type-correct map from vertex velocities to edge cochains; translations map to exact cochains while rotations around a protected loop carry nonzero harmonic circulation.", "sources": [ { "role": "primary", "url": "https://docs.google.com/document/d/1hc4odui8d3qg-SvMXofpp8NJ0Z3e_lr8avHSxds5GMI" } ], "identity_links": [], "certificates": [], "dependencies": [], "tests": [], "implementations": [] }, { "id": 76, "key": "FRM-76", "formalism": "Admissible Swarm Kernel Citizen", "domain": "Core algebra", "claim_status": "Exact / computationally verified", "canonical": true, "current": true, "modalities": [ "Proof", "Python" ], "evidence_band": "E0/E1", "last_reviewed": "2026-07-25", "summary": "Single type-correct kernel combining safety constraints with harmonic coordination, replacing the invalid product of projectors acting on different spaces.", "sources": [ { "role": "primary", "url": "https://docs.google.com/document/d/1hc4odui8d3qg-SvMXofpp8NJ0Z3e_lr8avHSxds5GMI" } ], "identity_links": [], "certificates": [], "dependencies": [], "tests": [], "implementations": [] }, { "id": 77, "key": "FRM-77", "formalism": "Persistence-Gated Dwell-Time Citizen", "domain": "Numerical / spatial", "claim_status": "Exact / computationally verified", "canonical": true, "current": true, "modalities": [ "Proof", "Python" ], "evidence_band": "E0/E1", "last_reviewed": "2026-07-25", "summary": "Control-law-independent certified interval during which the selected persistence class cannot fall below threshold under bounded agent speed.", "sources": [ { "role": "primary", "url": "https://docs.google.com/document/d/1hc4odui8d3qg-SvMXofpp8NJ0Z3e_lr8avHSxds5GMI" } ], "identity_links": [], "certificates": [], "dependencies": [], "tests": [], "implementations": [] }, { "id": 78, "key": "FRM-78", "formalism": "Consensus-Limited Certified Speed Citizen", "domain": "Numerical / spatial", "claim_status": "Exact / computationally verified", "canonical": true, "current": true, "modalities": [ "Proof", "Python" ], "evidence_band": "E0/E1", "last_reviewed": "2026-07-25", "summary": "Relates topological persistence margin to communication mixing time and yields a necessary certified maximum swarm speed.", "sources": [ { "role": "primary", "url": "https://docs.google.com/document/d/1hc4odui8d3qg-SvMXofpp8NJ0Z3e_lr8avHSxds5GMI" } ], "identity_links": [], "certificates": [], "dependencies": [], "tests": [], "implementations": [] }, { "id": 79, "key": "FRM-79", "formalism": "Persistence-Gated Execution Gate Citizen", "domain": "Engineering / applications", "claim_status": "Structural formalism", "canonical": true, "current": true, "modalities": [ "Symbolic", "Python", "Experimental obligation" ], "evidence_band": "OPEN_STRUCTURAL", "last_reviewed": "2026-07-25", "summary": "Basis-free execution gate combining persistence, Hodge spectral gap, separation, safety residual, and target Betti equality; commands fallback whenever any certificate condition fails.", "sources": [ { "role": "primary", "url": "https://docs.google.com/document/d/1hc4odui8d3qg-SvMXofpp8NJ0Z3e_lr8avHSxds5GMI" } ], "identity_links": [], "certificates": [], "dependencies": [], "tests": [], "implementations": [] }, { "id": 80, "key": "FRM-80", "formalism": "Babylonian Fixed-Point Kernel Citizen", "domain": "Core algebra", "claim_status": "Exact / computationally verified", "canonical": true, "current": true, "modalities": [ "Proof", "Python", "QuTiP", "Simulation" ], "evidence_band": "E0/E1 + E2 component", "last_reviewed": "2026-07-25", "summary": "Validated identity K_a(x)=x-1/2(x+a/x), with ker K_a={x>0:x^2=a}. Pedigree: E0 exact algebra; Python deterministic convergence; quantum state-encoding invariance; machine certificate 15/15 classical and 8/8 quantum checks passed.", "sources": [], "identity_links": [], "certificates": [], "dependencies": [], "tests": [], "implementations": [] }, { "id": 81, "key": "FRM-81", "formalism": "Quadratic Error Recursion Citizen", "domain": "Core algebra", "claim_status": "Exact / computationally verified", "canonical": true, "current": true, "modalities": [ "Proof", "Python", "Simulation" ], "evidence_band": "E0/E1 + E2 component", "last_reviewed": "2026-07-25", "summary": "Exact error identity e_{n+1}=e_n^2/(2x_n), machine-verified stepwise across multiple targets. Pedigree: E0 derivation; Python residual verification; 15/15 classical checks passed.", "sources": [], "identity_links": [], "certificates": [], "dependencies": [], "tests": [], "implementations": [] }, { "id": 82, "key": "FRM-82", "formalism": "Bounded-Depth Deterministic Approximation Citizen", "domain": "Numerical / spatial", "claim_status": "Exact / computationally verified", "canonical": true, "current": true, "modalities": [ "Python", "Simulation" ], "evidence_band": "E0/E1 + E2 component", "last_reviewed": "2026-07-25", "summary": "Fixed-depth map x_10=F_a^10(x_0) verified as deterministic and reproducible. Pedigree: E1 finite-step numerical certificate; Python machine verification; archived JSON certificate.", "sources": [], "identity_links": [], "certificates": [], "dependencies": [], "tests": [], "implementations": [] }, { "id": 83, "key": "FRM-83", "formalism": "Rational Coherence Gate Citizen", "domain": "Invariant grammar", "claim_status": "Structural formalism", "canonical": true, "current": true, "modalities": [ "Proof", "Python", "QuTiP", "Simulation" ], "evidence_band": "OPEN_STRUCTURAL + E2 component", "last_reviewed": "2026-07-25", "summary": "Exact rational admissibility relation 125x=47a, distinct from Newton convergence except at the unique compatibility point. Pedigree: E0 rational identity; Python verification; quantum projector completeness and invariance tests; machine certificate 8/8 quantum checks passed.", "sources": [], "identity_links": [], "certificates": [], "dependencies": [], "tests": [], "implementations": [] }, { "id": 84, "key": "FRM-84", "formalism": "Rational–Newton Compatibility Point Citizen", "domain": "Core algebra", "claim_status": "Exact / computationally verified", "canonical": true, "current": true, "modalities": [ "Proof", "Python", "Simulation" ], "evidence_band": "E0/E1 + E2 component", "last_reviewed": "2026-07-25", "summary": "Unique positive compatibility point a=(125/47)^2 where (47/125)a=sqrt(a). Pedigree: E0 exact theorem; Python numerical confirmation; machine certificate passed.", "sources": [], "identity_links": [], "certificates": [], "dependencies": [], "tests": [], "implementations": [] }, { "id": 85, "key": "FRM-85", "formalism": "Clock-Latency Lower Bound Citizen", "domain": "Engineering / applications", "claim_status": "Exact / computationally verified", "canonical": true, "current": true, "modalities": [ "Proof", "Python", "Simulation" ], "evidence_band": "E0/E1 + E2 component", "last_reviewed": "2026-07-25", "summary": "Arithmetic lower bound T_latency>=N_iter/f_clk verified for ten registered stages at 3 GHz, yielding at least 3.333 ns rather than 1.25 ns. Pedigree: E0 timing arithmetic; Python machine verification.", "sources": [], "identity_links": [], "certificates": [], "dependencies": [], "tests": [], "implementations": [] }, { "id": 86, "key": "FRM-86", "formalism": "Fixed-Point Residual Gate Citizen", "domain": "Invariant grammar", "claim_status": "Exact / computationally verified", "canonical": true, "current": true, "modalities": [ "Proof", "Python", "Simulation" ], "evidence_band": "E0/E1 + E2 component", "last_reviewed": "2026-07-25", "summary": "Convergence-valid criterion |x_n^2-a|