Home › Reproduce Reproduce a certificate Exact commands for named frozen outputs. Passing a run is implementation conformance for that named object. Conformance tests do not establish theorem validity. G₆ packaging is not a theorem joining the theories. The tuple exists definitionally because unrelated typed objects can always be placed in a tuple. A canonical hash proves equality of a named byte string. Aggregating separate maps into interfaces=PASS is a historical implementation outcome, not current source-map discipline. Agents: start at /archive/MACHINE.json (schema OMEGA_NAUGHT_MACHINE/1.0) for object-scoped commands, hashes, and claims_not_made. This page supplies. Acquisition recipes and named run commands for construction, proofs, arithmetic, cubature, and historical G₆. Hypotheses / scope. Each command is scoped to one object. A PASS is implementation conformance, not theorem validity. Evidence. Recorded execution where a named runtime is hosted. lake and Julia companion have not been run here. Publication: not peer reviewed. Independent third-party reproduction: none recorded. Full status record . Concrete uses Each demonstration names its returned data and verification method. Experimental pages keep their own setup and records. Uses with demonstrations and verification methods. Use Demonstration Verification Geometric interchange Export OMEGA_KERNEL_NODES/1.0 and rebuild the labeled kernel. Compare labels, frame, and true ε against the hosted node log. Deterministic arithmetic replay Forward floor map on a seed in D₁₅ using exact BigInt Q, S. ⌊Qd/S⌋ and remainder identity Qd = S d′ + ρ. Exact reconstruction Recover 399 from remainders of 399→135→45→15→5→1→0. Divisibility, remainder bounds, and reverse identity. Spherical polynomial integration Apply a published Class-I rule inside its certified degree. Exact moment identities on the named frequency; 23–24 coefficient payload not hosted. AI-assisted inspection Fetch MACHINE.json, resolve an object, verify hashes, run the named checker. Scoped PASS/FAIL with source and execution evidence. Independent axes stay independent. Acquisition and run recipes Worked AI workflow Fetch /archive/MACHINE.json (schema OMEGA_NAUGHT_MACHINE/1.0). Select a named object or claim. Independent axes stay independent. Retrieve its definitions and source artifacts. Verify the artifact hashes. Run only the specified checker for that object. Compare the result against the stated expectation. Return a scoped result with source and execution evidence. Resolve aliases certificate-f22-69, certificate-f22-70, and g6-release-1-1 in source_registry. Do not invent cubature 10–21 or 23–24 payloads. Software dependencies Setup transcription OMEGA_NAUGHT_Software_Dependencies.docx (45,009 bytes, SHA-256 3841413f…). It is not an eighth source paper. The G₆ and OMEGA_NAUGHT/1.0 Rust runners declare no third-party crates: after a Rust toolchain, Cargo, and platform build tools are installed, cargo run --release --offline --locked needs no crate download. Lean/Mathlib acquisition still needs Git and network for a visitor re-run; this archive's lake build PASS on 2026-09-13 is hosted at evidence/current/ . Julia companion uses standard libraries Dates, SHA, and TOML only. Plots is not required for that companion. Declared runtimes and libraries. Component Runtime and libraries Version status G₆ Rust runner Rust and Cargo; no external crates Edition 2021; lock format 4; compiler unpinned Rust conformance runner Rust and Cargo; no external crates Edition 2021; lock format 4; compiler unpinned G₆ Julia runner Julia; standard library SHA No compatibility bound in its Project.toml Julia proof companion Julia; standard libraries Dates, SHA, TOML Compatibility 1.11; recorded runtime 1.11.6 Lean formalization Lean, Lake, Git; Mathlib and eight inherited packages Lean 4.19.0; exact Git revisions in lake-manifest.json; lake build PASS on this archive 2026-09-13 Frequency-22 verifiers Python standard library; Julia SHA and Printf Archived PASS on Python 3.12.13 and Julia 1.11.6; Python 3.10+ is sufficient. Current Python revision r2 refuses python3 -O Typed-map audit Python and SymPy sympy>=1.12; no exact environment lock Geometry checks and drift Python and NumPy; local geometry module NumPy version unpinned Julia geometry plot Julia; LinearAlgebra, Printf; external Plots Plots is not required for the proof companion; install it in a separate environment Scalar-interface certificate Python standard-library fractions No third-party Python dependency Publication status: six Zenodo preprints and one Zenodo report. Paper VII is version 1.6 at DOI 10.5281/zenodo.22233573. Not peer reviewed unless a specific work is later linked to a peer-reviewed publication. Computational reproducibility: exact verifiers and/or finite certificates are supplied where listed. Independent third-party reproduction: none recorded on this site unless a named reproduction and its public evidence are linked. Historical G₆ artifact — G6_RELEASE/1.1 canonical record Implementations: Rust, Julia, and the pinned TypeScript snapshot . From an empty folder Download, extract if needed, verify hashes, install the named dependency, then run. Commands below use the public origin. mkdir g6-repro && cd g6-repro curl -fsSO https://omega-naught.grok.me/releases/G6_RELEASE_1.1/G6_RELEASE_1.1.zip curl -fsSO https://omega-naught.grok.me/releases/G6_RELEASE_1.1/G6_RELEASE_1.1.zip.sha256 curl -fsSO https://omega-naught.grok.me/releases/G6_RELEASE_1.1/RELEASE.json sha256sum -c G6_RELEASE_1.1.zip.sha256 python3 - <<'PY' import hashlib, pathlib got=hashlib.sha256(pathlib.Path('RELEASE.json').read_bytes()).hexdigest() assert got=='f63ae1c2d595b4805ba9d36687a828fd87200febe01079b184723f7d5eaf746c' print('RELEASE.json matches frozen envelope') PY unzip -q G6_RELEASE_1.1.zip cd G6_RELEASE_1.1/g6 # Requires an installed Julia runtime, a Rust toolchain, Cargo, and platform build tools. # The G6 Rust runner declares no third-party crates. julia --startup-file=no julia/run.jl (cd rust && cargo run --release --offline --locked) Copy run command Named run commands cd G6_RELEASE_1.1/g6 Copy run command julia --startup-file=no julia/run.jl Copy run command (cd rust && cargo run --release --offline --locked) Copy run command Expected: canonical_sha256=92187a21a7ad8ecef384eda3a654aaa49daf46a31422e168eb5871d218c949fa G6_RELEASE/1.1 RELEASE.json Legacy G₆ specification (noindex provenance copy) orbit_masses_f1_f9.csv Software-dependencies transcription Requires an installed Rust toolchain, Cargo, and the platform build tools. The G₆ Rust runner declares no third-party crates; cargo run --release --offline --locked is the conformance run. cargo test is the optional test suite, not the conformance run. The live specification HTML is a provenance copy of a frozen contract; it is not the current semantic architecture. OMEGA_NAUGHT/1.0 named manifest outputs Implementations: Python, Julia, Java, and Rust . From an empty folder Download, extract if needed, verify hashes, install the named dependency, then run. Commands below use the public origin. mkdir omega-naught-10 && cd omega-naught-10 curl -fsSO https://omega-naught.grok.me/conformance/omega_naught_conformance.py curl -fsSO https://omega-naught.grok.me/g6/OMEGA_NAUGHT_1_0.txt python3 omega_naught_conformance.py OMEGA_NAUGHT_1_0.txt Copy run command Named run commands python3 omega_naught_conformance.py OMEGA_NAUGHT_1_0.txt Copy run command omega_naught_conformance.py Web-copy .txt manifest Separate OMEGA_NAUGHT/1.0 conformance: Python, Julia, Java, and Rust. Frequency-22 exact certificate Implementations: Python 3.10+ (archived PASS on 3.12.13) and Julia 1.11.6, run separately . From an empty folder Download, extract if needed, verify hashes, install the named dependency, then run. Commands below use the public origin. mkdir omega-f22 && cd omega-f22 curl -fsSO https://omega-naught.grok.me/cubature/Omega_Naught_ClassI_f22_certificate_package.zip python3 - <<'PY' import hashlib, pathlib got=hashlib.sha256(pathlib.Path('Omega_Naught_ClassI_f22_certificate_package.zip').read_bytes()).hexdigest() assert got=='f63c43e1dbd1ac5b7009e66fe577b27e8a231f90fe6b01eef779147826ae55eb', got print('zip digest matches') PY unzip -q Omega_Naught_ClassI_f22_certificate_package.zip # Flat archive: files extract into the current directory. Python 3.10+ is sufficient. sha256sum -c SHA256SUMS.txt python3 Omega_Naught_ClassI_f22_exact_verifier.py julia --startup-file=no OmegaNaughtClassIF22ExactVerifier.jl # Current website revision r2. Not a zip member. Original inventory is unchanged. curl -fsSLo Omega_Naught_ClassI_f22_exact_verifier.r2.py https://omega-naught.grok.me/cubature/Omega_Naught_ClassI_f22_exact_verifier.r2.py python3 - <<'PY' import hashlib, pathlib got=hashlib.sha256(pathlib.Path('Omega_Naught_ClassI_f22_exact_verifier.r2.py').read_bytes()).hexdigest() assert got=='d9b2450ef16b138f73f89cbc1ee3a298010d27bcf1c184d5de57246a34376387', got print('r2 digest matches') PY python3 Omega_Naught_ClassI_f22_exact_verifier.r2.py # python3 -O Omega_Naught_ClassI_f22_exact_verifier.r2.py # must refuse before certificate computation Copy run command Named run commands sha256sum -c SHA256SUMS.txt Copy run command python3 Omega_Naught_ClassI_f22_exact_verifier.py Copy run command python3 Omega_Naught_ClassI_f22_exact_verifier.r2.py Copy run command julia --startup-file=no OmegaNaughtClassIF22ExactVerifier.jl Copy run command Omega_Naught_ClassI_f22_exact_verifier.r2.py (current revision r2) Omega_Naught_ClassI_f22_exact_verifier.py (archived original) OmegaNaughtClassIF22ExactVerifier.jl Current Python verifier is website revision r2: it refuses python3 -O, python3 -OO, and PYTHONOPTIMIZE before certificate computation. The original 16,972-byte verifier (SHA-256 ae615d26…) remains the zip and SHA256SUMS inventory member. Revision r2 does not change the certificate, the theorem, or the canonical solution digests. Published Julia source executed on official Julia 1.11.6; both the Python and Julia verifiers print CERTIFICATE PASS and the unchanged canonical solution digests. Implementation conformance: PASS. The corrected certificate package was executed with Python 3.12.13 and Julia 1.11.6 on Linux x86-64. Both exact implementations report (11, 11, 0) as the minimum positive degree-69 orbit, (21, 1, 0) as the negative degree-71 orbit, and identical canonical solution digests. Python and Julia pass separately. This is a two-implementation conformance check, not a claim of external independent reproduction. X₂₃ and X₂₄ existence theorem Implementations: Proof text and printed finite-audit extract; no hosted runnable verifier . From an empty folder Download, extract if needed, verify hashes, install the named dependency, then run. Commands below use the public origin. mkdir omega-f23-f24 && cd omega-f23-f24 curl -fsSO https://omega-naught.grok.me/cubature/X23_X24_positive_existence.md curl -fsSO https://omega-naught.grok.me/cubature/ClassI_Cubature_f23_f24_audit_extract_v1.1.json curl -fsSO https://omega-naught.grok.me/docs/OMEGA_NAUGHT_Typed_Network_Exact_Proof_Dossier_v1.0.pdf # No hosted runnable verifier. The 117 exact Q(√5) masses are not extractable from the dossier PDF. Copy run command X23_X24_positive_existence.md ClassI_Cubature_f23_f24_audit_extract_v1.1.json OMEGA_NAUGHT_Typed_Network_Exact_Proof_Dossier_v1.0.pdf The 5 September 2026 typed-network dossier cites a complete f=23,24 coefficient certificate, exact verifier, and 109-residual ledger as LaTeX filecontents. Those filecontents are not extractable from the hosted PDF. This archive enumerates the printed finite audit data (grid sizes, free orbits, rank witnesses, minima, canonical weight-text hashes, cited payload hashes) and the PDF itself. The 117 exact a+b√5 coefficient pairs and the runnable verifier are not hosted as separate artifacts. Implementation conformance is not run. Independent third-party reproduction is currently recorded as none. A same-environment replay quoted in the dossier is not a clean-room reproduction. Neither argument proves failure or impossibility at any higher degree. 15-bit successor search Implementations: Python 3 . From an empty folder Download, extract if needed, verify hashes, install the named dependency, then run. Commands below use the public origin. mkdir omega-successors && cd omega-successors curl -fsSO https://omega-naught.grok.me/dynamics/Omega_Naught_Successor_Search_Verifier.py curl -fsSO https://omega-naught.grok.me/dynamics/successor_search_certificate.json python3 Omega_Naught_Successor_Search_Verifier.py Copy run command Named run commands python3 Omega_Naught_Successor_Search_Verifier.py Copy run command Omega_Naught_Successor_Search_Verifier.py Finite exact facts against the frozen 60-decimal enclosure of λ. Not an accepted successor. Omega-Alpha July 2026 synthesis Implementations: Python 3 . From an empty folder Download, extract if needed, verify hashes, install the named dependency, then run. Commands below use the public origin. mkdir omega-alpha && cd omega-alpha curl -fsSO https://omega-naught.grok.me/omega-alpha/omega_alpha_reference.py python3 omega_alpha_reference.py Copy run command Named run commands python3 omega_alpha_reference.py Copy run command omega_alpha_reference.py The Python reference checks declared finite identities after the integer protocol constants are fixed. Decimal evaluation of φ, π, and λ is a reproducibility check, not symbolic exactness. Passing tests do not establish theorem validity for Papers I–VI, peer review, or independent third-party reproduction. Paper VII kernel generator Implementations: Python 3; verify_geometry.py requires NumPy. Optional Julia visualization requires Plots in a separate environment, not the proof companion. . From an empty folder Download, extract if needed, verify hashes, install the named dependency, then run. Commands below use the public origin. mkdir omega-kernel && cd omega-kernel mkdir -p generated regenerated curl -fsSLo omega_reference_geometry.py https://omega-naught.grok.me/geometry/kernel/omega_reference_geometry.py curl -fsSLo verify_geometry.py https://omega-naught.grok.me/geometry/kernel/verify_geometry.py curl -fsSLo omega_kernel_oriented_r3.jl https://omega-naught.grok.me/geometry/kernel/omega_kernel_oriented_r3.jl curl -fsSLo generated/OMEGA_local_kernel_v1_6_0.json https://omega-naught.grok.me/geometry/kernel/OMEGA_local_kernel_v1_6_0.json curl -fsSLo generated/OMEGA_local_kernel_v1_6_0.obj https://omega-naught.grok.me/geometry/kernel/OMEGA_local_kernel_v1_6_0.obj python3 - <<'PY' import hashlib, pathlib checks=[ ('generated/OMEGA_local_kernel_v1_6_0.json','b280522bcd2cf63927e8dfd6438f78fa3a2e7af0cbfd484ee9cd55994b9c3753'), ('generated/OMEGA_local_kernel_v1_6_0.obj','2654f85dab5881e9a0659985729450a89d7cc8df3b07035c22a4c4372b10a079'), ] for name, expect in checks: got=hashlib.sha256(pathlib.Path(name).read_bytes()).hexdigest() assert got==expect, (name, got) print('published JSON and OBJ match declared hashes') PY python3 -m pip install numpy python3 verify_geometry.py # Independent generation writes regenerated copies; do not overwrite generated/ published exports. # Generator defaults write into the current working directory; those CWD files are not the published pair. python3 omega_reference_geometry.py --json regenerated/OMEGA_local_kernel_v1_6_0.json --obj regenerated/OMEGA_local_kernel_v1_6_0.obj cmp regenerated/OMEGA_local_kernel_v1_6_0.json generated/OMEGA_local_kernel_v1_6_0.json cmp regenerated/OMEGA_local_kernel_v1_6_0.obj generated/OMEGA_local_kernel_v1_6_0.obj # Optional visualization. Plots is not a proof-companion dependency. julia --project=. -e 'using Pkg; Pkg.add("Plots")' julia --project=. omega_kernel_oriented_r3.jl Copy run command Named run commands python3 -m pip install numpy Copy run command python3 verify_geometry.py Copy run command python3 omega_reference_geometry.py --json regenerated/OMEGA_local_kernel_v1_6_0.json --obj regenerated/OMEGA_local_kernel_v1_6_0.obj Copy run command Expected: PASS all 8 conformance groups, including test_distributed_exports omega_reference_geometry.py verify_geometry.py OMEGA_local_kernel_v1_6_0.json OMEGA_local_kernel_v1_6_0.obj omega_kernel_oriented_r3.jl Place the published JSON and OBJ in generated/ before running the unchanged verifier. Generator defaults write into the current working directory; those CWD files are not the published pair. Independent generation should use --json/--obj into regenerated/. Direct evaluation of the closed landmark formulas, a sampled OBJ polyline, and an optional Julia binary64 visualization. Reconstruction of named coordinates, not a theorem checker for Paper VII. Kernel Construct node log and scalar certificate Implementations: Browser Construct mode; Python 3 standard library for the scalar certificate . From an empty folder Download, extract if needed, verify hashes, install the named dependency, then run. Commands below use the public origin. mkdir omega-construct && cd omega-construct curl -fsSO https://omega-naught.grok.me/geometry/construct/verify_scalar_interface_exact.py curl -fsSO https://omega-naught.grok.me/geometry/construct/omega-kernel-nodes.unit.true.json python3 verify_scalar_interface_exact.py Copy run command Named run commands python3 verify_scalar_interface_exact.py Copy run command Expected: OMEGA scalar interface exact algebra certificate: PASS OMEGA_Kernel_Construct_v1.1.0.pdf omega-kernel-nodes.unit.true.json verify_scalar_interface_exact.py Interface and presentation around paper-vii-kernel.ts. The node log is the transfer record of the proved planar kernel, not a unique shell. Replay stops at kernel stage 15. The Python certificate is exact for Ψ and Φ only; it does not prove Paper VII Euclidean uniqueness. Not independent reproduction. De-branded typed-map audit Implementations: Python 3 with SymPy ≥ 1.12 . From an empty folder Download, extract if needed, verify hashes, install the named dependency, then run. Commands below use the public origin. mkdir omega-typed-maps && cd omega-typed-maps curl -fsSO https://omega-naught.grok.me/network/typed_connection_proof.py curl -fsSO https://omega-naught.grok.me/network/requirements.txt curl -fsSO https://omega-naught.grok.me/network/README.txt python3 -m pip install -r requirements.txt python3 typed_connection_proof.py Copy run command Named run commands python3 -m pip install -r requirements.txt Copy run command python3 typed_connection_proof.py Copy run command Expected: FINITE FLOOR CERTIFICATE: PASS for every integer d in [0,32767] (32768 states; q<lambda certified) typed_connection_proof.py typed_connection_proof.runtime.txt requirements.txt README.txt Python 3 with SymPy ≥ 1.12. Symbolic identities; exact rational enclosures of √5, π, and λ; exhaustive floor equality on D = {0, …, 32767} with q < λ certified; exhaustive 23-step remainder reconstruction on all 32768 seeds; seven malformed-input classes rejected. No binary64 comparison is used in the floor certificate. Homothety of the six kernel marks is Euclidean scaling of the Paper VII configuration, not a unique shell. Radial template identities in the script are algebraic and are not a physical theorem. Passing the named runtime is implementation conformance of that audit, not independent third-party reproduction and not a joining theorem. Lean 4 geometric-provenance formalization Implementations: Python 3.10.21 for the axiom-coverage checker; Lean 4.19.0 / Mathlib v4.19.0 for lake build, which passed on this archive 2026-09-13 . From an empty folder Download, extract if needed, verify hashes, install the named dependency, then run. Commands below use the public origin. mkdir omega-lean && cd omega-lean curl -fsSO https://omega-naught.grok.me/formal/SHA256SUMS python3 - <<'PY' import hashlib, pathlib, urllib.request base='https://omega-naught.grok.me/formal/' for line in pathlib.Path('SHA256SUMS').read_text().splitlines(): line=line.strip() if not line or line.startswith('#'): continue digest, name = line.split(None, 1) dest=pathlib.Path(name) dest.parent.mkdir(parents=True, exist_ok=True) urllib.request.urlretrieve(base+name, dest) got=hashlib.sha256(dest.read_bytes()).hexdigest() if got!=digest: raise SystemExit(f'mismatch {name}') print('all listed members match SHA256SUMS') PY python3 scripts/check_axioms.py evidence/axioms.log python3 scripts/check_axioms.py evidence/current/axioms.log # lake build of these sources was run on this archive on 2026-09-13. # Transcripts: evidence/current/build.log (SHA-256 ddc10580…) and evidence/current/axioms.log (SHA-256 82dae064…). # Re-running lake build needs Lean 4.19.0 / Mathlib v4.19.0; the toolchain is not hosted. Copy run command Named run commands python3 scripts/check_axioms.py evidence/axioms.log Copy run command python3 scripts/check_axioms.py evidence/current/axioms.log Copy run command Expected: Checked 147 theorem reports; axioms: Classical.choice, Quot.sound, propext README.txt README.md Omega/Main.lean SHA256SUMS scripts/check_axioms.py evidence/axioms.log check_axioms.runtime.txt evidence/current/build.log evidence/current/axioms.log evidence/current/ENVIRONMENT.json Hosted .lean sources, lakefile, lean-toolchain, and author evidence logs match the package SHA256SUMS byte-for-byte (28/28). On 2026-09-13 this archive ran lake build and lake env lean Omega/AxiomAudit.lean against those sources: Lean 4.19.0 commit 6caaee842e94, Lake 5.0.0-6caaee8, Mathlib v4.19.0 c44e0c8ee63…. Fresh build.log (1,960 bytes, SHA-256 ddc10580…) ends with Build completed successfully; modules were Built, not Replayed. Fresh axioms.log (11,804 bytes, SHA-256 82dae064…) is byte-identical to the author log: 147 theorem reports; axioms {propext, Classical.choice, Quot.sound}; four theorems depend on no axioms. scripts/check_axioms.py PASS. Hosted sources contain no sorry, admit, or native_decide. The toolchain and .lake cache are not hosted. That kernel-check is machine-checking of the selected maps in this package. It is not an eighth source paper, not a joining theorem, not peer review of Papers I–VII, and not independent reproduction of those papers. Cubature 10–21 remains unpackaged; the 117 exact f=23,24 coefficient pairs are not hosted. Frozen G₆ bytes are unchanged. Julia mathematical proof companion v0.1 Implementations: Julia 1.11.6, standard library (author-supplied environment; not run on this archive) . From an empty folder Download, extract if needed, verify hashes, install the named dependency, then run. Commands below use the public origin. mkdir omega-julia-proofs && cd omega-julia-proofs curl -fsSO https://omega-naught.grok.me/julia-proofs/downloads/OMEGA_NAUGHT_Julia_Proof_v0.1.reconstructed-from-members.zip # This ZIP is labeled reconstructed; it is not the author-stated original container. printf '%s %s\n' 'b5d4e46ac32ac4ec08f96a6fc609fe8c8c3a291b7226809c2e79c3adac2e26ab' 'OMEGA_NAUGHT_Julia_Proof_v0.1.reconstructed-from-members.zip' | sha256sum -c - unzip -q OMEGA_NAUGHT_Julia_Proof_v0.1.reconstructed-from-members.zip cd OMEGA_NAUGHT_Julia_Proof_v0.1 sha256sum -c SHA256SUMS # Requires Julia 1.11.6. Author O0/O3 logs are archived evidence, not a site run. julia --startup-file=no --project=. scripts/check_inventory.jl julia --startup-file=no --project=. run_proofs.jl Copy run command Named run commands julia --startup-file=no --project=. scripts/check_inventory.jl Copy run command julia --startup-file=no --project=. run_proofs.jl Copy run command julia --startup-file=no --project=. scripts/reproduce.jl Copy run command julia --startup-file=no --project=. examples/reconstruction.jl Copy run command Expected: O0 and O3 exit 0; six identical certificate files; 147 indexed declarations. Not generated on this archive. Julia companion page SHA256SUMS README.md THEOREM_GUIDE.md THEOREMS.toml evidence/O0.log (author transcript) Word transcription The 68 original members were recovered from OMEGA_NAUGHT_Julia_Proof_v0.1_Complete_Verbatim.docx and match SHA256SUMS byte-for-byte (74,508 source lines). Author-supplied Julia 1.11.6 O0/O3 run records are archived evidence and are not a run performed by this site. The reproduction driver updates run metadata, so archived evidence should be retained separately from any later execution. The author-stated original ZIP SHA-256 is recorded; those exact container bytes were not recovered from the Word file. This package does not supply public certificate packages for 10 ≤ f ≤ 21 and does not supply the missing exact-weight/verifier payload for f = 23 and f = 24. lake build of the Lean package was run on this archive on 2026-09-13; see /formal. OMEGA drift experiment v0.1 Implementations: Python 3 with NumPy . From an empty folder Download, extract if needed, verify hashes, install the named dependency, then run. Commands below use the public origin. mkdir omega-drift && cd omega-drift curl -fsSO https://omega-naught.grok.me/geometry/drift/omega_drift_experiment.py curl -fsSO https://omega-naught.grok.me/geometry/drift/results.json python3 -m pip install numpy python3 omega_drift_experiment.py Copy run command Named run commands python3 omega_drift_experiment.py Copy run command omega_drift_experiment.py results.json Numerical experimental control of a hypothesis-layer 4D rotation. Not a theorem of Papers I–VII. The published results.json is the named run (seed 20260831).
