Projections, formulae, diagrams, reductions and recovered notebook references are classified before display. A mathematical identity or archived computation is not evidence of an arithmetic–cosmic mechanism. No entry here authorizes a controlled run or establishes physical support.
The preserved investigator-A primary run reports local rank/elevation coherence against the locked NULL-MAP-001 arithmetic rank-permutation null. It rejects that null at α = 0.01 for the single preregistered endpoint.
T = −mean(|elevationᵢ − elevationⱼ|) on the fixed k = 10 arithmetic neighbor graph; larger T means greater local coherence. Exceedances count T_null ≥ T_observed. The locked correction is p = (1 + 0) / (999 + 1) = 0.001, the smallest attainable p-value with 999 permutations, not zero. The cohort selects curve-number-1 isogeny representatives.
This arithmetic null does not test a survey-selection-matched cosmological null or distinguish ACSC from other arithmetic structure. No cosmological correspondence or physical ACSC support is established. Independent rerun and replication remain outstanding; archive/hash inspection is package verification. The 160 browser fixtures and canvases are illustrations, separate from this recorded result.
Current registry gates: experiment execution eligible: true; dataset execution eligible: true; controlled-support eligible: false; physical-support eligible: false. Execution eligibility is recorded for the experiment and dataset. A source-locked runner preflight is still required for each controlled run. Earlier package descriptions of disabled execution describe their historical state.
Preserved primary transaction: 20261016T041335361140Z-e60fd05117fc · source revision 1b0f2d7853608bfbab79cf2dc04b002f1f193eb2.
EXP-MAP-A03: preregistered; execution eligible: false. Its pre-execution archive is separate from an original controlled run or independent replication.
Observational sky releases admitted for display: 1. Display admission authorizes neither cross-matching nor population inference or physical support.
DATA-VIZIER-ALFALFA100 · hi_centroid · 31,502 publisher rows · approved_display_only. Read display review receipt
Candidate theorem with an exact symbolic certificate; independent mathematical review pending.
Primary investigator-A execution is preserved separately in merged PR #104; independent replication is not established. The DOI above archives the earlier preregistration/activation package, not the later run. Controlled-support and physical-support eligibility remain false; no BSD proof, cosmological correspondence, or SFR result is established.
Publicly archived, author-produced pre-execution reference verification, not independently replicated inference, an A03 activation, or controlled/physical support. The frozen release package's pre-publication wording is historical; this external citation records the subsequent publication without editing its SHA-256-locked contents.
Repository snapshot SHA-256: add889ce3af29f7982aa607d388fcd9b5273c190df575f31bc9c85eb1c3d15c4. Publication descriptions come from the hashed repository README; DOI links do not independently verify deposited bytes. This deployed snapshot is not a live GitHub status feed.
Displaying 12 of 12 reviewed catalog records.
Φ(E) = (log|Δ_E|, log N_E, α · r_E)
A deliberately selected projection of arithmetic invariants into geometric coordinates. α is a historical scaling parameter, not a physical conversion.
Limit: Does not establish a unique mapping, bijection, rank–time equivalence, or cosmic correspondence.
Controlled execution: false · Controlled support: false · Physical support: false
View cited repository sourceΦ versus Φ_MCJ, Φ_PTD, Φ_FT
Modular j-invariant, primarily algebraic and Frobenius-trace families are alternative controls to the historical mapping.
Limit: No mapping family is independently validated as a cosmic coordinate system.
Controlled execution: false · Controlled support: false · Physical support: false
View cited repository sourceL_cosmo(s) = Σ_(n≥1) a_n · n^(−s)
In the supplied historical report, a_n counts galaxies in bins of log stellar mass, redshift and Petrosian radius. This is a constructed statistic, not an elliptic-curve L-function.
Limit: The report's average five-fold MSE 0.4266 is an unverified historical claim, not controlled SFR performance. Bin indexing and target leakage require independent audit.
Controlled execution: false · Controlled support: false · Physical support: false
View cited repository sourcea_n ≥ 0 and Σa_n > 0 ⇒ L_cosmo(1) = Σ_(n=1)^B a_n/n > 0
For finitely many nonnegative galaxy-bin counts, any occupied bin makes the Dirichlet sum positive at s=1. This is a mathematical limitation of the reported rank analogy, not a claim about physical data.
Limit: Therefore a nonzero derivative L′_cosmo(1) does not establish a first-order zero, BSD rank one, or a number of independent star-formation drivers.
Controlled execution: false · Controlled support: false · Physical support: false
View cited repository sourceSFR ~ a·logmass + b·z + c·L_cosmo(1) + d·dec + e·petroRad_r + f·environment + g·(logmass·z)
The uploaded report presents a symbolic additive candidate using ordinary astrophysical quantities and the bin-count statistic alongside a Random Forest training narrative.
Limit: Random Forest feature importance does not estimate coefficients a through g. The displayed equation has no verified coefficient fit, protected split or independently reproduced performance.
Controlled execution: false · Controlled support: false · Physical support: false
View cited repository sourceReported fold MSEs: 0.3904, 0.4312, 0.4420, 0.4322, 0.4371; stated mean 0.4266 ± 0.0185
The historical report gives five fold-level values and an aggregate, retained as reported provenance only.
Limit: No audited inputs, training-only transformations, split indices, model coefficients, null comparison, or independent holdout verifies these numbers. The reported aggregate is not controlled statistical or cosmological evidence.
Controlled execution: false · Controlled support: false · Physical support: false
View cited repository sourceβ₀: components · β₁: independent loops · β₂: cavities
These are mathematical meanings of Betti numbers in the chosen filtration. Persistent homology describes topology across scales.
Limit: β₁ is not the number of astronomical filaments and β₂ is not automatically the number of cosmological voids.
Controlled execution: false · Controlled support: false · Physical support: false
View cited repository sourceArithmetic → Geometry → Topology → Observation → Dynamics → Physics
A methodological ordering from Charter v0.2. Physical interpretation is downstream of independently tested observational correspondence.
Limit: Arrows express a proposed research workflow, not a proven causal or physical reduction.
Controlled execution: false · Controlled support: false · Physical support: false
View cited repository source(∂ₜΦ)² = −K + 2M/Φ + ΛΦ²/3
A class-restricted Szekeres–Szafron metric reduction documented in the registered E1a derivation.
Limit: Subject to the registered assumptions and reviewer audit; not a theorem that arithmetic geometry causes cosmic structure.
Controlled execution: false · Controlled support: false · Physical support: false
View cited repository sourceinputs → coordinate audit → spherical search → rejection/null tests → versioned outputs
A prospective reconstruction pathway for two historically invalid 1,495-row matched outputs.
Limit: No reconstructed match is certified. The historical two-arcsecond failures remain negative data-quality evidence.
Controlled execution: false · Controlled support: false · Physical support: false
View cited repository sourceIf θ = dℳ, then dθ = d(dℳ) = 0
For a globally defined smooth scalar ℳ, the exterior derivative is nilpotent: d²ℳ=0.
Limit: A nonzero cohomology class cannot follow from d(dℳ); it requires a separate closed non-exact structure.
Controlled execution: false · Controlled support: false · Physical support: false
View cited repository sourcearchived output JSON — non-executable
A saved output derivative from the recovered CasJobs.ipynb. The full original notebook and execution environment have not been certified by this entry.
Limit: The JSON file is inert provenance, not an executable or independently reproducible notebook.
Controlled execution: false · Controlled support: false · Physical support: false
View cited repository source