Riemann zeta function: Split-Zero arithmetic comparison and research readers

Abstract

This collection records a literature-linked research programme on the Riemann zeta function and its explicitly constructed geometric, arithmetic and fluid interfaces. The September 12 calculation edition adds a complete reader for the Split-Zero programme: scalar algebra, support fibres, Rees filtrations, the actual arithmetic theta comparison, finite operator kernels, homology, quotient retractions and chain homotopies. A separate Unified Flow reader works through clocks, entropy and spectral probes in a specified Schwarzschild/Hartle-Hawking model. Start with the calculation reader 08-splitzero-arithmetic-calculations.pdf is the primary preview. It begins by defining the objects and explaining why the programme looks toward Deligne's Weil II method. It then preserves the complete selected mathematical notes, including their equations, proofs, constructions, exceptions, references and formalization history. The notes study the semiring G(R), where supported zero is retained separately from absence, and the actual theta quotient Q = B/Theta(V). The finite arithmetic comparison is expressed using g = 2 xi, the completed Riemann zeta function. This is the explicit zeta connection, rather than a claim that different presentations are automatically equivalent. The calculation moves from filtration defects and arithmetic traces to finite polynomial quotients, chain descent, continuous quotient representatives, homotopy classification and rank-two boundary control. It retains the tests that failed, the corrections, and the precise extent of the successful written and formal results. These calculations are presented as a genuine research attempt. They do not establish the global positivity or purity statement needed for RH, and no counterexample to RH is claimed. 09-unified-flow-calculations.pdf is a separate worked calculation. It specifies the black-hole geometry and thermal state, distinguishes the detector and field probes, and computes the clock, energy, entropy and spectral maps with their units and parameters retained. It is not a claim of a universal equivalence of all flows or a solution of quantum gravity. 10-splitzero-cohomology-and-weight-control.pdf is a separately authored, 88-page continuation, frozen as release_20260912b. It develops Split-Zero carriers, arithmetic operator comparisons, chain retractions, homotopy control, source metrics, Christoffel kernels and weighted-jet topology. Its second part preserves six complete earlier source notes with their original revisions and attribution. This volume is not silently identified with the integrated GitHub snapshot: its own exact source manifest, five finite checkers and build instructions accompany it in 12-tandem-calculation-sources.zip. Source-metric positivity and shrinking absolute Gram matrices are distinguished from the relative arithmetic estimate the programme still seeks. Sources and verification Every selected note has an immutable repository source link and revision. The accompanying source package supplies the authored calculations and reproducible checkers. Lean workflow records certify their specified source versions and declared targets; finite symbolic tests are not relabelled proofs of the full analytic programme. The reader keeps those scopes explicit. Novelty and independent peer review are not asserted. The six readers from the September 9 edition remain available as separate, unchanged PDFs. They contain the main zeta reader and the fluid, heat-flow, Connes, geometric-complexity and vacuum interfaces. The new calculation volumes are additions, not silent replacements for those frozen pages. Live research repository: Zeta function research reader. Related corrected Navier-Stokes reader: 10.5281/zenodo.22678406. Per-file source rights remain in force. Primary literature is cited; private transcripts, the local literature corpus, credentials and standalone font files are not included. AI-assisted contributions remain attributed as recorded in the source notes.