The River and the Whirlpool: A Flowing-Space Reading of General Relativity, with Registered Dark-Sector Forecasts

This deposit is a timestamped priority record of an ongoing independent research program that interprets exact general relativity through a "flowing-space" (river) picture, together with a set of pre-registered, falsifiable forecasts for the dark sector. Contents. The record includes the working paper "The River and the Whirlpool" (Draft v0.4.2); four registered forecast memos that state quantitative predictions with explicit kill conditions — the a0(z) saturating-law redshift scaling, the conditional DESI dark-energy wager, the sound-speed commitment, and Addendum 3 (REVISED), which withdraws an amplitude coincidence as numerology following the program's own pre-deposit red team; a provenance map linking this work to the author's original 2020 publication; and a complete working-record archive. Method. The program operates under a refutation-first discipline. Each headline claim carries an explicit honesty stamp (DERIVED, MOTIVATED, FITTED, UNFORCED, NUMEROLOGY, or FATAL) and is subjected to an adversarial red team before public deposit. One such red team, included here, deflated the program's own amplitude claim to numerology prior to release. What is registered is the falsifiable shape of the predictions, not their aesthetic appeal. Provenance and authorship. The conceptual foundation was first published by the author in 2020 as "The Illusion of Gravity" (Apple Books; see related identifiers, the included provenance map, and the original file bearing 2020 internal timestamps). That 2020 work is solo and was written without AI assistance. The present mature theory and its quantitative forecasts were developed in 2026 with AI used as an analytical and drafting tool; all claims, framings, and honesty judgments are the author's own. Where the mature theory supersedes 2020 placeholders (for example, the early "TyPoe particle," now treated as medium flow rather than a particle), the evolution is documented in the provenance map rather than by editing the original. Status. This is an evolving preprint deposited for priority and open scrutiny; it is not peer-reviewed. Future revisions will be added as new versions under the same concept DOI rather than overwriting this record. Version 2 (July 25, 2026). Adds the post-deposit research round of July 25, 2026, eight days after first deposit. Headline addition: "Registered Forecast Memo — Addendum 4 — The Ledger Wager," the framework's first dark-energy registration, filed prior to DESI DR3: dark energy never decreases; no phantom equation of state (w < −1) at any epoch; w = −1 exactly today; fingerprints in dark-matter dilution (exponent 3 + ε) and suppressed late-time structure growth rather than background expansion — with four kill conditions, the currently adverse DESI DR2 datum named in the filing. Supporting chain: "RD-2 Derivation Session 1 — The Sign of the Ledger" (an exact, machine-verified identity in unimodular gravity, Λ̇ = 8πG Q; a channel analysis isolating a unique surviving source; the sign result Q ≥ 0 conditional on the framework's entropy formulation; numerical phenomenology, including the on-the-record correction of two earlier sketches); the RD-2 reconnaissance memo (rev 2) mapping the Josset–Perez–Sudarsky lineage and the 2025–26 dark-degeneracy analyses of DESI DR2; the "Research Directions — Post-Deposit Round 1" memo (its header misdates its filing as July 17; the correct date, July 25, is recorded in the reconnaissance memo; deposited unaltered per the no-overwrite policy); and "RD-5 — The Exchange-Onset Cosmogony" (rev 2), a marked-speculative origin narrative whose sole observable content is inherited from Addendum 4. A "What's New in Version 2" note is included as the entry point. All Version 1 files stand exactly as deposited July 17, 2026.