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NS-INRS

Independent Navier–Stokes Research Series · 63/63 built (round DCRP59 missing) · global regularity OPEN

This sub-line's files were originally filed inside NTLA-O's own source drop, and this site's earlier account of them was: "the researcher reprocessed NS-DCRP's same-numbered papers through the NTLA-O observer lens, producing cross-reference files." Reading the original files' frontmatter paper by paper required a correction to that account: this batch self-identifies as an "Independent Navier–Stokes Research Series," a parallel continuation of NS-DCRP starting from round 42, not a reinterpretation of old papers — DCRP43 itself states "using the newly established NTLA-O distinction, re-advancing DCRP42's conclusions," continuing onward in sequence to DCRP105, produced steadily between 2026-08-17 and 2026-08-20 — later-closing than either of the two official folders, NS-DCRP (ending at 55/59) or NS-X72 (ending at 71).

Rounds 43 through 58 (including one correction round, 43-QC) share numbering with — but differ in content from — the already-live official NS-DCRP rounds 43-58: they're a parallel result produced by the researcher attacking the same DCRP42 branch point with a different theoretical tool (NTLA-O's observer/gauge distinction), consistent with what this site's own homepage has said all along ("two batches of files sharing numbering are parallel results, not a version conflict — both are kept"). The real watershed is DCRP60: that round's own text states plainly, "rank-two local geometry is now exhausted; the only new observation coordinate that can break the loop comes from X72, and the compound DCRP/X72 round numbering formally begins here" — a line the source document draws itself, not a guess made by this page. After DCRP60 (rounds 61 through 105), the numbering no longer overlaps with anything already built — it is entirely new research that exists only in this batch of files.

The 63 rounds form a single continuous chain of STOP-D nodes, deeply interwoven with the real rounds of the already-built NS-DCRP and NS-X72 (each round explicitly cites specific round numbers like "X72 Round37" or "DCRP31's PFET," not vague gestures). Round DCRP59 is missing — not included in this batch; both DCRP58's and DCRP60's own text mention it, but the file itself isn't in the source drop, honestly flagged the same way every other missing round on this site is, not an oversight on this page's part. The current frontier is DCRP105/X72-R88 — its closing text uses the same "Next autonomous step" format as the 13 rounds before it, listing eight concrete to-dos for the next round, DCRP106/X72-R89, with no language anywhere suggesting a stop, a pause, or a planned close. It is the current latest frontier simply because this batch of files ends at 105 — not because the research itself called a halt.

A note on this English page: unlike every other sub-line on this site, NS-INRS's own source .md files were already written directly in English by the research process — they required no translation at all. What this English hub and its 63 detail pages translate is only the site's own Traditional-Chinese descriptive wrapper (this page's lede and notices, and each round's title, status tag, and summary paragraph above the paper itself); the linked "Download original .md" file is byte-identical between the Chinese and English versions of every round.