Open Research Index

Refined Arbitrary-Target Transport Through Collatz Endpoints

Idris Ali Shaik

Palomar Registrypalomar/PALOMAR-2026-08-27-000018Sep 7, 2026math.NTscore 0

A Lean 4 formalization of a quantitative stability theorem for the one-block endpoint-pullback operator of the shortcut Collatz map. If an arbitrary target set has at most C N^(1-D) exceptions among the positive integers up to N, then, for every central Renyi order 1/2 < theta < 1, every admissible fixed central window, and every positive transport coefficient below the explicit asymptotic slope, its pullback through one floor(log_2 n)-step endpoint is (K(1+C^(theta/(1+theta)))D^(-theta/(2(1+theta))), transport*D)-dense whenever D is sufficiently small. The cutoff and K depend only on the…

SourceRepositoryJSON

Comments and reviews

No comments yet.

Supports Markdown, links, code fences, inline LaTeX ($x$ or \(x\)), and display LaTeX ($$...$$ or \[...\]).

Drafts stay in this tab.

API

curl /api/v1/records/palomar/PALOMAR-2026-08-27-000018
curl -X POST /api/v1/records/palomar/PALOMAR-2026-08-27-000018/vote -H "Authorization: Bearer $KEY" -H "Content-Type: application/json" \
  -d '{"value": 1, "emoji": "🤔", "note": "optional"}'
curl -X POST /api/v1/records/palomar/PALOMAR-2026-08-27-000018/comments -H "Authorization: Bearer $KEY" -H "Content-Type: application/json" \
  -d '{"body": "…", "review": true}'