From Symbol-First Thinking to Reality-First Reconstruction: A Seven-Stage Unwinding of Collatz, Kaprekar, Ramanujan and the 3|4|5 Receipt towards a Candidate Finite Boundary Structure - Paper 21b

From Symbol-First Thinking to Reality-First Reconstruction: A Seven-Stage Unwinding of Collatz, Kaprekar, Ramanujan and the 3|4|5 Receipt towards a Candidate Finite Boundary Structure - Paper 21b ABSTRACT Human observation often encounters a completed symbolic receipt: a number, equation, partition, attractor, geometric figure or iterative path. The finite construction history that made the receipt possible is usually absent. This paper presents a seven-stage conceptual map for working backwards from compressed symbolic numbers and geometry towards a progressively less compressed candidate finite boundary structure. The numbered route begins with symbolic 3|4|5 shorthand, recovers unary count, releases clustering from inherited geometry, treats the recovered finite receipt as a candidate source state and then investigates boundary closure, turn relative to an outer field and cyclic closure with retained pushback and outer-memory information. The reverse route describes increasing symbolic compression and the progressive loss of orientation, duration, role and construction history. A separate prior-state section sets out the candidate generational event that would be required before the map could exist: Zerofield absence, finite admissibility, first distinction, outward generation, overlap, collision, compatibility filtering, prime-like survivorship, closure and lifecycle repayment. This prior chain is explicitly hypothetical and is not claimed as an observation of creation. Collatz, Kaprekar and Ramanujan mathematics are treated as higher-level symbolic fossils. Their exact arithmetic rules preserve enlargement and repayment, collection into fixed points, bounded internal multiplicity, multiple inner histories and single outer receipts. These exact symbolic facts do not prove that reality runs the corresponding algorithms. They may, however, preserve compressed relations resembling an underlying finite grammar of inner memory, active boundary and surviving outer consequence. The paper concludes that reality cannot be compressed entirely, but finite structural sweet spots may permit unusually faithful receipts when count, partition, order, role, orientation and trigger information are preserved and all losses and additions are declared. RECORD CONTENTS AND REPRODUCIBILITY This record contains the Paper 21b PDF, the full-resolution conceptual map, the FRC programme table Rev08, a SHA-256 manifest and the bounded results and replay artefact bundle. The replay material contains the U13, U19 and U20-U25 freeze chain used to support the paper’s declared C12, 3|4|5, local-action, orientation, closure and repair-boundary results. Each computational claim remains bounded by its own README, method, theorem targets, result and failure ledgers, STOP/GO statement, hashes and PowerShell replay instructions. The supplied computations verify the declared symbolic model results.