From Ledger to Born: The Square is Forced

From Ledger to Born: The Square is Forced Version: 2.0First public release: 2026-05-11Current release: 2026-06-26Concept DOI: 10.5281/zenodo.20118242Author: Ali AttarWebsite: quantumtraction.org This paper gives the Quantum Traction Theory derivation of the Born rule as a finite address-capacity theorem. In standard quantum mechanics the Born rule is empirically secure but introduced as an operational probability postulate. QTT asks what object is counted before probability is read. The counted object is a finite-capacity, address-indexed, real-\(J\) ledger. Conditional on QTT A1--A7 and on the ordinary laboratory requirement of a calibrated repeated preparation, the Born rule is derived as a theorem. The square is not an interpretive convention; it is the unique positive additive \(J\)-basis-invariant address-capacity law. The resolved ledger law is \[ p(α M) = ∑_w \|ρ(w)\|_J^2 ψ_w|Π_αψ_w_J = Tr_J(ρeffΠ_α), \] where \[ ρeff = ∑_w \|ρ(w)\|_J^2 |ψ_wψ_w|_J. \] In the laboratory-pure projection sector this reduces to the familiar position rule \[ P_J(X) = ∫_X \|Ψ( x,τ)\|_J^2\,d^3x. \] Version 2.0 is a corpus-standard overhaul release. It adds QTT Onboarding for scientists who encounter this paper first, first-public-release provenance, a load-bearing axiom and QTT-exclusive concept map, website deep anchors, an Artian's Universe statement, concept-DOI-only internal citation discipline, and a clearer AI-assistance and review-function disclosure. It preserves the central claim: inside QTT, conditional on A1--A7 and calibrated repeated preparation, Born's rule is derived and the square is forced. Main status labels: GREEN: BORN-RULE-LEDGER-THEOREM-DERIVED GREEN: ADDRESS-CAPACITY-SQUARE-FORCED GREEN: FIXED-ADDRESS-GLEASON-BUSCH-RAIL-CLOSED GREEN: SOURCE-READOUT-PROBABILITY-FIREWALL-CLOSED STRUCTURAL: HIGHER-ORDER-INTERFERENCE-NO-VIOLATION-ANCHOR YELLOW: INDEPENDENT-ACCESS-LAW-SUBSTRATE-TESTS-PENDING QTT Onboarding summary: Why this paper exists: textbook quantum mechanics uses the square rule but does not name the finite source object being counted. Object being built: a finite address-capacity probability interface for QTT records. First unfamiliar terms: real-\(J\) dial, address ledger, calibrated repeated preparation, ergodic tick sector, instrument equivalence, and Access Law. What is settled: the frequency module, capacity-square module, fixed-address effect law, resolved Born trace formula, and falsifier classes. What remains live: the deeper empirical status of the QTT axiom base, future higher-order-interference tests, and independent access-alignment tests. Related QTT anchors: Main book: 10.5281/zenodo.17527179 Observation as Access: 10.5281/zenodo.20114403 From Rotor to Wavefunction: 10.5281/zenodo.20119662 Two-clock projection constant and CHSH: 10.5281/zenodo.19979594 A7U distributed-bundle ontology: 10.5281/zenodo.20097247 Website anchors: Corpus Tree family Derivation Atlas: Born node Observatory: Born/no-higher-order row Lexicon: Born rule Two Universes comparison Included files: PDF paper, Version 2.0 Complete reconstruction package zip with LaTeX source, local load-bearing style module, Zenodo description HTML, render audit, README, and hashes