Paper P-05d: Bounded Finite Source-Locked Proof and the Named Reality Correspondence Ladder - Internal FRC Bounded Proof and Rhyme Classification Object

Paper P-05d: Bounded Finite Source-Locked Proof and the Named Reality Correspondence Ladder - Internal FRC Bounded Proof and Rhyme Classification Object Abstract This record publishes Paper P-05d of the FRC programme: Bounded Finite Source-Locked Proof and the Named Reality Correspondence Ladder. The paper records an internal FRC bounded proof and correspondence-classification object, supported by a source-locked proof route, named reality ladder, exact/close/rhyme classification tables, Collatz-like rhyme gate material, supporting visual/data images, and a peer reproducibility addendum. The central claim is deliberately scoped. Inside the internal FRC proof route, finite source-locked correspondence is claimed only where the finite source, count, operator and boundary are recoverable. Public observations and large-scale reality examples are not promoted into formal proof. They are classified as exact, close or rhyme according to their recoverability, measurement boundary, scale, operator history and composite overwrite. The submission includes the main P-05d paper, supporting information on the 10^20 veil and pre-material admissibility, named reality ladder tables, Collatz-like rhyme-gate material, source-route register, supporting visual/data images from the Collatz / Prime+1 and Rev08 audit route, and a peer reproducibility addendum. The publication is intended as a complete, citable record for external audit, criticism, replay, comparison and peer review. Description This Zenodo record contains the complete Paper P-05d submission package prepared for external audit, criticism, comparison, replay and peer review. The submission is part of the Finite Reality Closure (FRC) programme and is positioned after P-05a finite prime-support closure work, P-05b prime structural masonry / hydrogen-seed support work, and P-05c Collatz finite-duration and cap-free Lock-B closure work. P-05d does not replace those papers. It follows them by separating bounded proof, named real observation, close correspondence and large-scale rhyme. The proof-bearing claim is not that Zenodo publication itself constitutes peer review. The claim is that the uploaded internal FRC paper and supporting pack record a bounded finite source-locked proof route, where exactness is asserted only for recoverable finite source/operator histories. Outside that bounded route, public observations are treated as reality tests, close correspondences or rhyme-classified structures. External mathematical and scientific review remains open. The paper introduces the Named Reality Correspondence Ladder. The ladder moves from Primitive 0 and Zero / Zerofield through defined constants, particles, atoms, molecules, biological structures, Earth-scale boundaries, stellar systems and black-hole boundary observations. Each named item is classified as exact, close or rhyme. Exactness is reserved for bounded recoverable cases. Close correspondence is used where finite reality is recorded through scale, instrument, unit, rounding or public-record boundary. Rhyme is used where lifecycle, boundary, expansion, contraction, recurrence, repayment, survivor or failure grammar appears, but the full operator history is not recoverable. The revised Collatz material is included as rhyme-classified support. The claim is not that physical reality literally executes 3n + 1. The claim is that Collatz exposes, in exact symbolic miniature, an admissibility grammar that FRC also sees in finite reality: no Zero as object, no realised infinity, no expansion without repayment, and no continuation without boundary permission. The supporting visual/data images are included as audit and morphology context. They include Collatz / Prime+1 crossover fields, heatmaps, Rev08 transform-control sheets, Rev08 cross-domain contact sheets and Rev08 threshold/phase sheets. These images are not presented as standalone proof. They are included as bounded visual and data-rhyme material supporting the separation between exact finite proof and broader lifecycle morphology. Included files: 1. Main paper:P-05d Bounded Finite Source-Locked Proof and the Named Reality Correspondence Ladder, Rev09AW, with revised Collatz Admissibility Invariant section. 2. Supporting information:Supporting insert on the 10^20 veil and pre-material admissibility, including the Primitive absence-boundary -> unseen admissibility layer -> boundary-tested relation -> material memory / observable scar framing. 3. Named reality ladder:Exact / close / rhyme classification table for named items from Primitive 0 / Zero through constants, atomic and molecular examples, biological and Earth-scale structures, stellar systems and black-hole boundary observations. 4. Collatz-like rhyme gate:A bounded rhyme-classification file for Collatz-like gates, loops, expansion, contraction, repayment, renewal, ejection and failure sequences. 5. Source-route register:Public and framework source routes used to support named values, observations, audit context and paper positioning. 6. Supporting visual/data images:Collatz / Prime+1 crossover image, Collatz / Prime+1 heatmap, Rev08B transform-control contact sheet, Rev08E cross-domain contact sheet and Rev08E threshold/phase contact sheet. 7. Peer reproducibility:Peer reproducibility markdown and addendum ZIP containing replay instructions and bounded package-check scripts. This record publishes a complete internal FRC bounded proof and correspondence-classification submission. The work claims bounded finite source-locked proof where the source/operator history is recoverable. It does not claim universal proof, physical proof, black-hole proof, Collatz proof, Prime+1 scaffold proof, external peer review, or independent third-party reproduction. Status: internal FRC bounded finite source-locked proof route published; named reality ladder and Collatz-like rhyme classification published; external review open. References: Bloggs, Joe. The Zero Boundary: A Two-Sorted Mathematical Framework Eliminating Singularities in Physics. Zenodo. DOI: 10.5281/zenodo.17752602. Bloggs, Joe. Reality-Constrained Arithmetic Below One. Zenodo. DOI: 10.5281/zenodo.17831753. Bloggs, Joe. [FRC Paper / related work]. Zenodo. DOI: 10.5281/zenodo.19312440. Bloggs, Joe. [FRC Paper / related work]. Zenodo. DOI: 10.5281/zenodo.20158452. Bloggs, Joe. Paper P-05c: Collatz Finite Duration and Cap-Free Lock-B Closure - Internal FRC Computational Theorem-Chain Proof Object. Zenodo. DOI: 10.5281/zenodo.21162117. BIPM. The International System of Units and the mole definition. NIST/CODATA. Fundamental Physical Constants. PubChem. Water compound record. USGS. Watershed and hydrology reference material. NOAA. Shoreline / coastline measurement reference material. NASA/JPL. Planetary and solar physical data reference material. Event Horizon Telescope Collaboration. M87* black-hole image / shadow / ring observation papers.