BCRD (boundary-complete relational dynamics) is a finite quantum-spin research programme studying whether relationally accessible records inside a finite closed system can support their own effective dynamics. This archival v0.1 release records the reviewed programme frontier as of 14 September 2026 using a workflow that separates construction, hostile review, reconciliation, and prospective preregistration.The reviewed finite results include a sufficient finite-range mediator repair of an earlier locality failure; representative-specific native transport distinct from a Feynman-cursor control; predictive records that do not automatically self-update; exact reconstructive closure from one-known-spin erasure correction; approximate common-CPTP-map compatibility for six exposed N=8 transitions of a proper coarse record; and finite process results separating one-time coarse channels from honest semigroup dynamics. The first legal N=8 causal-break memory test remains unresolved above its apparatus floor.A direct recoupling lane establishes a model-specific adjacent-pair Racah 6j² transition probability in a historically declared pair-Lüders interface. This is explicitly not claimed to be a coherent Racah amplitude, physical F-move, pentagon/Pachner dynamics, Ponzano-Regge/Regge sector, continuum gravity, or quantum gravity. A phase-sensitive N=4 recoupling study has been prospectively frozen but no outcome from that study is included in v0.1.This deposit is intended as a durable public priority and provenance record, including explicit negative results and nonclaims. It is not a final journal manuscript and does not claim that BCRD has established quantum gravity.
BCRD (boundary-complete relational dynamics) is a finite quantum-spin research programme studying whether relationally accessible records inside a finite closed system can support their own effective dynamics. This archival v0.1 release records the reviewed programme frontier as of 14 September 2026 using a workflow that separates construction, hostile review, reconciliation, and prospective preregistration.The reviewed finite results include a sufficient finite-range mediator repair of an earlier locality failure; representative-specific native transport distinct from a Feynman-cursor control; predictive records that do not automatically self-update; exact reconstructive closure from one-known-spin erasure correction; approximate common-CPTP-map compatibility for six exposed N=8 transitions of a proper coarse record; and finite process results separating one-time coarse channels from honest semigroup dynamics. The first legal N=8 causal-break memory test remains unresolved above its apparatus floor.A direct recoupling lane establishes a model-specific adjacent-pair Racah 6j² transition probability in a historically declared pair-Lüders interface. This is explicitly not claimed to be a coherent Racah amplitude, physical F-move, pentagon/Pachner dynamics, Ponzano-Regge/Regge sector, continuum gravity, or quantum gravity. A phase-sensitive N=4 recoupling study has been prospectively frozen but no outcome from that study is included in v0.1.This deposit is intended as a durable public priority and provenance record, including explicit negative results and nonclaims. It is not a final journal manuscript and does not claim that BCRD has established quantum gravity.
BCRD (boundary-complete relational dynamics) is a finite quantum-spin research programme studying whether relationally accessible records inside a finite closed system can support their own effective dynamics. This archival v0.1 release records the reviewed programme frontier as of 14 September 2026 using a workflow that separates construction, hostile review, reconciliation, and prospective preregistration. The reviewed finite results include a sufficient finite-range mediator repair of an earlier locality failure; representative-specific native transport distinct from a Feynman-cursor control; predictive records that do not automatically self-update; exact reconstructive closure from one-known-spin erasure correction; approximate common-CPTP-map compatibility for six exposed N=8 transitions of a proper coarse record; and finite process results separating one-time coarse channels from honest semigroup dynamics. The first legal N=8 causal-break memory test remains unresolved above its apparatus floor. A direct recoupling lane establishes a model-specific adjacent-pair Racah 6j² transition probability in a historically declared pair-Lüders interface. This is explicitly not claimed to be a coherent Racah amplitude, physical F-move, pentagon/Pachner dynamics, Ponzano-Regge/Regge sector, continuum gravity, or quantum gravity. A phase-sensitive N=4 recoupling study has been prospectively frozen but no outcome from that study is included in v0.1. This deposit is intended as a durable public priority and provenance record, including explicit negative results and nonclaims. It is not a final journal manuscript and does not claim that BCRD has established quantum gravity.
Discrete approaches to quantum geometry take the 6j symbol as a dynamical object: in the Ponzano-Regge state sum the 2-3 Pachner move is the Biedenharn-Elliott identity read as a coherent sum over an internal edge label. We ask whether a finite relational record model — a spin-1/2 chain in its total-spin-zero sector, with gating registers that select which adjacent bonds are active, and with an explicitly declared operational interface — realises recoupling in that dynamical sense.The answer is negative, and the obstruction is structural rather than quantitative. We show: (i) every operational datum of the declared interface reduces to a trace of a word in Temperley-Lieb generators at loop value 2, and is reproduced identically by realisations carrying no SU(2) at all, so the data are not evidence of SU(2) recoupling specifically; (ii) in any quantum system an amplitude proportional to a recoupling coefficient forces the dynamics to commute with one of the two coupling schemes, so the transition kernel is independent of the dynamics; (iii) within a register configuration the declared dynamics acts as the identity on the coarse intertwiners, so recoupling data are never dynamically sampled; and (iv) on all three readings of "a recoupling move as a process" — passive, active relabelling, and selected dissipative — physical composition fails to realise the pentagon, while the abstract Biedenharn-Elliott identity holds exactly, as it does in every SU(2) system. The one internal-label sum the model does select is incoherent, weighted by ballot multiplicities rather than (2x+1), and signless: the wrong object on three independent counts. The pentagon numerics rest on three independent implementations sharing no code, which agree exactly; the compatible-intermediate criterion separates all six two-move compositions correctly, four giving exactly zero and two giving 47/216 and 245/324. We state the scope precisely. Every result is relative to the declared interface fixed in Section 2. This is not a general no-go for finite relational record dynamics, and it establishes nothing about quantum gravity positively or negatively. The mathematics used — Racah and Wigner recoupling, the Biedenharn-Elliott identity, Schur-Weyl duality, Wedderburn theory — is standard and is not claimed. The contribution is the identification of which structures fail, and why, for this class of models.
This preprint studies exact reconstructive autonomous closure in finite total-spin-zero quantum systems. The central construction uses the exact recoverability of erasure of one known spin on the relevant singlet sector. That recoverability permits an exact effective CPTP update for associated finite record constructions. The result is explicitly reconstructive: the retained record remains sufficient to recover the microscopic state on the proved domain. The paper therefore distinguishes exact autonomous closure inherited from reversible encoding from autonomous closure after genuine information loss. The finite BCRD applications treated here are the reviewed J2, J4, and J6 record constructions at N = 8, 10, and 12. One-particle-loss immunity of singlet/decoherence-free subspaces is treated as established prior art; no priority claim is made for that result. The paper does not establish genuinely lossy autonomous coarse dynamics, strict minimality, a common cross-N map, thermodynamic irreversibility, continuum physics, geometry, gravity, or quantum gravity. Author: Tobias Croydon-McRaeAotearoa New Zealand
We study finite-data identification of a common effective update from a coarse quantum record in a fixed finite N=8 system. A rigorously certified CPTP map fits four exposed transitions below tolerance 10^-2 but fails two prospectively selected unseen transitions with large reviewed lower bounds. After those transitions are added as constraints, the unchanged physical map class remains feasible on all six transitions. The result therefore establishes finite-data non-identification, or set-membership ambiguity, in this finite quantum coarse-dynamics setting. It does not establish universal estimator failure, map-class misspecification, arbitrary-time autonomy, Markovianity or non-Markovianity, hidden-state necessity, continuum physics, geometry, gravity, or quantum gravity. Related resource: Tobillicious/bcrd terminal public custody SHA: 3d2b2781c1b20f04639d338263f1bc1f3f0363f7
STATUS (18 October 2026). The physics programme that motivated this work was concluded in October 2026 and its claim of a unified derivation withdrawn. The results in this paper do not depend on that programme and stand as stated. Can an exact account of recorded events also determine what happens next? We examine this question in a finite quantum model with 48 preparations and an apparatus with ten distinguishable outcomes. Two reversible evolution rules reproduce exactly the same first-use specification but predict different results when the apparatus is used again. A separate example fixes one evolution rule: two possible histories then have identical counts of reads, commits and service events, yet different probabilities for the next outcome. Counts alone are therefore insufficient for prediction in this model. What remains visible depends on the observation. At eight preparations, even the complete individual-read distributions agree between the two rules, while correlations between the reads distinguish them. We classify two explicitly specified families of observations and determine exact ranges for the simpler family, showing both how distinctions are lost and how they can survive. The results separate event accounting, the choice of evolution, retained memory and the conversion of records into measured responses. They are conditional finite-model results, not a derivation of a physical dynamics or a measured coupling. The contribution is a set of exact counterexamples and classifications, rather than new principles of quantum theory. Exact computations and explicit proofs identify the additional response, weighting and sampling choices that a predictive physical interpretation must supply. Version 0.2 incorporates corrections following an author-requested preprint review. The deposit supplies the PDF, editable LaTeX with three TikZ figures, bibliography, exact fixture data for 96 two-read processes over 48 preparations, and a portable Python/SymPy verifier. The revised verifier passes 2,926 exact assertions. These are conditional finite-model results; no physical law, bridge, weighting or sampling measure is selected. The unchanged historical audit sources are available in a separately linked companion archive. Frozen audit sources and INT99 result dossier: https://doi.org/10.5281/zenodo.22541080.
A durable quantum record, the location of its coherence, and a uniquely actual outcome are different physical questions. We study their separation in a supplied finite-dimensional quantum theory. An explicit, time-independent apparatus couples a system–detector encoding to a controller, a distinct archive, and a finite returning source. A conditional energy penalty suppresses release of the original record without deleting its return coupling. An invariant reduction and a one-sided spectral-gap estimate yield a certified interval with archive occupation above 0.98438, controller-latched occupation above 0.99161, and filled-but-unlatched weight below 2.402 × 10^-7 in one stated design. The same record statistics admit different source-label overlaps and hence different coherence on a specified retained boundary. A conserved product of complementary exchanges accesses that coherence when the finite source is included. Given a calibrated multiregister reader, its finite-duration response separates the coherent apparatus from an independently added archive-gated reduction law, with the added process left active during readout. A conservative example retains a response gap above 0.01717 after separately stipulated one-percent error allowances. The contribution is the finite construction and its quantitative retention, access, and readout interfaces. Quantum carriers, Hamiltonian couplings, trace readout, source preparation, and the reader are supplied; local reader synthesis, empirical calibration, absolute rate selection, and unique-event actualization are not established. Paper code: CFQR-P1 (Complementarity-First Quantum Records — Paper 1). The associated bundle contains the technical supplement, editable LaTeX, numerical checking programs and rational certificates, and selected Lean sources with returned build and axiom-audit evidence. The 39 supporting declarations are partially formalized; eleven recorded type excerpts contain printing elisions. This is not end-to-end formalization, external human peer review, an experimental detection of fundamental collapse, or a derivation of unique-event actualization. Author-owned manuscripts, documentation and mathematical data are CC BY 4.0; author-owned software is MIT, subject to the bundle’s licence map and third-party notices.