The boundary-defined null connection (BDNC) framework [Zhang 2026, DOI:10.5281/zenodo.20032379] identifies unsorted-marginal stability as the diagnostic location where any predictively distinct extension of standard quantum mechanics would have to depart, but stops short of supplying a BDNC-specific predictive law: a generic future-state weighting ansatz amounts to a no-signaling violation rather than a BDNC-specific signature. This paper supplies one candidate. We propose the *Null-Boundary Response* postulate: in experiments with multiple coherent null alternatives and a future absorber boundary that partitions the channels, the joint source-absorber probability differs from standard quantum mechanics by a small response term proportional to the boundary-sensitive imaginary coherence between alternatives, antisymmetric across complementary absorber channels. The antisymmetry forces Σ_m Δ P_m = 0 by construction, so no-signaling is preserved exactly: the NBR candidate predicts no raw marginal violation. The imaginary-coherence form Im[Psi_A* Psi_B] follows from a first-order expansion under the future-boundary-dependent path-dependent phase twist; the natural distinguishability window from the marker-induced reduction is W(D) = D√(1−D²), peaking at D = 1/√2. The experimental signature is a small in-quadrature phase-shift residual in the coincidence-difference fringe pattern of a phase-scanned delayed-choice quantum eraser, antisymmetric across complementary post-selection channels and invisible in the unsorted marginal. The signature carries a six-feature fingerprint that distinguishes it from generic no-signaling violation, ordinary decoherence, detector bias, and standard two-state-vector imaginary weak values; in particular, the weak-trace "past of a quantum particle" interpretation underlying recent TSVF demonstrations [Vaidman 2013; Aharonov-Cohen-Elitzur 2017] is itself contested [Hance-Rarity-Ladyman 2023; Vaidman 2023], and NBR's predictive content must be (and is) sharper than either position in that exchange. We sketch the experimental protocol, identify basis-calibration as the principal systematic (β = 0 throughout denotes the independently calibrated real post-selection basis), and discuss what would constitute genuine confirmation versus confounding. A realistic target statistical sensitivity at N ~ 10^8 pair detections is ε ~ 10^-4, contingent on systematics control. The framework is restricted to two-path single-photon experiments with binary or finitely-multinary future-absorber channels; the multi-photon and massive-particle extensions are out of scope.
The boundary-defined null connection (BDNC) framework [Zhang 2026, DOI:10.5281/zenodo.20032379] identifies unsorted-marginal stability as the diagnostic location where any predictively distinct extension of standard quantum mechanics would have to depart, but stops short of supplying a BDNC-specific predictive law: a generic future-state weighting ansatz amounts to a no-signaling violation rather than a BDNC-specific signature. This paper supplies one candidate. We propose the Null-Boundary Response postulate: in experiments with multiple coherent null alternatives and a future absorber boundary that partitions the channels, the joint source-absorber probability differs from standard quantum mechanics by a small response term proportional to the boundary-sensitive imaginary coherence between alternatives, antisymmetric across complementary absorber channels. The antisymmetry forces Σ_m Δ P_m = 0 by construction, so no-signaling is preserved exactly: the NBR candidate predicts no raw marginal violation. The imaginary-coherence form Im[Psi_A* Psi_B] follows from a first-order expansion under the future-boundary-dependent path-dependent phase twist; the natural distinguishability window from the marker-induced reduction is W(D) = D√(1−D²), peaking at D = 1/√2. The experimental signature is a small in-quadrature phase-shift residual in the coincidence-difference fringe pattern of a phase-scanned delayed-choice quantum eraser, antisymmetric across complementary post-selection channels and invisible in the unsorted marginal. The signature carries a six-feature fingerprint that distinguishes it from generic no-signaling violation, ordinary decoherence, detector bias, and standard two-state-vector imaginary weak values; in particular, the weak-trace "past of a quantum particle" interpretation underlying recent TSVF demonstrations [Vaidman 2013; Aharonov-Cohen-Elitzur 2017] is itself contested [Hance-Rarity-Ladyman 2023; Vaidman 2023], and NBR's predictive content must be (and is) sharper than either position in that exchange. We sketch the experimental protocol, identify basis-calibration as the principal systematic (β = 0 throughout denotes the independently calibrated real post-selection basis), and discuss what would constitute genuine confirmation versus confounding. A realistic target statistical sensitivity at N ~ 10^8 pair detections is ε ~ 10^-4, contingent on systematics control. The framework is restricted to two-path single-photon experiments with binary or finitely-multinary future-absorber channels; the multi-photon and massive-particle extensions are out of scope.
Single-photon interference and delayed-choice experiments resist any account that treats the photon as a localized object carrying a private classical history. We propose the boundary-defined null connection (BDNC) view: a photon event is a null spacetime relation completed jointly by emission and absorption, with observable behavior fixed by the complete experimental boundary. The null-relation primitive itself is not novel — it appears in Kastner's relativistic transactional interpretation, Sorkin's causal-set null-link program, and the all-at-once / TSVF / Fixed Point Formulation literature. The contribution is unifying language: BDNC compresses these into a single vocabulary and identifies one operational criterion — whether the boundary modifies only post-selected correlations or also unsorted marginals. The latter case, parameterized by a generic future-state weighting ansatz, amounts to no-signaling violation rather than a BDNC-specific law; we outline two marginal-stability protocols and one weak-measurement consistency check that would constrain such deviations. The principal claim is therefore a unifying diagnostic, not a new falsifiable prediction: any predictive version must derive a BDNC-specific functional form for the future-state weighting. §11 sketches Twistor-Boundary Phase Geometry as a possible mathematical language for the framework, with the explicit caveat that minimal TBPG is empirically equivalent to standard twistor / gauge / QED. The paper is paired with a companion predictive extension: "Null-Boundary Response: A No-Signaling-Preserving Predictive Extension of the Boundary-Defined Null Connection Framework" (Zhang 2026, TBD Zenodo DOI), which proposes a candidate predictive law that produces a no-signaling-preserving channel-antisymmetric correction to coincidence statistics, with a six-feature experimental fingerprint testable in a phase-scanned delayed-choice quantum eraser.
Modern quantum measurement theory relies on successful but ontologically incomplete instrumental formalisms, such as decoherence theory, Lindblad dynamics, POVMs, and consistent histories. While these frameworks describe the operational behavior of measurement, they lack a structural account of outcome uniqueness. This paper demonstrates that Boundary-Induced Collapse (BIC), derived from the Theory of Axiomatic Necessity (TNA), provides the foundational ontology from which these formalisms emerge as partial projections. Within this framework, collapse is redefined as a deterministic structural minimization governed by the realizability functional F(psi,B), where B represents the boundary operator encoding experimental and environmental constraints. We establish explicit mathematical correspondences showing that standard quantum formalisms are operational shadows of an underlying boundary-controlled necessity. Quantum randomness is thus characterized as an epistemic consequence of unresolved boundary degrees of freedom, rather than a fundamental stochasticity. Finally, we prove that boundary projections form a complete POVM resolution of identity, naturally recovering the Born rule through boundary ensemble averaging. Diagram https://drive.google.com/file/d/1TxZtBJpwCAzkOGBU3sEpLwhV7DoC3tFA/view?usp=drive_link Boundary engineering: https://zenodo.org/records/18290437 Short explanatory video summarizing the Boundary-Induced Collapse (BIC) framework and its ontological motivation https://vimeo.com/1157778709?share=copy&fl=sv&fe=ci This framework remains physically undecidable until subjected to boundary-engineered experimental collapse, presented in DOI https://zenodo.org/records/18295265 "Technical Note: Empirical Validation of the BIC-TNA Model"DOI https://zenodo.org/records/18306759 "Experimental Predictions of Boundary-Induced Collapse (BIC) in Quantum Devices" Reader’s Guide: Given the high density of the TNA formalization, readers primarily interested in how this framework resolves standard quantum paradoxes (Bell’s non-locality, unitarity, and the Born rule) may find it efficient to first consult the FAQ/Appendix E. This section addresses the most common interpretative frictions by deriving them as structural consequences of the boundary-induced model, providing a clearer context for the technical derivation in the main body. Dedication “To my grandfather, a casino manager, who taught me that roulette cylinders are changed every week.”
How a finite real cycle acquires a complex structure and a rule for composition Quantum theory uses a common imaginary unit when individual systems become a composite. This framework constructs that compatibility from finite real source histories. On the complete contrast sector of a three-cycle, the forward and backward comparisons give J=3P−P2,J2=−I The complex structure appears after the real comparison is specified. At a qualified unmarked boundary, opposite reference shifts select QAB=2I−JA⊗JB The range is the balanced complex tensor product. Its many-source composition is associative. A finite controlled contact supplies a nonfactorizable complex-linear operation, and exact residual bounds quantify departure from the selected sector. A source model that produces the contact A reversible controller compares operation orders on 24 proper signed frames. Its ordered, arrow-insensitive axis detector produces the retained cyclic response. The contact algebra gives [[G,G],[G,G]][G,G]≅C3. The construction prints the controller, scratch cleanup, full contrast probes, admissible operations and refusal states. A triaxial real response tensor realizes the detector and provides an explicit map between material contrasts and event-count contrasts. A record must survive the test of future operations A present tensor can hide a material marker that a later operation reveals. The framework derives independent force-gradient calibration and a delayed odd-field release. With a nonzero release field, energy and vector torque reconstruct the entire marker change: DU=−Δp⋅E,Dτ=Δp×E.Δp=∣E∣2E×Dτ−DUE The test includes shared calibration errors, stray fields, finite release pulses, marker relaxation and a complete operation inventory. It distinguishes detection of a retained record from agreement with its frozen prediction and from discrimination between physical theories. From proved structure to existing experiments The paper adds a conditional probability-correspondence theorem for the balanced composite, examines independent-source quantum-network experiments, and reproduces all eight measured rows of a public torque dataset. These supply composition benchmarks and demonstrated apparatus capabilities. Their published significances are kept attached to the hypotheses they actually test. The calibrated material release law is also a conventional electrostatic prediction; it is not presented as a QTT-exclusive signal. One material coefficient, two readouts A new archival calculation transfers a published same-particle libration calibration to a separate precession measurement. In the qualified rotor regime, the cross-readout relation is Ξ=ωlib2EpωsΩElcosϕl=alibaprec. An unchanged dipole-to-inertia coefficient gives unity. The calculation yields a slope of 2.909 from the libration calibration, compared with the published precession slope of 2.950, a central difference of 1.4135%. This shared electrostatic consistency relation eliminates the separate dipole and inertia; unequal field gains, dynamical corrections and shared uncertainty remain explicit. Reversal and long-term dipole-stability observations identify complementary laboratory capabilities. The complete matched-tensor delayed-release test remains an experimental target. When do two descriptions differ in any future experiment? The finite-reference extension follows a controlled source contact through shared references, fresh references, inverse operations, intermediate measurements and feedback. Its complete order-three response is gn=∑k=02pkζkn,ζ=e2πi/3,g3=1,g2=g1. A finite observable-span algorithm tests two fully specified models across every permitted future word. It either certifies agreement or returns the preparation, operation sequence, terminal outcome and exact probability difference. In the populated compatible-instrument benchmark, the complete quantum representation gives the same records without an additional target fit. A source-selected physical coupling or preparation remains a distinct route to predictive value. The framework includes nine vector figures, the retained source proofs and countermodels, complete reference-history benchmarks, calibration and vector-reconstruction theorems, runnable exact and numerical checks, published-input receipts, a data assessment and an experimental packet specification. The introduction defines the QTT terms needed to follow the construction without prior familiarity with the corpus. The probability-interface theorem, finite-memory bounds and covariance-weighted witness specify which further laboratory comparisons can distinguish physical models. Source anchors QTT Main Book, especially pp. 56, 248-250, 352 and 827-829; Artian's Completed-Event Four-Capacity Theorem; Frame-cycle derivation map, completed-event lexicon, and Artian's Universe and laboratory readout. Stable citation: 10.5281/zenodo.22882084.
We give a self-contained explicit counterexample for the existential unregularized bounded-region fermion question on printed page 371 of Oberwolfach Report 7/2025, with pointwise operator-norm topology distinguished from strong-operator topology on page 365. In dimension three, one fixed smooth nonnegative radial compactly supported pair potential and one fixed interaction ball give a fixed smooth normalized annihilation mode whose Heisenberg norm differences tend to the maximal value 2. Explicit packed finite-particle Slaters and times pi/(2N+1-kappa) witness the same vector-norm limit, a stronger vector asymptotic, and changing normal-state values tending to 4. Both diagonal-density and normal-ordered interactions are covered with ordered-pair coefficient 1 and no ultraviolet smearing. A fixed smooth-cutoff commutator, Slater second moment and two-sector Duhamel comparison give error O(N^(-1/6)+N^(-1/3)). The kinetic energy acts on all of R³. Continuity on every fixed vector and in every fixed normal state remains valid. Siebert's arXiv:2609.34402v1, submitted 28 September 2026 before the original 7 October candidate, supplies the earlier high-density cluster and localized phase mechanism. Its stated theorem concerns full-space difference potentials, but its proof directly adapts to this bounded symmetric cutoff kernel and yields the qualitative existential conclusion. Its Proposition 2.6 explicitly gives maximal norm 2 for the full-space constant-number reference. The present note gives an explicit free-Slater transfer to the fixed spatial cutoff. A separately checked audit-time energy bootstrap also recovers the cutoff maximal limit through the earlier localized phase mechanism. These cutoff implications are deductions made in the audit, not literal cutoff theorems attributed to the prior paper. No first solution, first quantitative refinement, historically certified novelty, or continued open status through October 2026 is claimed. The bounded primary-source priority audit records access and indexing limitations. This five-page unrefereed research note is accompanied by its identical authored PDF/LaTeX source, unchanged 26-file historical candidate and independently authored analytic, operator-algebra, computational, source/model, priority and priority-mapping audits. The fresh computational family has 2,668 exact finite predicates and 558 floating diagnostics; finite tests supplement the universal written proof, and numerical diagnostics are not rigorous interval enclosures or formal proof certificates. Historical optimized-assertion and inventory weaknesses are repaired by externally pinned closed regular-file validation and isolated nonoptimized checker execution, while all original bytes and the original 1/5 candidate count are preserved. Historical result outputs are not claimed byte-identical to current replays, and runtime source-byte checks are explicitly omitted. AI tools were used extensively in development, verification, adversarial review and writing. Independent AI-assisted review is not human or journal peer review; neither is claimed. No copied third-party source bodies are distributed. No all-potential, all-region, dimension-one/two, fixed-density/energy, thermodynamic, fixed-state-discontinuity or CAR-invariance result is asserted.
This work presents a minimal, experimentally testable deviation from standard two-path interference. The deviation arises from an underlying discrete phase structure and appears as a small first-harmonic bias in the interference fringe. The predicted effect does not introduce higher harmonics or alter the qualitative form of the fringe. Instead, it manifests as a coupled visibility rescaling and phase offset that can be absorbed into standard sinusoidal fits. For this reason, the deviation is not directly visible at the level of fringe shape alone. To distinguish the effect from conventional systematics, a phase-cycling discriminator is introduced. Under controlled quarter-phase shifts, the residual is predicted to exhibit a structured quadrature rotation that is not generically reproduced by noise, detector imbalance, or calibration drift. A set of null-control conditions is provided to isolate this behavior experimentally. A characteristic magnitude for the effect is estimated under a class of structural assumptions, yielding a candidate scale on the order of 10−410^{-4}10−4, with a more strongly suppressed regime near 10−710^{-7}10−7. These values lie near the sensitivity threshold of high-precision interferometric measurements. The result is a concrete, falsifiable prediction: either a stable first-harmonic residual with the specified phase-cycling structure is observed, or the corresponding parameter regime is constrained. This document isolates the observable prediction and experimental test, independent of the broader theoretical framework from which it is derived.
Boundary-Condition Quantum Mechanics (BCQM): Primitives and Emergence This note proposes a minimal, amplitude-first foundation for BCQM built from three primitives—events, directed edges, and complex edge amplitudes—and a single hop-bounded, locally windowed selection rule that realizes the next event with probability proportional to |K_r|^2. Two operational scales anchor the construction: a short-window envelope (w_env) that controls locality in path sums, and a coherence horizon (W_coh) that reflects an empirical floor on recoverable interference. We give operator-level guarantees (Neumann-series control for the truncated kernel; LLN/CLT for hop counts under a local-boundedness principle), show that no-signalling is preserved, and motivate the envelope from GKLS-type local dephasing. To encode persistent records, inertia-like drift, and curvature from inhomogeneities, we introduce a strictly local back-reaction (Axiom 6) that remodels edge amplitudes near each realized event; we provide concrete, equivariant examples and a small menu of remodeling maps. An appendix outlines simulations with falsifiable hooks: S1: straight-line drift from phase gradients (inertia proxy) S2: PSD knee ≈ 1/W_coh in tick/jitter spectra S3: Zeno-like stall as w_env → 0 S4: stochastic anisotropy with 1/√M self-averaging S5: efficient truncated-kernel computation for hop balls This is a concise, testable proposal; continuum limits and full gravitational dynamics are deferred to follow-ups. v2 note 2025-11-18: This version adds an explicit “Outlook: entangled clusters” paragraph in the Primitives section. It clarifies that the current primitives are intentionally single-particle and that a configuration-space primitive for entangled clusters—consistent with BCQM II’s joint q-wave structure—is deferred to BCQM IV–V. No core definitions or results are changed; the update is conceptual and expository. Build notes: Compiles with biblatex/biber (Overleaf: set the main .tex and recompile twice).