Fragment-size-averaged Holevo-information curves omit the identities of environmental fragments. We construct a restricted four-qubit example in which two equal-prior orthogonal pure-branch ensembles have exactly the same fragment-size-averaged Holevo curve (0, 1/6, 1/2, 1) and all four labeled singleton Holevo values equal to zero, while their minimum pure-common-rest carrier sizes differ (2 versus 4). Subject to the correctness of a reduced entropy formula and validated directed interval arithmetic, this coincidence persists for every choice of six raw amplitude coordinates in an explicit product box, with a unique two-coordinate correction inside a common root box. The solution family is open in the six free coordinates, not in the full coefficient or observational space. Analytic exact-rational sign bounds show that the two ensembles are separated by the pattern of labeled two-site fragment information (one positive pair versus three). Combining quantum Pinsker's inequality and an exact-rational simplex bound yields a permutation-invariant second-moment gap larger than 0.6128 bit², conditional on the existence certificate. The release includes the manuscript source, exact reports, four frozen phase source packages, original figure data, checksums, code, and AI-assistance disclosure. This is an unreviewed preprint, not a theorem about general carrier estimation, operational quantum data hiding, local indistinguishability, or finite-shot measurements. Independent priority assessment and comprehensive external peer review remain outstanding.
Fragment-size-averaged Holevo-information curves omit the identities of environmental fragments. We construct a restricted four-qubit example in which two equal-prior orthogonal pure-branch ensembles have exactly the same fragment-size-averaged Holevo curve (0, 1/6, 1/2, 1) and all four labeled singleton Holevo values equal to zero, while their minimum pure-common-rest carrier sizes differ (2 versus 4). Subject to the correctness of a reduced entropy formula and validated directed interval arithmetic, this coincidence persists for every choice of six raw amplitude coordinates in an explicit product box, with a unique two-coordinate correction inside a common root box. The solution family is open in the six free coordinates, not in the full coefficient or observational space. Analytic exact-rational sign bounds show that the two ensembles are separated by the pattern of labeled two-site fragment information (one positive pair versus three). Combining quantum Pinsker's inequality and an exact-rational simplex bound yields a permutation-invariant second-moment gap larger than 0.6128 bit², conditional on the existence certificate. The release includes the manuscript source, exact reports, four frozen phase source packages, original figure data, checksums, code, and AI-assistance disclosure. This is an unreviewed preprint, not a theorem about general carrier estimation, operational quantum data hiding, local indistinguishability, or finite-shot measurements. Independent priority assessment and comprehensive external peer review remain outstanding.
Fragment-size averages of the pointer Holevo information summarize how quantum environmental records are accessed without specifying their microscopic locations. We give a focused N=4 non-identifiability result: assuming the previously archived interval-certified root for a four-qubit two-branch witness, a second, two-carrier pure-branch ensemble exists with exactly the same complete size-averaged Holevo curve (A1, A2, A3, A4). The key additional step is a rational-interval verification of g(c) < 4A1 < 2g(sqrt(c)), where g(t) = h2((1+t)/2) and c is the overlap of the original branches. Continuity then provides the matching two-carrier ensemble, and the support-projection identity forces agreement at the remaining fragment sizes. Independent 16-dimensional state-vector calculations reproduce the matching averaged curves to floating-point precision; these diagnostics are not used as a substitute for the existence proof. The result concerns one certified curve in an equiprobable two-branch pure-state model, not equality of every individual fragment's information, an open family of curves, or arbitrary environment sizes. The original Krawczyk certificate is a documented imported premise and was not rerun in the present extension audit. Unrefereed preprint. Scientific claims are conditional on the archived original OBS01 certified-root premise. Supporting files provide numerical and interval checks, recorded base certificates and their hashes. Base Krawczyk/Arb computations were not rerun in this extension. This is not a claim of global priority or experimental realization. Manuscript, original notes and data are CC BY 4.0; original Python code is MIT; embedded archived materials retain their applicable component notices and rights. AI-assisted work is disclosed in the manuscript.
Correction in version 1.1 (2026-10-18) The Decimal/Fraction interval engine distributed with version 1.0 used context-sensitive Decimal unary negation and absolute value on interval endpoints. These operations can round inward, so the recorded P02G certificate in v1.0 should not be treated as a rigorously outward-rounded enclosure. Version 1.1 repairs those operations using exact copy_negate() and copy_abs(), hardens the second interval implementation's row-bound selection, and regenerates the interval reports, checksums, and reproducibility manifest. The certified rectangle, theorem scope, and all 34 mathematical environments in the manuscript remain unchanged. Repaired P02G and the separately implemented mpmath.iv P02J both pass the original theorem gates. The result remains conditional computer-assisted mathematical evidence, not formal machine verification or external peer review. Previous version (v1.0): https://doi.org/10.5281/zenodo.23438614 This unrefereed research preprint establishes a computer-assisted, quantitatively certified non-identifiability result for fragment-size-averaged Holevo information in an N=4 environment with two equiprobable pure pointer-conditioned branches. For every point in an explicitly specified closed rational rectangle of coordinate area 4 × 10^-14, two realizations of the complete averaged Holevo information curve exist: one with minimum pure-common-rest carrier size two and another with carrier size four. The proof combines a uniform parameterized contraction mapping, directed interval arithmetic with a second interval implementation, and an intermediate-value construction. Reproducibility materials include the certification programs, frozen numerical certificates, SHA-256 checksums, and a standalone 200-state numerical comparison against direct 16-dimensional partial traces. Both interval implementations share the underlying analytic Holevo reduction and do not constitute independent symbolic proofs. The conclusions are restricted to N=4, equiprobable pure branches, fragment-size-averaged Holevo information, and the specified carrier definition. They do not establish non-identifiability for arbitrary N, mixed states, unequal priors, or individual labeled-fragment information. This is an unrefereed preprint, not a formally verified or peer-reviewed mathematical theorem. Comprehensive novelty priority is not claimed. Licensing: The manuscript and original documentation/data are provided under CC BY 4.0 where applicable. Original Python research code is provided under the MIT License. The accompanying reproducibility archive specifies licenses on a per-file basis. AI assistance disclosure: OpenAI ChatGPT assisted with mathematical analysis, Python implementation, numerical and interval verification, manuscript preparation, and quality assurance. Claude contributed critical assessment and adversarial review assistance. Neither AI system is a coauthor or an external scientific referee. The human author, Yoichi Tsujisawa, assumes responsibility for the research and its publication.
Environmental fragments provide indirect access to pointer information, but fragment-averaged accessibility need not determine where microscopic branch dependence resides. For an environment of N subsystems, we quantify fragment pointer information by the Holevo quantity, which upper-bounds accessible classical information, and average it over fragments of equal size. Assuming two pure pointer-conditioned environmental branches share an identical, branch-independent rest outside a carrier, we establish an exact support-projection identity and a hypergeometric formula for the complete averaged accessibility curve. A carrier of size at most two is sufficient for a finite-N order-2 constraint; for N = 4, this yields A2 = A4/6 + 4A1/3 and A3 = A4/2 + A1. The converse fails in general: an interval-certified, computer-assisted N = 4 state-space construction satisfies these relations while having minimal carrier size four. We distinguish this distributed state-space witness from realizations in the tested five-qubit controlled-gate circuits. Using the pre-operation conditional branch state and the known gate, a prospectively frozen mechanism catalog correctly classified 417/417 protocol-defined, outcome-conditioned scored events at theta = pi/2; 28 post-R0 events among 445 eligible instances were handled separately. Paired sampled-parameter tests classified 320/320 scored events at each of theta = pi/3 and 2pi/3; these paired evaluations are not independent circuit replications. A separate retrospective numerical census classified 70/70 near-zero-residual R0 events as low-carrier within the sampled circuit population. Finally, an exact product-local preservation lemma supplies a sufficient condition for invariance of fragment accessibility, not a complete characterization. Together, these results separate exact operational constraints, nonunique microscopic realizations, and circuit-specific dynamical selection.
We study the local Holevo information of binary coherent-state ensembles restricted to a wedge of two free, minimally coupled scalar fields in AdS3. Canonical local subsystems, operator bounds on spectral tails, and certified ball arithmetic yield rigorous continuum enclosures. A centered coherent reference extends the transfer inequalities to arbitrary prior probabilities. The manuscript develops a stopping criterion and diagonal convergence under explicit algebra-exhaustion and faithfulness hypotheses. For theta = 3/5, occupation n = 1 and prior p = 1/2, the certified reference enclosure is 0.05969787 <= chi_B <= 0.06078801 nats. The original retained channel exhibits a certified separation of at least 0.01886667 nats between its Holevo information and an upper bound for Gaussian-measurement information. This comparison does not identify single-copy accessible information. The deposit includes the English and Spanish preprint, current LaTeX sources, Python programs, exact rational parameters, serialized interval certificates, dependency specifications and a complete verification/recomputation recipe. The original survey contains 31 certificates for 24 ensembles; subsequent studies examine spectral cutoffs, thermal selection, directed profiles, angles, occupations and uncompressed Gram upper bounds. Scope: free quantum fields on a fixed curved background. This is a preprint; no claim of peer-reviewed acceptance, universal optimality or absolute bibliographic priority is made.
Preprint and reproducibility archive; not peer reviewed. What this record contains. The full text of the manuscript "Identical Few-Particle Gauge Hamiltonians, Programmable Collective Charge Response" (M. J. Baek), its Supplementary Information with complete proofs, and the archive that certifies every closed-form value the paper states. The result. Few-particle dynamics are routinely used to infer collective response in paired quantum matter. This work constructs finite-range interacting response twins that defeat that inference exactly. For any prescribed finite p, two positive finite-range parents have complete static gauge Hamiltonians that coincide at every Peierls link phase on every sector N ≤ p and first separate at N = p+1; their zero-twist finite-density ground rays are the same Dicke condensate, yet their collective charge curvatures differ extensively. The obstruction has no universal depth, and the paper locates it exactly: the blind depth equals the spectator body order, the algebraic bound is independent of geometric range, and bounded range still bounds depth only through the number of sites a ball can hold — so no arbitrary-depth family of uniformly fixed range is claimed. Conversely, a structurally closed exact-pair tower closes at depth two. What is hidden is designable: with d(d+1)/2 displacement families the whole symmetric response-tensor difference is locally realizable at interior filling, and a triangular-lattice twin pair differs only in shear while both diagonal responses stay equal. A 4×4 hard-core-qubit discriminator gives an exact factor-of-two contrast with an internal null control and a state-preparation certificate in 17 equal-time settings. What is certified, and what is not. Results proved in closed form are stated as theorems and proved in full in the Supplementary Information; results established by exact rational or symbolic computation are labelled computer-assisted and carry the script that produces them; the 16-qubit discriminator is a blueprint with an end-to-end noise simulation, not a hardware demonstration, which is not claimed anywhere. Scope limits, open proof lines and one refuted conjecture are recorded explicitly rather than omitted. The archive. response_twins_unified_v1.0.zip contains the manuscript and Supplementary sources, the proof notes, the complete fail-closed verification harness (31 executed stages in release mode — 27 claim-bearing certificate stages, 1 non-claim diagnostic stage and three fail-closed gates — and 24 in quick mode) with one frozen log per stage, independent reimplementations of the load-bearing calculations, negative controls that must fail, the exact-arithmetic certificates behind every closed-form value in the paper, the figure-generation scripts, the scientific claim and provenance record (79 rows with status and scope notes, 50 of them naming the in-archive script or certificate that checks them, the rest saying in words why not), and a per-file SHA-256 manifest of all 209 payload files. Verifying it. Extract the archive and run python3 REPRODUCIBILITY/run_all.py --mode quick for the fast subset or --mode release for all 31 stages; bash BUILD.sh rebuilds both PDFs from source. The three gates check journal-format limits, the release payload against its manifest, and every number the documentation states about the artefacts. Running the harness does not modify the archive: all runtime output is written outside the immutable tree, so verification cannot invalidate the manifest. README.md separates reproducing the content (TeX Live 2023 or newer) from reproducing the archived PDF bytes, which needs the exact producing build recorded inside the PDFs. Licences. Manuscript, Supplementary Information and documentation CC BY 4.0; source code MIT; certificate data CC0 1.0. LICENSE.md is the authoritative per-file mapping and is included both in the archive and as a separate file on this record.
This source-only preprint gives a four-qubit counterexample to the arbitrary-phase extension of the first-excited parity conjecture discussed in Wong, Bravyi, Gosset and Liu, Lee-Yang tensors and Hamiltonian complexity, arXiv:2602.03605v1, Section 5.6. For an unweighted four-cycle with phase pi on one edge and a common parameter 0 <= s < 1, it derives the complete 16-dimensional spectrum and an exact parity threshold. The rational value s = 2/3 is an explicit witness; a specified fixed-witness robustness interval is also proved. The original zero-phase conjecture and the general all-graph gap problem remain open. Ground-state uniqueness and the non-strict gap bound are known inputs, explicitly credited to Wei, arXiv:2609.26802v2, Corollary 5.8 and Section 5.4, and Bravyi, Gosset, Liu and Wong, arXiv:2607.14401v1, Theorem 1. The concrete phase counterexample, complete spectrum and threshold are distinguished from these known results. The primary-source comparison is dated and bounded; worldwide priority is not certified. Read the unchanged PHASE_EPR_FINAL_MANUSCRIPT_v0.1.3_R2_20261010.tex or .md first, together with the current public source/verification supplement and PUBLIC_RELEASE_NOTE. Older versions and administrative private-draft wording, if present as provenance, describe historical preparation stages and do not define this public version or its reviewed scope. Auxiliary six-qubit exploration is outside this paper's completed claim. Shunpei Shimizu initiated and directed this personal independent project, arranged verification, and coordinated the materials. No university or institutional affiliation is declared. AI systems performed research exploration, proof construction, computational checks, analytical review and manuscript preparation. The reviews are internal AI analyses; independent human verification of every proof, specialist human peer review and complete proof-assistant verification are not claimed. No PDF of editorial revision R2 has been generated or visually verified: the available compiler failed during environment setup. Editable TeX, a readable Markdown manuscript and verification materials are provided. This is a limited, unrefereed research preprint, released under Creative Commons Attribution 4.0.