2026/08/01 by JEREMY H. CARROLL · 1 voice
Physics and Astronomy · Mathematics · #Quantum many-body systems #Quantum Mechanics and Applications #Advanced Operator Algebra Research #Projection (relational algebra) #Equivalence (formal languages) #Product (mathematics) #Observer (physics) #Hilbert space #Calculus (dental) #Argument (complex analysis)
paper · doi:10.5281/zenodo.21752743
openalex publication_date 2026/08/01 · openalex created_date 2026/08/03 · openalex updated_date 2026/08/03
Title. Projection Obstruction Anchor: Product Projections and Exact Short-Time Defect BoundsAbstract. Product-state projection of finite many-body dynamics defines local normal residuals. A declared family of local observation maps can turn those residuals into a 1-cochain; calling that cochain a coboundary additionally requires a specified repair differential and an exactness witness. Under explicit replica-extensive observer axioms, finite cochains admit a conditional edgewise ℓ¹ diagnostic. For finite one- and two-local Hamiltonians, a direct double-commutator argument gives an exact short-time lower bound for the raw two-site product defect, De(t) ≥ νet − 24g²t² depending on local quantities g and νe, and becoming system-size uniform under explicit uniform family hypotheses. Results are finite-carrier and finite-time. Quotient/exactness claims are restricted to finite-dimensional or closed-range presentations; quantum claims sit inside an imported finite-dimensional host. Why a researcher should care. Mean-field, Hartree–Fock, product-state ansatz, and tensor-factor approximations compress correlated states into tractable product data. This paper isolates a finite structural cost of that compression: a direction-valued normal rate, a declared route from local residuals to measurements, and an exact short-time defect-density theorem. The value is diagnostic rather than metaphysical. What this does not claim. This paper does not claim a finite-structural ℓ¹ norm, a thermodynamic-limit theorem, infinite-time persistence, global trace-norm equivalence for the declared edge-sum diagnostic, exclusion of arbitrary nonlinear smooth conjugacies, or a new physical theory. A positive product-retraction defect certifies non-product correlation, not entanglement. The paper does not derive Hilbert space, Born uniqueness, continuum physics, or governance authority. It grants no AuthorityEffect. Key closed forms (replayable). Result Formula / value Bell product-retraction defect (Ex. 6.1) D12(π/(8|J|)) = 1/√2 + 1/4 ≈ 0.9571067811865476 (both signs of J) TFIM normal rate (Ex. 6.2) νe = 2|J| (e.g. J = 1 ⇒ νe = 2) Short-time lower bound (Thm 5.1) De(t) ≥ νet − 24g²t² Tripartite local-green / global-red (§7.4.5) I(s) = 6, watched Jα = [0, 0, 0] Reproduction. Unpack the deposit and run: python -m pytest tests -q -p no:debugging python verifycertificate.py One-click notebook launchers: publicexport/runnotebook.bat (Windows), publicexport/runnotebook.sh (POSIX). Interactive falsification sandbox: jupyternotebooks/004falsificationsandbox.ipynb. Version / DOI chain. - Concept DOI 10.5281/zenodo.18896776. - Preceding published version v5.6: 10.5281/zenodo.20650922. - This package is published v6.0, version DOI 10.5281/zenodo.21752743.