The spacetime weave and its consequences: theorems, mechanizations, and a falsifiable register (TQNT)

Abstract

Version 2 (August 31, 2026): acronyms, postulate labels and the bibliographic apparatus introduced and wired throughout (TQNT expanded, "Framework and notation" paragraph, name-first postulate glosses with point-of-use references, all 19 bibliography entries cited in text, STAR 2021 Breit-Wheeler reference added); the physics content is unchanged. Within the Topological Knot Quantum Theory (TQNT), we present the spacetime weave: spacetime as the continuous undulation of a single field chi, graduated in action (the pitch is h) — a three-dimensional ocean of which we are the waves. From this single object the paper derives its consequences: the birth of matter in the rails (nodal lines of the standing undulation: an entered wave magnetizes and knots at closure — particle = knot; light = the never-entered population), gravitation by depletion (a particle confiscates undulation; the neighbours' compensation gradient is the quantum gravitational field), and a fully mechanized cosmology: the flat Friedmann law and Omega_tot = 1 as theorems (expansion is the push of the weave paying for the wells it digs), local elasticity (why bound systems do not expand), the river theorem (the weave responds to density, not to individual motion — hence no weave-MOND), structure growth (sigma_8 deduced) and w = −1 constant by construction. The central thesis is epistemologically unusual: the observational indistinguishability from Lambda-CDM + GR is not an empirical finding of the framework — it is one of its theorems. Its counterpart is a register of dated, falsifiable absence predictions: zero GRB vacuum dispersion, zero drift of the constants (integer lock k = 135), zero curvature, w(z) must regress, non-replication of the large-scale CMB anomalies across independent probes, standard sirens giving the global H0, never a fourth family. G has a single equation: G = hbar·c / M_Pl² — the amplitude of the bare weave (the response to deficits); the nucleonic formula (12/7)·alpha^18·hbar·c/m_base² is the reading of the Planck rigidity by the nucleon (m_base = M_Pl·sqrt(12/7·alpha^18)), not a second equation. Predicted value −0.05% vs CODATA, with the declared, significant residual −4.9×10⁻⁴ as an attached prediction (metrology must converge downwards). Epistemic honesty as an argument. Every statement carries its status (derived, theorem, conditional, calibrated, hint, measured); the paper closes with a 16-line dated falsifiability table (each line a single sufficient contrary observation) and the refutation register of the programme — 11 dated entries with reasons (including the Li-7 'ashes of the freeze-out' mechanism, refuted the very day of its consolidation at the efficiency wall) — because a theory is also judged by what it knows how to reject. The four inherited mysteries (H0, S8, Li-7, muon puzzle) are declared as such. Bundle contents. French and English editions (LaTeX sources + PDFs, 25/24 pages) and the bilingual weave and funnel figures. Focused extract of the TQNT V6 monograph (version of 2026-07-28).