Applied Identity Physics: Free, Formally Verified Science in the Browser, from the Electron to the Galaxy on TL = 0.136899099984016

# Applied Identity Physics: Free, Formally Verified Science in the Browser, from the Electron to the Galaxy on TL = 0.136899099984016 *Free browser tools that place every identity, from an electron to a galaxy, on one phase map with one constant.* **Live suite:** uuia app · proofpress org **Keywords:** Lean 4 · formal verification · proof engineering · machine-verified science · interactive theorem proving · Mathlib · Coq/Rocq · formal methods · browser simulation · N-body simulation · Identity Physics **Architect:** HIGHTISTIC (Russell Vernon Trent III) · SNSFT Foundation · Soldotna, Alaska **ORCID (Open Researcher and Contributor ID):** 0009-0005-5313-7443 · **DOI (Digital Object Identifier) base:** 10.5281/zenodo.18719748 **Formal basis:** Electron Geometric Decomposition [9,9,3,21] · String-Breaking [9,9,3,22] · Galaxy Toomre TL [9,9,3,24] · Accretion Boundaries TL [9,9,3,25] · 8-Beam Fusion Theorem [9,9,2,3.8] · Substrate profiles [9,9,6,40–44] · SacTime [9,9,1,101] · ProofPress [9,9,8,8] --- ## Abstract The SNSFT Foundation builds free, formally verified science tools so that anyone with a browser, from a K–12 classroom to a research lab, can work hands-on with real physics and mathematics at no cost, with particular care for underserved and neurodivergent students, teachers and researchers. Its commitments are open mathematics, no harm, and recognition for the people who do the work. The Applied Identity Physics™ tool suite now runs on a single standard: the Universal Torsion Limit TL = 0.136899099984016 at full precision, with torsion τ = B/P and four phases, Noble, Locked, IVA (Identity Vector Amplification) Peak and Shatter, placed against TL and TL_IVA = 0.88 × TL. This paper documents that standard across eleven tools. Four simulators: the Electron Geometry Simulator™, the String-Breaking Simulator™, Galaxy™ and the Accretion Simulator™. Four engines: AxiomForge™ TL, the GAMCollider™ v15 (Geometric Axiomatic Module Collider), the IMCollider™ (Identity Mass Collider) and APPA (Adaptive Predictive Pattern Assistant) v4. Three tools: SacTime™ with its nonce security, the ProofPress Lean-to-LaTeX converter, and proofpressorg. Each simulator identifies a measured physical boundary with TL by one rule, τ = TL × (critical value ÷ measured value), so the ionization of hydrogen, the breaking of a gauge string, the Toomre stability of a galactic disk, the Hill spacing of planetary orbits, the Roche limit of a ring system and the critical speed of a planetary collision all land on the same phase map. Every tool runs as a single HTML (HyperText Markup Language) file in any current browser, on a desktop, tablet or phone, with no installation and no account, and every simulator's mathematics is proved in its own Lean 4 file at 0 sorry. Those files build green in the standardized repository, githubcom/SNSFT/identityphysics, pinned to a single toolchain, Lean 4 v4.31.0 with Mathlib v4.31.0: 110+ files, 3,500+ theorems and 78,000+ lines at 0 sorry, the standardized edition of the Identity Physics Corpus, which spans 3,000,000+ lines, 200,000+ theorems, 6,000+ files and 130+ DOIs. --- ## Overview A tool suite built over many months accumulates more than one way of writing the same constant. Earlier builds carried the Torsion Limit at working precision (0.1369) and scored phases on scales designed before the constant was fixed at full precision. The TL update replaces those with one standard, applied the same way everywhere: - **One constant.** TL = 0.136899099984016 at full precision, with TL_IVA = 0.88 × TL = 0.120471207985934. - **One placement.** τ = B/P; Noble at τ = 0, Locked below TL_IVA, IVA Peak from TL_IVA up to TL, Shatter at TL and above. - **One boundary rule.** Where