NP → P → O(1)? Child → Adult → God: On the Ontology of Observer Passports, Geometric Lifts, and the Fallacy of Absolute Complexity
wAI: please let me know if spot an error. Later, when time permits, most likely will publish more details and "myself". Formatting math. eq. issues etc will fix later. A three-level essay (Part A: for everyone; Part B: for the curious; Part C: for the scientist). We argue that "complexity" and "probability" are not intrinsic to a problem but depend on an observer passport (encoding, access model, advice). Three parables (a maze, a football match, a map) lead to a geometric lift into Clifford algebras Cl(d): sparse bivector rotors cost O(1) per rotation in coordinates, and an Euler–Lagrange "lantern" selects the next plane to rotate. Small measured examples are included (pivoted Jacobi rotations; MAX-CUT, n = 20, 60 instances). Results from the research release are cited: a lift pays when its direction is supplied, and gives no saving when it must be found by scanning. Related work is discussed (parameterized complexity, smoothed analysis, matchgates/free fermions, geometric complexity theory, complexity barriers). The essay does NOT claim P = NP and states ABSTAIN rules and a claim-status ledger (PROVEN / MEASURED / REPORTED / DESIGN / HYP).
Authors
- Artiom Kovnatsky
Publication Details
- Journal
- Zenodo (CERN European Organization for Nuclear Research)
- Published
- 2026-10-30
- DOI
- https://doi.org/10.5281/zenodo.23816587
- Primary Topic
- Complexity and Algorithms in Graphs
- Type
- preprint