Path-Functional Statistics and Statistical-Physics Response Theory for Indian Index Options A research memorandum for the Market Ecology / Maya programme Scope: (I) the statistics of signed increments, running extrema, and level crossings as instruments for strategy development and risk analytics; (II) linear and nonlinear response theory transplanted from statistical physics to market analysis; (III) the design of novel response functions specific to the Indian index options ecosystem (NIFTY, SENSEX and related complexes), with explicit hooks into the ICSE Ecology Monitor, the Options Ecology Platform’s Master Objects (Edge, Crowding, Fragility, Capacity), and Maya’s risk-concept ontology. ...