{"slug":"oip-axiom-a0","title":"Axiom A0 — Inversion","body":"**A₀ — Inversion.** No concept is valid until tested against its negation. What survives negation is invariant; what collapses is contingent. This is the validity test applied to every other axiom, including itself. (Its negation — \"concepts are valid untested\" — collapses on contact with any adversarial environment.)\n\n---\n\n## Corpus map\n- Next: [Axiom A1](/a/oip-axiom-a1)\n- Canonical book: [Law I — The Ground](/a/oip-ground) · [Total Structure root](/a/oip-total-structure)\n- Sibling formalization: [Systems Design — The Premise](/a/systems-design-the-premise)\n- All axioms: [A0](/a/oip-axiom-a0) · [A1](/a/oip-axiom-a1) · [A2](/a/oip-axiom-a2) · [A3](/a/oip-axiom-a3) · [A4](/a/oip-axiom-a4) · [A5](/a/oip-axiom-a5) · [A6](/a/oip-axiom-a6) · [A7](/a/oip-axiom-a7) · [A8](/a/oip-axiom-a8) · [A9](/a/oip-axiom-a9)\n\n---\n\n## Bedrock status\n\nA0 is **foundational bedrock**, not a derived theorem. Hierarchy: [Axiom hierarchy](/a/oip-axiom-hierarchy). Negation of A0 is rejected as operational suicide, not self-proven inside the system.\n","register":"standard","tags":["OIP","axiom","philosophy","objection-11","bedrock"],"category":null,"style":{},"claims":[{"id":"c1","text":"No concept is valid until tested against its negation.","section":"A₀ — Inversion","tier":"speculative","source_ids":[],"source_status":"unsourced","why_material":"Core definition of the inversion validity test."},{"id":"c2","text":"What survives negation is invariant.","section":"A₀ — Inversion","tier":"speculative","source_ids":[],"source_status":"unsourced","why_material":"Defines the outcome of the negation test for validity."},{"id":"c3","text":"What collapses under negation is contingent.","section":"A₀ — Inversion","tier":"speculative","source_ids":[],"source_status":"unsourced","why_material":"Defines the outcome of the negation test for validity."},{"id":"c4","text":"Inversion is the validity test applied to every other axiom, including itself.","section":"A₀ — Inversion","tier":"speculative","source_ids":[],"source_status":"unsourced","why_material":"Establishes scope of the axiom as meta-test."},{"id":"c5","text":"The negation of A0 ('concepts are valid untested') collapses on contact with any adversarial environment.","section":"A₀ — Inversion","tier":"speculative","source_ids":[],"source_status":"unsourced","why_material":"Provides self-application example of the test."}],"sources":[],"prov":{"model":"Fable 5 (Claude Code)","action":"write"}}