A City Proof is eligible for citizenship when it is a distinct mathematical object born from credentialed parent identities and carries its own exact statement, ambient type, dependency graph, evidence class, executable or symbolic witness, review state, provenance, correction lineage, claim boundary, and transit passport.
$(C_1,\ldots,C_n)\longrightarrow P\longrightarrow \mathcal A(P)\longrightarrow \text{Citizenship}$
Birth rule: validated parents confer admissible substrate, not automatic truth. The descendant proof must satisfy its own proof obligations. Duplicate rule: restatements reconcile to the existing citizen; only a genuinely new theorem, invariant, construction, algorithm, or executable result receives a new identity. No-sprawl rule: proof citizenship is recorded in the existing City Proof Archive and Citizenship Registry; no new page layer is created.
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ONE-GLANCE RESEARCH OPERATING SYSTEM
Use this panel to see where new mathematical objects are, what remains unresolved, and which office owns the next action. The City updates existing structures in place. Routine automation creates no new child-page sprawl.
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Discovery → Identity → Verification → Machine Certificate → Citizenship → Borough Routing → Citadel Broadcast
Every object must retain its exact expression, ambient type, evidence class, provenance, correction state, destination, and claim boundary throughout transit.
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CITY SPINE · KARTEKEYA
Open Kartekeya — The Projection Spine of the Mathematical City
The City now treats $K\to\ker K\to P\to H=I-P\to x_\infty=Px_0$ as its central civic mechanism. Every borough inherits the operator, kernel, projector, evidence, and boundary discipline without changing its own domain.
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