Zhou Lu
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When can a learner make only finitely many prediction errors along every infinite sequence labeled by a fixed, unknown hypothesis? We characterize this form of consistency for arbitrary binary hypothesis classes in ZFC, without requiring a uniform mistake bound. The characterization uses a single linear order on finite realizable traces. Each trace selects its least subtrace, and the order must satisfy two conditions: conflicting traces select different subtraces, and the order is well-founded on the traces of each fixed target. These conditions induce a learner whose selected evidence decreases on every mistake. Conversely, a consistent learner yields such an order through canonical mistake transcripts and the Kleene--Brouwer ordering. The result provides a representation of consistent prediction by finite evidence, answering a question of Lu (2024).
The same record, over MCP at https://syntology.ai/mcp:
get_harvested_code_for_paper("2609.28551")
get_code_for_paper("2609.28551")
have("2609.28551")
The run record, dated, one paper per request, free:
curl https://syntology.ai/api/ran/2609.28551.json
A badge for a README (the split and the date, never a ratio):
[](https://syntology.ai/paper/2609.28551)
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