Alphabeta Math
ExampleConstruction: AI-adaptedVerification: AI-generatedPipeline-generated
How statement and proof provenance work

The first chip identifies the source of the statement or construction; the second identifies the source of its local proof or verification.

  • Literature-sourced: the exact statement appears in a cited source; only wording and notation differ.
  • AI-adapted: a semantically identical restatement of literature-sourced material, modulo indexing, notation, and boundary cases adopted by the library.
  • AI-generated: a genuinely novel statement formulated by AI, with no source for the claim itself.

These labels describe origin, not correctness: citations and verification chips remain separate evidence.

An above-cutoff product moves mass into the reported reservoir

Statement

On a grid ending at cutoff R=4, an aggregation event between two particles of mass 2 has product mass 4 and stays in range, while an event between masses 2 and 3 has product mass 5>R and removes retained mass 5 while adding reservoir mass 5.

Facts & Assumptions

Given: A finite sectional grid containing pivots 2,3,4 and the reported-overflow rule.

[F1]

Finite sectional coagulation-fragmentation balance with reported overflow: when xi+xj>R, both parents are removed and the sum of their masses is added to L.

[F2]

Finite sectional event dynamics preserve positivity and retained-plus-reservoir mass: each overflow event has zero augmented-mass change.

Proof

1.1givenF1algebra

For masses 2 and 3, their sum is 5, which exceeds R=4. The rule [F1] therefore consumes masses 2+3 and increments the reservoir by 5.

2.1F1F2step 1.1algebra∎

The retained mass change is −(2+3)=−5 and the reservoir change is +5, so augmented mass change is zero, as asserted in [F2]. This reservoir entry has no later fragmentation dynamics under [F1].

Depends on

Used by

Nothing in the library uses this result yet.

Dependency tree · two levels

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Sources