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Theorem dependency and correction alerts
Edition: 8 October 2026. Initial decision: Prototype now. The product interpretation and pricing are hypotheses; independent proof and buyer validation remain open.
Research finding
The 7 October history records a sign error that invalidated one manuscript and two dependent papers. Other corrections changed hypotheses and companion citations. The release preserves prior versions, enabling a concrete regression fixture for dependency tracking.
Problem and buyer
Research teams and engineering teams adopting new algorithms need to know whether a correction invalidates a result they rely on. A changed PDF filename or bibliographic citation does not explain the affected assumptions or downstream implementation.
What the finding could enable
A monitored dependency graph can show the path from a changed lemma to a manuscript claim and then to a software component or experiment. It enables scoped review tasks and correction alerts tied to actual use rather than a generic news feed.
Technical and commercial limits
A citation is not always a logical dependency. Automated extraction must label inferred edges and allow human confirmation. The actual three withdrawn manuscripts require explicit withdrawal fixtures; family membership alone must not imply invalidity of unrelated papers.
Minimal architecture
Revision watcher -> citation and theorem-link parser -> dependency graph -> change classification -> affected-component report. Store graph edges with evidence spans, revision hashes and reviewed status. Keep historical snapshots instead of replacing the source record.
Existing alternatives and differentiation
Crossmark already distributes correction and retraction metadata. The proposed differentiation is theorem-level impact across Git repositories and software usage; bibliographic status alerts by themselves are weak differentiation.
Monetization hypothesis
Hypothesis: AUD 200-1,000 monthly for a research team and AUD 5,000-20,000 annually for an institutional integration. Buyers and budgets remain unvalidated. An audit service around one dependency-heavy project is the narrow entry point.
Validation experiment
Use the repository's withdrawal history as a retrospective fixture. Recover the three stated withdrawals and their stated dependency relation without flagging every paper in the same field. Have a mathematician review ambiguous edges.
Conditions to reject or defer
Reject a general subscription if alerts are too noisy, logical edges cannot be reviewed economically, or free correction metadata meets the user's needs.
Next concrete action
Extract the withdrawn manuscript notices and their archived-version links, then build an explicit three-paper fixture and a dependency impact report.
Source evidence
Repository sources are pinned to revision fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb. Selected scope notes and manuscript statements have been reviewed to the extent described above; these links do not represent successful kernel checks.
Family 032
Subject: The rational Hodge conjecture for CM abelian varieties.
- The rational Hodge conjecture for CM abelian varieties
- Algebraic Kuga–Satake correspondences and Hodge conjectures on a K3 quadratic locus
- Weil classes and Hodge classes on abelian powers
- Abelian covers, Gale correspondences, and the Hodge conjecture for powers
- A Conditional Reduction for Algebraic Kuga–Satake Correspondences
Family 149
Subject: Classwise permanence for weakly reversible mass-action systems.
- Uniform Permanence in Weakly Reversible Mass-Action Systems
- Boundedness and persistence of weakly reversible mass-action systems
- Formal scope notes
Family 376
Subject: Universal computation in forced Navier–Stokes flows.
A Fixed Particle Test for Computation in a Forced Viscous Flow
Universal Computation with Eventually Stationary Navier–Stokes Forcing
Velocity-Field Detection of Computation in Forced Navier–Stokes Flows
Scalar Potentials and Slow Clocks for Forced Fluid Computation
Current alternative sources
Primary documentation reviewed on 8 October 2026. Product availability demonstrates alternatives, not demand or willingness to pay for this proposal.