Start with the research
NSRW turns mathematical questions into source-linked results, checked proofs and executable scientific computations. The present study starts with OpenAI's outgoing-profile construction and investigates how two differently weighted histories cancel.
The central finding
For every fixed source Profile F, there is a positive threshold depending on F. For every positive parameter below that threshold, a point strictly inside the first repair window has M = 0 and J > 0 at the same point.
M is the source mass history; J is its H-weighted angular history. Separated repair supports and unequal relative weights explain why their cancellations do not coincide. This gives a concrete obstruction to using the candidate ratio Q = J/(M H) at that point.
The quantitative extension gives a positive lower bound for local J at every qualifying first-window mass zero. Normalization and a cutoff plateau replace an exact bump integral with a conservative computable lower bound.
Choose a route
- Understand the mathematics: read P01, then inspect the named Lean statements.
- Run a concrete computation: use the core-scalar method and second-backend check.
- Replay the proofs: follow REPRODUCE. It distinguishes proof execution checkpoints from later document revisions.
- Follow the next research step: see the math-to-code bridge.
- Read the research process: P02 explains the implementation and observed failure cases.
Important source documents
The following documents contain detail beyond the papers. They retain dated research history; use their headings and dates when reading an older task state.
- P2 mathematical investigation: candidate ratio, rejected endpoint-first-zero assumption, repair geometry and weighted-tail argument.
- Quantitative receipt: ten named quantitative and normalization propositions.
- Z-core receipt and Z+J receipt: the source-facing existence and same-witness results.
- Equation to Artifact roadmap: the broader route to reusable operations and scientific use.
Practical direction
Two useful outputs are being pursued: mathematical computation primitives (normalization, certified bounds and cancellation diagnostics) and research workflow primitives (source/result consistency and regression checks).
The next numerical milestone is a certified moment witness: an admissible evaluable model, strict mass signs around an interval, and a positive J lower bound applying to the same exact zero. A reusable diagnostic can then be evaluated against a baseline in a selected scientific workflow.