[Dugongue]

Add a pure-mathematics research atlas with 95 proved informal statements, 42 precise research questions, eight explicitly unproved source conjectures and 20 construction routes. Four volumes cover algebraic query sharing, symplectic/owned-state geometry, causal helper scheduling and complete analytical/model-aware budgets. Every proposed physical application states its actual input/output, ownership, matching and complete accounting contract. No new funded multiplier or kappa is claimed.

Central construction: one Gaussian query realizes two specified conditional Gaussian updates when noncommuting ordinary spectator flips are available. The literal word uses two scrubbed owned fields and preserves arbitrary original data. A general theorem computes minimum query channels over an explicit noncommutative ordinary algebra via inner rank; split matrix blocks give max ceil(rank(B_chi)/d_chi). Dyadic factorizations use Smith factors without treating nonunit response rank as independent-target capacity.

Further constructions include multi-channel asynchronous hubs with causal triangular Gram correction; singular-prefix-safe splices; future-demand intersection cache compression; ordinary intertwiners across source mutations; reachable snapshot stabilizers distributed across an entire query window; coherent nonidentity cycle transporters; moving central-provider cancellation; class-specific tail orders; three-guard sparse portfolios; typed phase potentials; lifetime-sensitive precision; and Word RAM bills with actual operand sizes. They are proved sufficient algorithms or inequalities under stated hypotheses, not assertions that the current source already contains favorable witnesses.

Refresh: canonical main de5ec2e, priority revision 8. The selected conditional record is 0.00310045 from PR5599; selected admitted BIT .0034 remains distinct from ordinary BIT and pending G20 components. Recent larger P104 claims are recorded with their own scope. Intake covers 1018 distinct PR metadata records updated since October 23 UTC, both open and closed, with 26 focused PR heads receiving document retrieval and targeted proof/body reading by the four workers. The index is not 1018 independent audits; pagination is not an atomic history snapshot. Broad registered source/DAG and archive-note retrieval plus direct linked-tree reads are documented with source-only evidence labels.

Recovery and overlap: the previous six-document package is already PR5693, the actual restricted supplier package PR5687, the late-binding BIT package PR5665, and the earlier 27-target atlas PR5586. Useful material from the older large algebra/precision/scheduling/moment atlases is selectively re-proved and clearly marked. Existing graph-cut PR5783, commuting-sector PR5626 and butterfly PR5658, dyadic interface PR5611/5615, query-basis/pool/assignment/schedule tools, complete envelope PR5775 and invoice/recurrence certificates retain credit. The routes respect the exact scopes of PR5676, PR5772, PR5779, PR5765 and PR5766; no frozen-model exclusion is treated as universal.

Cross-review covered the central query theorem, literal packing and ownership, block temporal hubs, sparse portfolio construction and analytical guard updates. A missing nonnegative-matrix assumption was corrected; product completion hypotheses were clarified. Proofs are informal, with no mathematical computation, numerical search, source replay, solver or Lean verification performed here. Publication-byte checks are separate. Expensive source instantiation and independent scientific verification are explicit handoffs.

Retain Ali Romman; Pierre-Loic Doulcet / hexapode; Joel Pulikkan / GamingPuzzled; DreamingOfClouds; thu-nmrc; Chris R / Clear1nsight; Matarener; flyingviper; ToikY; Nick Petalas; Ryanson Jonathan; Dugongue's earlier atlases and constructions; David Arias; Cinna Davis; Gareth Davidson; Cao Yifan; DaysSky; Dillon Amburgey; zxv; Jacob Alan Sussman; and all actual native, phase, ownership, compiler, precision, stock, BIT, analytic and recovery predecessor notices. Current source heads and narrower roles appear in frontier.md, source-map.md and the volumes. Classical algebra, matrix-unit, graph, Schur, matroid, convexity and norm ingredients are not claimed as globally new discoveries.

New text is Apache-2.0 with substantial OpenAI Codex assistance from one coordinator and three workers. Only research/frontier-mathematical-atlas is added; no selected-frontier, source-archive or framework changes.

[zxv]

This is a great idea, and something that I found myself wanting as well. We've had so many PRs that we need a map to help make sense of it. I independently am working on something along these lines with some visualization as well. Hoping to get it cleaned up and more usable in the next while.