Exact in this model
The all-common source trap has a closed-form width.
In the frozen homogeneous equal-prize model, the exact trap width is p(1−p)/N; a separate finite audit and negative result define the boundary.
Key findings
Findings
What the evidence says about gathering information and spreading action across a search portfolio.
Evidence and sources
The source of a clue changes what agreement means.
Sharing and attention
Useful evidence need not belong in every hand.
Verified theorem
The first reader can help; duplicate use can reduce discovery.
In DD-012's frozen access-gated follow/private model, the first shared-signal reader improves discovery exactly when q exceeds p, while every later reader has a strictly negative marginal discovery effect.
Checked independently
Equilibrium can overuse a shared clue.
The registered 175-cell equal-split census contains 63 excessive-attention cells and 24 all-attend equilibria despite a unique one-reader planner optimum.
Checked independently
One reader can be the discovery-maximizing audience.
In DD-013's binding follow/private class, the optimal audience is one recipient when q exceeds p; the claim does not prescribe general information restriction.
Action portfolios and thresholds
Better rankings do not automatically create better search portfolios.
Canonical fixture
Same clues can produce different action portfolios.
The canonical fixture separates one shared answer, private clue-following, and a coordinated pooled portfolio; their discovery values differ because information aggregation and action allocation are distinct.
Verified finite theorem
Pooling one more point signal weakly lowers discovery.
Under DD-020's registered one-action point-channel protocol, each adjacent move replaces independent rescue with a pooling block and weakly lowers discovery, strictly unless signals are perfect.
Verified finite theorem
Sharing helps exactly when pooled error contracts fast enough.
In the registered finite protocol, the next sharing step improves discovery exactly when pooled error contracts by more than the independent-rescue factor it removes.
Theorem plus exact bounded census
A full-capacity centralized action list recovers the private baseline.
Posterior top-L authority always recovers the declared direct-private baseline by L=min(N,M), but 126 of 177 registered scenarios require more than one pooled action.
Incentives and equilibrium
Rewards and equilibrium selection shape who searches where.
Completed finite study
A bounded mechanism class contains strict rows.
The exact joint-mechanism census contains strict truthful-and-obedient rows under declared observability and subsidy assumptions; it does not establish an unrestricted mechanism result.
Verified selected-equilibrium theorem
Sharing can strictly improve selected autonomous discovery.
At p=3/5, the posterior-only anonymous symmetric shared equilibrium strictly exceeds the private anonymous symmetric Bayes-Nash equilibrium exactly for rho between the certified algebraic threshold and one.
Measurement and identification
Architecture comparisons require more than one score.
Bounded synthetic Atlas
Tradeoffs leave multiple coherent designs standing.
The bounded synthetic Architecture Atlas preserves multiple nondominated cells under its declared discovery, quality, value, cost, budget, and round objectives.
Limits and counterexamples
The boundary of a result is part of the result.
Preserved negative result
The registered conditional-policy theorem is not unrestricted.
DD-014's separate two-label raw-policy audit finds complementary constant policies above the best embedded private/public profile in every audited cell.
Scope-defining counterexample
One-person accuracy does not determine the sign of incremental sharing.
At the same one-person accuracy, the registered noisy-point profile falls while the guaranteed-shortlist profile rises. This bounded comparison does not establish a general channel order.
Preserved bounded negative result
No mixed sharing curve appears in the frozen general registry.
Both exact methods find zero curves with both positive and negative adjacent increments among 177 registered scenarios; this bounded null is not an arbitrary-channel theorem.
Preserved selection caveat
The positive-sharing result depends on equilibrium selection.
Constant split private equilibria attain discovery one, and ownership-aware shared rules can split on disagreement, so the strict posterior-only comparison is not an every-equilibrium theorem.