DD-016
Threshold Discovery
Verified minimum-viable-team theorem and independently reproduced exact threshold and occupancy census.
Completed finite studyChecked independently
The question
How should posterior evidence be converted into a portfolio of actions when a candidate is discovered only if at least tau agents choose it?
What we found
- DD-C-0071: In the frozen atomic threshold-opening model, a deterministic planner's optimal discovery value is the sum of the largest min(floor(N/tau),M) posterior masses, and an optimum exists that assigns exactly tau agents to each selected candidate before placing leftovers.
- DD-C-0072: If every other agent independently selects candidate j with probability x_j, equal splitting gives payoff V*pi_j*E[1{K_j>=tau-1}/(K_j+1)]; at tau=1 its share factor is [1-(1-x_j)^N]/(N*x_j) with zero limit one, and at tau=2 it subtracts (1-x_j)^(N-1) and has zero limit zero.
- DD-C-0073: In DD-016's canonical M=16, N=8, p=1/5, tau=2 fixture, common deterministic mode, selected independent uniform mixing over tied posterior modes, private clue-following, and the paired planner have exact discovery 37916217637/98876953125, 275661897594857/576650390625000, 194017/390625, and 223779310319051/333709716796875 respectively; the selected mixture has exact expected distinct count 222783285994256/129746337890625, viable count 4605284003019928/3243658447265625, largest crowd 21276151146203888/3243658447265625, and pair-collision probability 3368373871489/4449462890625.
- DD-C-0074: Across tau=1 through 8 in the canonical DD-016 fixture, both common deterministic mode and registered tied-mode mixing lower discovery relative to private clue-following at tau=1 and 2 and raise it at tau=3 through 8; the deterministic planner strictly exceeds the selected tied-mode result at every threshold, only one viable coalition can form at tau=5 through 8, and planner diversification strictly beats common mode at tau=1 through 4 before tying it at tau=5 through 8.
What this result covers
Checked independently. The formal evidence wording and registry state remain available below.
Technical details
- Study phase
complete-bounded-study- Registry status
complete-bounded-study- Evidence status
two-verified-proof-claims-and-two-independently-reproduced-exact-censuses
Reproducible evidence
20260722T021526Z_DD-016_00271ff8_123b2809e3
Files and data
- Frozen threshold-discovery model and protocol boundaries
- Living execution and validation plan
- Deterministic planner and strategic-payoff derivations
- Focused adjacent-literature and novelty-risk review
- Exact bounded results, phase diagram, and verification report
- Public-safe exact canonical threshold metrics
- Public-safe exact tau-one-through-eight phase data
- Exact two-method state-count and agreement certificate
- Four registered corruption rejections
What comes next
preserve PR 102, the immutable run, and selected-equilibrium boundary while DD-017 proceeds