DD-021
General Sharing Frontier
Verified the error-contraction and full-capacity theorems and independently reproduced the complete 177-scenario exact registry, witnesses, recovery budgets, and bounded mixed-curve null.
Completed finite studyChecked independently
The question
Inside the declared finite target-symmetric protocol class, when does one more shared signal improve, preserve, or reduce group discovery, and how many centralized pooled actions recover the named direct-private portfolio?
What we found
- DD-C-0097: In the registered finite target-symmetric block-sharing protocol, with pooled error e_s=1-C_s and constant conditional direct-action accuracy q, G_(s+1)-G_s=(1-q)^(N-s-1)[(1-q)e_s-e_(s+1)]; therefore the next sharing step helps, is neutral, or hurts exactly when e_(s+1) is respectively below, equal to, or above (1-q)e_s.
- DD-C-0098: Under the registered protocol, the centralized posterior top-L pooled value at L=min(N,M) weakly exceeds the declared N-action direct-private discovery value, so the recovery budget L* always exists and satisfies L*<=min(N,M); moreover L*=1 exactly when full consensus C_N weakly exceeds the private baseline P_N.
- DD-C-0099: Across DD-021's complete 177-scenario exact registry, 126 sharing curves are strict compression-dominated, 16 are strict aggregation-dominated, 35 are all-neutral, and none are mixed; full sharing yields 78 Shared Discovery Paradox cases, 16 strict aggregation-dominated consensus cases, 83 boundary cases, and no strict no-one-action aggregation-gain case.
- DD-C-0100: Under DD-021's frozen minimization order, the first same-baseline strict opposite-sign witness occurs at M=4,N=2,q=1/2 and private discovery 3/4: the noisy-point sharing step is -1/4, while the guaranteed two-shortlist step is +1/12.
- DD-C-0101: DD-021's minimized registered witnesses include an M=3,N=2 noisy two-shortlist Shared Discovery Paradox with q=3/8<C_N=27/64<P_N=39/64, an M=4,N=2 guaranteed two-shortlist strict consensus-dominance case with P_N=3/4<C_N=5/6, and an M=3,N=2 uninformative point case with C_N=q=1/3<P_N=5/9 and therefore no useful one-action aggregation gain.
- DD-C-0102: DD-021's exact recovery budgets are L*=1 in 51 scenarios, L*=2 in 55, L*=3 in 64, and L*=4 in seven; the first same-accuracy recovery separation is at M=3,N=2,q=1/2, where the noisy point requires two pooled actions and the guaranteed two-shortlist requires one.
- DD-C-0103: No mixed sharing curve—one having both a positive and a negative adjacent increment—appears in DD-021's complete 177-scenario registered grid.
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-theorems-four-independently-reproduced-computational-results-and-one-verified-bounded-negative-result
Reproducible evidence
20260722T185924Z_DD-021_3cdbbc40_2fea269a9a
Files and data
- Frozen finite protocol, baselines, and authority boundary
- Bounded exact scope, resource audit, and execution gates
- Theorem, registry, and recovery objectives
- Primary-source adjacency review and theorem-name boundary
- Error-contraction and full-capacity analytic proofs
- Separate internal proof-consistency audit
- Frozen exact channel registry, resource bounds, and certificate contract
- Audited analytic results, bounded census, witnesses, and limitations
- Complete exact 177-scenario registry
- Exact minimal registered witnesses and mixed-curve bounded null
- Exact two-method and witness-minimality agreement certificate
- Eight rejected registered corruptions
What comes next
preserve the immutable run, exact scope, claim audits, output-connected Lab, and centralized-authority boundary; the historical paper hold was satisfied by DD-022 and the deployed working paper