DD-020
Incremental Sharing and Independent Rescue
Verified exact aggregation-rescue identity and point-channel monotonicity theorem, plus independently reproduced point and five-channel profiles.
Completed finite studyChecked independently
The question
For recommendation-like signals, what happens to group discovery as one more independent searcher is absorbed into a shared-answer block that takes one common action while all remaining searchers retain private actions?
What we found
- DD-C-0092: In the registered target-symmetric block-sharing protocol with pooled MAP accuracy C_s and constant conditional private-action accuracy q, group discovery is G_s=1-(1-C_s)(1-q)^(N-s), and its adjacent difference is (1-q)^(N-s-1)[C_(s+1)-C_s-q(1-C_s)].
- DD-C-0093: For every finite M>=2 and symmetric noisy-point accuracy p in [1/M,1], two-signal uniformly tie-broken pooled MAP accuracy is C_2=p; hence G_1=1-(1-p)^2, G_2=p, and G_2-G_1=-p(1-p), strictly negative for p<1.
- DD-C-0094: For every finite M>=2, N>=2, symmetric noisy-point accuracy p in [1/M,1], and adjacent block sizes s and s+1, the registered discovery profile satisfies G_(s+1)<=G_s; the inequality is strict for p<1 and equality for p=1.
- DD-C-0095: Across DD-020's 73 registered (M,p) cells, N=2 through 8, and all block sizes, the 2,555-row exact census has 1,848 strictly negative adjacent discovery increments, 196 zero increments, and no positive increment; every zero is a p=1 boundary row.
- DD-C-0096: In the M=4,N=3 DD-019 extension, the noisy point, noisy two-shortlist, guaranteed two-shortlist, explicit exclusion, and confidence-point incremental-sharing profiles are respectively (7/8,3/4,7/12), (387/512,11/16,35/64), (7/8,11/12,17/18), (19/27,17/27,16/27), and (485/512,113/128,295/384); the noisy point and guaranteed shortlist both have one-person accuracy 1/2 but have strictly decreasing versus strictly increasing profiles.
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
three-verified-analytic-results-and-two-independently-reproduced-exact-computational-results
Reproducible evidence
20260722T142551Z_DD-020_3854fff6_37c11a850a
Files and data
- Frozen incremental-sharing protocol and baseline semantics
- Living bounded execution and validation plan
- Primary-source adjacency review and explicit novelty boundary
- Human-readable aggregation-rescue proofs and theorem boundary
- Separate internal proof-consistency audit
- Frozen exact point-channel census and resource bounds
- Audited analytic and bounded exact findings with limitations
- Exact five-channel incremental-sharing profile plot
- Exact future-Lab channel profile data
- Rendered figure inspection record
- Complete public-safe exact point-channel census
- Exact five-channel curves and increments
- Independent method agreement and exact validation
What comes next
preserve the immutable run, scope boundaries, editorial ownership, and deployed output-connected Lab; require a new bounded gate for later work