Compendium of the Harbor coordination program's executed results R1–R17 — information floor, split-digest theorem, derived regret head, digest-zoom frontier, hypervisor-as-supervisory-control, sheaf equivocation verdict (with the consistency-radius theorem), inspection tower, work-unit machine, sealed-room noninterference, ε-ledger conservation, canary/SPRT detection power, no-mint reputation inheritance, engine substitution and resurrection soundness, costly-escalation tuning band, Erlang-C specialization boundary, context paging under a corrupted pin oracle, and the tractable deontic-conflict fragment — with exact statements, verified-vs-internal numbers, honest boundaries, paper mapping, and the tacit lessons behind them. Use when extending, citing, presenting, implementing, stress-testing, or planning follow-on work (papers, proofs, product claims) on any of these results. NOT for general math/CS reference, Port Daddy product features outside these results, or writing style (see harbor-exposition).
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Compendium of the Harbor coordination program's executed results R1–R17 — information floor, split-digest theorem, derived regret head, digest-zoom frontier, hypervisor-as-supervisory-control, sheaf equivocation verdict (with the consistency-radius theorem), inspection tower, work-unit machine, sealed-room noninterference, ε-ledger conservation, canary/SPRT detection power, no-mint reputation inheritance, engine substitution and resurrection soundness, costly-escalation tuning band, Erlang-C specialization boundary, context paging under a corrupted pin oracle, and the tractable deontic-conflict fragment — with exact statements, verified-vs-internal numbers, honest boundaries, paper mapping, and the tacit lessons behind them. Use when extending, citing, presenting, implementing, stress-testing, or planning follow-on work (papers, proofs, product claims) on any of these results. NOT for general math/CS reference, Port Daddy product features outside these results, or writing style (see harbor-exposition).
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{"category":"Research & Knowledge","tags":["harbor","coordination","theorems","results","multi-agent","oversight"],"version":"1.0.0","pairs-with":[{"skill":"harbor-exposition","reason":"The presentation style these results ship in"},{"skill":"falsification-first","reason":"The discipline that produced and validated these results"}]}
Harbor Results: The Executed Corpus (R1–R17)
Seventeen results, executed and reproducible (program seed 20260816), each with a one-breath statement here and full depth in the references.
When to Use
✅ Use for: citing or restating any R1–R17 result precisely; choosing which result underwrites a product claim; extending a result or checking whether a "new" idea is already covered or already refuted; packaging results into papers; onboarding a collaborator to the program.
❌ NOT for: general information theory / game theory / security reference unrelated to these nine; Port Daddy engineering outside the results (kernel schemas, CLI); exposition mechanics (harbor-exposition); running the validation discipline itself (falsification-first).
The Seventeen, in one breath each
R1 — Information floor. No digest below log₂C(N,k) − log₂C(m,k) bits can guarantee catching all k critical items among N while opening m; survived falsification (0/16 violations).
R2 — Split-digest. One scalar summary serves two readers iff their orders are comonotone; successor-agent and operator provably are not; joint zero-miss floors are super-additive (≈2.13×, not 2×).
R3 — Derived regret head. stakes × irreversibility × anomaly = exact expected unrecoverable loss iff anomaly is a calibrated posterior; optimal surfacing is the likelihood-ratio test; reputation enters only through the posterior.
R4 — Digest-zoom frontier. Two-constraint rate-distortion R(δ,f) with the old floor as its zero-miss corner (R(0)=H(p), e.g. 0.286 bits at p=0.05); adaptive zoom needs ≈k·log₂(F/k) opens vs F flat — only in the sparse-flagged regime.
R5 — Hypervisor = supervisory control. A policy is preventable (regimentable) iff controllable w.r.t. the uncontrollable event set (Ramadge–Wonham K̄Σᵤ∩L̄⊆K̄); "no egress after reading a secret" IS regimentable — gate the channel, never the token.
R6 — Sheaf verdict. Cohomology detects equivocation beyond pairwise comparison iff the missing edge lies on a cycle (cocycle sum ≠ 0); on a cut edge, never. Conditional commit with that exact scope.
R7 — Inspection tower. ρ* = G/(dB); sealed sampling from C cliques makes bribery uneconomical (profitable iff G_k > C·B), corruption decays (1−ρd)^k; reputation is amortized verification (Θ(log T) or O(1) audit spend).
R8 — Work-unit machine. Six safety invariants hold in all 536 reachable states; all five guards proven load-bearing by mutation (shortest crimes: 4, 2, 4, 1, 7 steps).
R9 — Sealed-room noninterference. Erin's view identical across equal-parity secrets under every interleaving to depth 7; schedule secret-independence checked separately; leaky-gate and bypass mutations caught with witnesses.
R10 — ε-ledger conservation. The release ledger's atomic append+add conserves σ = Σ_Λ εᵢ ≤ εmax under every concurrent interleaving (single-writer serialization); sequential/advanced DP composition gives the sum its meaning; recorded spend only — mediation is R5's job.
R11 — Canary power + SPRT. k smuggled canaries are caught w.p. 1−β^k; uniform planting gives the hypergeometric operating curve Pr(detect)=f(leak size); Wald's SPRT turns leak intensity into expected time-to-detection with errors at or below target.
R12 — No-mint inheritance. Fork priors conserve iff split = transfer (the source is debited): total live creditable reputation never exceeds total witnessed; copy-full inheritance mints 8.2× from one episode — the quorum attack the invariant blocks.
R13 — Engine substitution. Unattested, swapping a cheap engine behind a good record pays Δc at every price (Akerlof unraveling inside one identity, threshold μ*); engine attestation flips the incentive to Δc−Δθ — the planner's rule at zero audit stake; resurrection across providers is sanction-sound iff all three migration clauses hold, with a shortest attack per dropped clause.
R14 — Escalation tuning band. Monotone benefit and validation give a unique escalation threshold u*(δ) (Spence-style separating equilibrium; u* = δw/(1+δw) uniform-linear); the feasible debit set between alarm fatigue and distress silencing is an interval that can be EMPTY — then the fix is capacity or evidence quality, not tuning.
R15 — Specialization boundary. A sole specialist beats the pool iff μs/μg ≥ g(ρ,c) = cρ + c(1−ρ)/(c(1−ρ)+C(c,ρ)) — the whitepaper's proposed threshold falsified in both directions; with mortality ξ and succession rate η, pooling dominates at EVERY skill premium once ξ/η > D* — the price of the succession rule.
R16 — Context paging. Landlord's k/(k−h+1) competitiveness imports to variable-size context spans; a pin oracle corrupted at rate φ costs only an ADDITIVE φN·c_refetch with repair-on-touch — and exactly one blind-trusted corruption costs Θ(N); φ is R1's forgeable-feature budget, shared.
R17 — Deontic conflict fragment. Inside Horn + ground intervals + difference constraints, commitment-conflict detection is polynomial with a witness per conflict; one expressive step out (disjunctive obligations) is NP-complete — the fragment boundary is the exact price of proposal-time checking.
R6 theorem (CR). The completion residual r is a certified lower bound on any injected lie (equality at the completion), localizes to cycles through the equivocator, and computes in Õ(|E|·L); single-equivocator only — coalitions on a cycle can cancel to r = 0.
Routing
flowchart TD
Q[Query about the program] --> A{Need the precise statement,\nnumbers, boundary, or paper home?}
A -->|yes| C[references/results-compendium.md\nload the matching R-section]
Q --> B{Extending, re-deriving, implementing,\nor building a similar experiment?}
B -->|yes| L[references/l3-tacit-lessons.md\nread the matching lesson FIRST\nto avoid re-hitting known traps]
Q --> P{Planning papers or next wave?}
P -->|yes| C2[compendium end sections:\npaper map + remaining roadmap]
Anti-Patterns
The Unpriced Side Channel
Novice: "My simulation's oracle knows the answer; I only charge bits for output resolution."
Expert: Information bounds constrain what a channel carries; charge bits for identification, not tie-breaking. A sim that smuggles identity past the meter will appear to beat the floor (R1's 8/14 spurious violations before the fix).
Detection: Any experiment "beating" an information-theoretic bound.
Cohomology of the Sheaf, Not the Data
Novice: "dim H¹ of the sheaf detects the inconsistency."
Expert: dim H¹ of the abstract sheaf is a property of restriction maps, data-independent. Equivocation is an obstruction of the observed assignment (is the disagreement cochain a coboundary?). And the value-add exists only where the missing edge lies on a cycle.
Timeline: Both wrong turns hit and documented 2026-08; they located the boundary.
Detection: Computing H¹ without the observed data anywhere in the computation; testing on a bridge/tree topology.
Zoom Everywhere
Novice: "Group testing always beats flat inspection."
Expert: It pays ≈F/(k·log₂(F/k)) only when positives are sparse in the flagged set; dense flags make splitting overhead dominate. Zoom is for the miss-averse over-flagging regime — exactly where a safe digest operates.
Detection: Claiming zoom savings without stating flagged-set density.
References
references/results-compendium.md — Load when citing, restating, packaging, or checking scope of any R1–R17: boxed statements, [verified] vs [internal] numbers, applications, boundaries, paper map, reproducibility pointers, and the treatise-corrections consensus.
references/l3-tacit-lessons.md — Load BEFORE extending or re-implementing anything here, or designing a related experiment: the hard-won lessons (bugs hit, boundaries found, conventions that change answers) with transferable rules.
Scripts (regenerate every [internal] number)
Self-contained; deps: numpy, scipy, matplotlib, networkx; seed 20260816 fixed inside each. Run from the skill root when re-verifying a number before citing it, or after modifying any claim these underwrite.
python3 scripts/b6_probation.py — B6: front-loaded probation dominance — 0 dominating schedules in 4,000 random instances (76,000 schedules tested), matching the closed-form exchange argument; exit nonzero on violation.
python3 scripts/zoom_bound_check.py — Paper 1's zoom theorem verified: Q <= 2k*ceil(log2(F/k)) + 4k on every tested instance (random + adversarial placements), exact tightness at F=4096,k=32 (511), bound dominates the measured ~163 opens at the b1 point; exit nonzero on violation.
python3 scripts/b7_escalation_band.py — R14: costly-escalation threshold equilibrium (single crossing, closed forms u*=δw/(1+δw) and Lambert-W) + the two-sided debit tuning band tied to R3's constants; empty-band regime exhibited; zero-debit and excessive-debit mutants caught; exit nonzero on violation.
python3 scripts/b4_deontic_fragment.py — R17: polynomial witness-producing conflict checker for the Horn+interval+difference deontic fragment (3000-instance oracle sweep, 0 disagreements) + the 3-SAT NP-completeness reduction one expressive step outside it, verified both directions on 16/16 instances; Horn-propagation mutant misses 100/885 conflicts; exit nonzero on violation.
python3 scripts/b5_engine_substitution.py — R13: Akerlof unraveling inside one identity (swap gain price-independent, μ* threshold, death spirals), the IC flip under engine attestation (swap gain Δc−Δθ, audit stake → 0), and resurrection soundness (747-state migration machine, 0 Def-III.6.1 violations intact; 4 mutants caught with shortest crimes 1,2,2,2); exit nonzero on violation.
python3 scripts/sheaf_consistency_radius.py — R6 theorem (W8 tail): CR-1/2/3 verified — soundness (r = exact minimum lie, 0/600 violations; closed form r = |s|·√(1−R_eff), the R6 1.2247 number derived), localization (328/328 noise-free, electrical-flow support), complexity (per-coordinate Laplacian decomposition, CG slope 0.65 vs dense 1.88); coalition-cancellation boundary exhibited; D2 mutant caught; exit nonzero on violation.
python3 scripts/b9_context_paging.py — R16: Landlord k/(k−h+1) import verified vs exact OPT (122 pairs, cycles at equality) + linear φ-degradation under a corrupted pin oracle (additive φN·c_refetch bound, 0 violations incl. adaptive corruption; slope 1.9% of ceiling, R²=0.994); blind pin-trust mutant catastrophic (Θ(N) staleness from one corruption); exit nonzero on violation.
python3 scripts/b8_specialization.py — R15: exact Erlang-C specialization boundary g(ρ,c) (falsifies the proposed 1+(c−1)ρ/(1−ρ) threshold in both directions, crossing at ρ=(3−√5)/2) + succession-price theorem W_bd closed form, D* = ηK/(1−ηK); DES/matrix-geometric/CTMC cross-checks, 60-instance sweep, breakdown-blind mutant caught; exit nonzero on violation.
