Price the plane-port u=2 screen against the rank-8 cell's 16-child sl…

research/rank8-u2-plane-port-slack/README.md

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+# The plane-port u=2 screen misses the rank-8/u2 16-child slack
+
+**Negative pricing result. No new κ.** The selected conditional result stays
+`836330098538459/500000000000000000` (`0.001672660197076918`).
+
+PR #3889 shows that the ideal cell `selected centre + all local mass at rank ≤ 8
++ two unpaid coordinates` still clears `κ = 1/99` after integer rounding, with
+room for **16** added rank-1 children on the nine-call uniform pool and not 17.
+That cell is not a producer. This package prices the recorded contract that
+actually leaves two unpaid coordinates, and it does not fit that room.
+
+## Result
+
+The selected line-port word `{1:2412, 2:418, 3:432, 4:142, 5:82, 8:8}` has mass
+5586 per call and idle 1646 under PR1012's identity `72W + 64N`. It is not a
+rank-8 delivery of that mass. The recorded u=2 endpoint is ctoth's plane-port
+contract (source `E → FULL`, target `0 → E⊥`), as screened in
+`research/plane-port-copy-budgets`.
+
+1. **Source-bound copy invoice.** The direct native bill in
+   `research/paired-plane-native-payload` uses 112 rank-2 drops per call, so
+   `C = 224`. Two unpaid coordinates free only `2·(896/9) = 1792/9` units per
+   call. `224 > 1792/9`, and the demanded mass is
+   `71·896 + 224·9 = 65632` against capacity `73·896 = 65408`, ratio
+   **293/292**. Idle would be negative. This invoice cannot be added to any
+   histogram that already meets the u=2 law, including the ideal rank-8 cell.
+
+2. **Decoder-free screen.** Drop that invoice and remove the 224 data units as
+   rank-1 children, which is the favorable `shrink` row at charge 0. Its
+   relaxation moment at `a = 1/98` has lower bound strictly above 1. Charging
+   each rank-1 child at the upper enclosure `(1/73)^(97/98)`, at least **68**
+   such children would have to be removed before that lower bound can fall to 1.
+   The same test gives **147** on the `unchanged` row. The ideal cell's moment,
+   after the 16 children that still pass, remains strictly below 1, so the
+   shrink screen also sits at least 68 maximum-cost rank-1 children above that
+   saturated bill.
+
+The shrink word has maximum rank 5 and mass 5298. It is not the rank-8
+histogram `{8:698, 2:1}` whose nine-call repeat is the integer cell. No
+source-bound rank-8/u2 producer was found in the pinned inputs.
+
+## What was recomputed
+
+From `research/complex-local-word-ceiling/ceiling.py` and the selected mass:
+
+| Object | Nine-call certificate at a = 1/98 |
+|---|---|
+| Ideal paid `{8:6282, 2:9}` plus idle `{51:272, 46:1}` | Moment upper bound `< 1`. Adding 16 rank-1 children still passes; 17 fails. |
+| Plane-port shrink, centre 0, fractional idle | Moment lower bound `> 1` by at least 68 rank-1 children. |
+| Plane-port unchanged, centre 0 | Moment lower bound `> 1` by at least 147 rank-1 children. |
+| Copy charge `C = 224` | Coverage overspend 224; ratio 293/292. |
+
+The 16/17 boundary uses the same additive model as PR #3889: extra rank-1
+children increase the moment and do not receive idle-mass credit. The plane-port
+rows use `ceiling.relax`, whose fractional idle packing is optimistic relative
+to an integer idle histogram. A failure there rules out every integer idle
+packing of the same local word.
+
+## Scope
+
+Card `complex-new-helper-inventory`, scope **changed**. The card asks for a new
+physically realizable inventory. The handoff asks for a priced rank-8/u2
+contract or a stop. This is the stop. It does not construct a decoder, change
+the coverage law, or admit a supplier.
+
+Not claimed: a lower bound on every possible u=2 mechanism, a bit-side twin, or
+a proof that no future rank-8 delivery exists. Joint two-array primitives
+outside the one-array copy interface are a different contract. The plane-port
+exactness check in discussion 1587 is used as published and is not re-run.
+
+## Reproduce
+
+Python 3.12, standard library only, from the repository root:
+
+```sh
+python3.12 -I -B research/rank8-u2-plane-port-slack/verify.py
+python3.12 -B scripts/research_package.py --package research/rank8-u2-plane-port-slack
+```
+
+Expected line:
+
+```text
+PASS_RANK8_U2_PLANE_PORT_SLACK extra_pass=16 shrink_deficit=68 unchanged_deficit=147 above_saturated_cell=true native=293/292 no_new_kappa=true
+```
+
+`verify.py --write` regenerates `RESULT.json`. The checker hashes the pinned
+ceiling engine and reads `CWORD`, `CDATA_DROP` and the template constants from
+the pinned plane-port verifier without executing it. Controls reject a moved
+selected κ, a rank-8 optimum other than `{8:698, 2:1}`, a line-port word that
+passes `a = 1/98`, and a near-empty u=2 word that fails it.
+
+Not run: Lean, Docker, the selected cold replay, and the plane-port bit screen.
+
+## Open next questions
+
+1. Is there a u=2 producer whose paid children have rank at most 8 and whose
+   additive bill is at most 16 rank-1 children on this nine-call cell? That is
+   the only way this integer margin could survive contact with a producer.
+   First step: one literal histogram rerun at `a = 1/98`. Blocker: the selected
+   line-port word pays the unpaid=1 identity, and no rank-8 delivery of mass
+   5586 is pinned here.
+2. Can the 112 rank-2 drops be replaced by a charge of at most `1792/9` per
+   call without losing the `I_2` endpoint? `C = 224` is already impossible
+   inside this coverage law. First step: one native word on the 56 matched
+   planes with `C ≤ 199` and a checked transfer. Blocker: the one-array
+   interface needs two totals per block; a joint two-array primitive is a
+   different contract.
+
+## Credit
+
+The integer 16/17 boundary is Nick Petalas's question as answered by ToikY in
+PR #3889 (`research/lever-integer-twins`, head
+`a18b03ea76fb373aeb00acc9c4fe119ac617ac83`), on the grid in PR #3874. The
+plane-port screen is ctoth's contract in discussion 1587, packaged by
+JosieElliston in `research/plane-port-copy-budgets`. The copy-mass obstruction
+`293/292` is the accounting in `research/paired-plane-native-payload` (Jeremy
+Diviney / the PR2203 lineage) and is recomputed here. The moment engine is
+Douglas Colkitt's `research/complex-local-word-ceiling`. The coverage identity
+is Sagar Thakrar's PR1012.
+
+Prepared by unpaidmoon with substantial Cursor Grok assistance. No independent
+human or formal-kernel review is claimed. New work is Apache-2.0.

research/rank8-u2-plane-port-slack/RESULT.json

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+{
+  "ideal_extra_rank1_pass": 16,
+  "ideal_moment_high": "3704354446484012002304355223322905223550337644480295345499911721712485226114421/3705346855594118253554271520278013051304639509300498049262642688253220148477952",
+  "native_mass_ratio": "293/292",
+  "native_overspend": 224,
+  "no_new_kappa": true,
+  "shrink_c0_moment_low": "115918230524473042007406295047798346987035028812436289993517137146310558101631/115792089237316195423570985008687907853269984665640564039457584007913129639936",
+  "shrink_max_rank": 5,
+  "shrink_rank1_deficit": 68,
+  "status": "PASS_RANK8_U2_PLANE_PORT_SLACK",
+  "target_a": "1/98",
+  "target_kappa": "1/99",
+  "unchanged_rank1_deficit": 147
+}

research/rank8-u2-plane-port-slack/SOURCES.json

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+{
+  "schema_version": 1,
+  "base_commit": "bb4bccbf42844d2801487450727c2f63e10d1d0f",
+  "files": [
+    {
+      "path": "certificates/selected-result.json",
+      "usage": "provenance",
+      "git_blob": "b1fea0c94436b236cc2b7d41a7be032811b94c81",
+      "sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129"
+    },
+    {
+      "path": "docs/research/agent-task-catalog.json",
+      "usage": "provenance",
+      "git_blob": "67f085acd86acd7d4e03922d9cf4b26bca66fed5",
+      "sha256": "47b42433f5a85809a3aadd29c2c339da2c6ed728e4f7762df6b88bccb7874cf0"
+    },
+    {
+      "path": "research/complex-local-word-ceiling/ceiling.py",
+      "usage": "input",
+      "git_blob": "6c0f54527d879396f689523bfde19928a9b6157c",
+      "sha256": "86a1432870b3b21d8454106ec9162fddc0471472d9214c590a1420f2426cedfc"
+    },
+    {
+      "path": "research/plane-port-copy-budgets/verify.py",
+      "usage": "input",
+      "git_blob": "7f8effca7c25f1439a55188fc99f59a5fea26cd4",
+      "sha256": "54e731474e07ac7da1f1afb1b7e432869569e4ef03e8ae78584188b7cd3f9ef1"
+    }
+  ]
+}

research/rank8-u2-plane-port-slack/TASK.json

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+{
+  "schema_version": 1,
+  "task_id": "complex-new-helper-inventory",
+  "priority_revision": 6,
+  "base_commit": "bb4bccbf42844d2801487450727c2f63e10d1d0f",
+  "original_card": {
+    "id": "complex-new-helper-inventory",
+    "question": "Can a new local cost interface change the deficit-to-recursive-cost ratio beyond current packing?",
+    "starting_points": [
+      "docs/research/research-family-status.md",
+      "research/complex-local-word-ceiling/README.md",
+      "research/heterogeneous-owner-assembly/README.md",
+      "certificates/selected-result.json",
+      "research/selected-k8-unrestricted-ends/README.md"
+    ],
+    "methods": [
+      "Propose a changed helper inventory and derive an optimistic exact moment.",
+      "Design a small completed instance and independently verify its endpoint and rank bill."
+    ],
+    "acceptance_gate": "A new physically realizable contract outside the frozen catalogue whose per-call profile, screened with ceiling.ceiling(), beats the selected word's packing ceiling; a lower cap does not establish identical circuitry or order attainable optima, and is insufficient to pass the stronger-budget target under this model. A scoped local result may be retained without a complete supplier. Expanding it into further construction rounds requires the family-level budget and obligation gate in research-family-status.md; an optimistic passing relaxation alone is not acceptance.",
+    "first_step": {
+      "command": [
+        "python3",
+        "-B",
+        "research/complex-local-word-ceiling/verify.py"
+      ],
+      "expected": "PASS_COMPLEX_LOCAL_WORD_CEILING",
+      "inspect": "Read the selected word's per-call local profile, its packing ceiling and the lever table; run levers.py for the ideal budget of the lever you target.",
+      "scope": "Positive control and planning budget only; this is not a new construction or full cold replay."
+    },
+    "first_experiment": "Before any synthesis, write the candidate per-call local profile (and centre charge / unpaid coordinates if changed) and screen it with ceiling.ceiling(); reject it if even the ideal ceiling does not beat the selected word's by your stated margin.",
+    "bottleneck_link": "Packing of the selected word is capped at +0.87% (ceiling model); only a lower local excess spend or a changed coverage law raises the cap.",
+    "allowed_variations": [
+      "Narrow to one changed boundary or helper type with explicit counts.",
+      "If the coverage law, template or guard changes, derive an applicable fully charged replacement bound instead of applying the incumbent ceiling outside its scope."
+    ],
+    "scope_change_triggers": [
+      "Mixing only providers already inside the pinned catalogue.",
+      "Only changing helper terminal subspaces and monotone frames within the fixed scalar word, entrances and cleanup contract already covered by #1995/#2013.",
+      "Continuing a partial cost improvement while leaving the same unpriced consumer, restoration or central-readout obligation unresolved; refresh the family expansion decision first. Local product-retiming evidence has a narrow scope and is not a ban on changed graphs or contracts."
+    ],
+    "overlap_terms": [
+      "helper inventory",
+      "heterogeneous-owner",
+      "mutable leaver"
+    ]
+  },
+  "scope_status": "changed",
+  "actual_scope": "Price the recorded plane-port u=2 screen against the 16 rank-1 slack of the selected-centre/rank-8/u=2 integer cell. Stop without naming a new producer.",
+  "scope_change_reason": "The card asks for a new physically realizable helper inventory. Discussion #1166 comment 19029639, following PR #3889, asks first for a source-bound rank-8/u2 contract priced against that cell. The selected line-port word is not that contract. The recorded u=2 endpoint is the plane-port screen, and it fails the cell stop test.",
+  "bottleneck_link": "The complex side binds. The rank-8/u2 cell is the tightest ideal lever combination that clears kappa 1/99 in the published grid, with only 16 rank-1 children of integer slack on nine calls. A u=2 screen that misses this slack cannot be cited as headroom for a new helper inventory.",
+  "budget_minutes": 60,
+  "stop_rule": "Stop once the source-bound C=224 invoice is outside the u=2 coverage law and the decoder-free shrink screen fails a=1/98 by more than 16 rank-1 children. Do not search for another ideal ceiling.",
+  "outcome": "completed",
+  "evidence": "PASS_RANK8_U2_PLANE_PORT_SLACK. Ideal nine-call cell passes 16 added rank-1 children at a=1/98 and fails 17. Plane-port shrink moment lower bound is above 1 by at least 68 rank-1 children; the unchanged screen by at least 147. Native copy charge 224 exceeds two unpaid coordinates per call, mass ratio 293/292.",
+  "author": "unpaidmoon",
+  "ai_assistance": "Substantial: Cursor Grok selected the handoff, wrote the verifier and README, and ran the checks. No independent human or formal-kernel review is claimed.",
+  "open_questions": [
+    {
+      "question": "Is there a u=2 producer whose paid children have rank at most 8 and whose additive bill is at most 16 rank-1 children on this nine-call cell?",
+      "why_it_matters": "That is the only way the rank-8/u2 integer margin could survive a physical contract. The plane-port screen does not.",
+      "first_step": "Name one literal producer, write its child histogram, and rerun this package moment test at a=1/98.",
+      "blocked_by": "The selected line-port word pays the unpaid=1 identity. No rank-8 delivery of mass 5586 is in the pinned sources."
+    },
+    {
+      "question": "Can the 112 rank-2 plane drops be replaced by a charge of at most 1792/9 per call without losing the I_2 endpoint?",
+      "why_it_matters": "C=224 already exceeds the two unpaid coordinates, so the copy invoice is impossible inside this coverage law before the moment test.",
+      "first_step": "Give one native word on the 56 matched planes with copy mass C <= 199 and a checked I_2 transfer.",
+      "blocked_by": "paired-plane-native-payload proves two independent totals per block under the one-array interface; a joint two-array primitive is a different contract."
+    }
+  ]
+}

research/rank8-u2-plane-port-slack/VERIFY.json

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+{
+  "schema_version": 1,
+  "status": "ready",
+  "python": "3.12",
+  "requirements": [],
+  "inputs": [
+    "research/complex-local-word-ceiling/ceiling.py",
+    "research/plane-port-copy-budgets/verify.py"
+  ],
+  "commands": [
+    {
+      "argv": [
+        "{python}",
+        "-I",
+        "-B",
+        "{package}/verify.py"
+      ],
+      "timeout_seconds": 60,
+      "checks": "Recompute the 16/17 rank-1 boundary of the rank-8/u2 integer cell; certify plane-port shrink and unchanged moments above 1 at a=1/98; certify the C=224 coverage overspend 293/292; reject a moved selected kappa."
+    }
+  ]
+}