Research: rank-16 delivery survives every legal rank-1 surcharge

research/rank16-rank1-surcharge-screen/README.md

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+# Rank-16 delivery survives every legal rank-1 surcharge
+
+**Negative screen. No new kappa.** The selected record is unchanged, and
+`research/complex-local-word-ceiling/ceiling.py` is not edited.
+
+## Scope
+
+Chooser seed `fb1b693e95073cda2220efd59e654728` drew `p104-side-correction`
+first. That experiment is already open for flag 0. The same seed's unclaimed
+helper 600/601 sign test is PR #4061. This package is the other bounded screen
+on `complex-rank-shape-decoder`: one candidate profile, accepted only if its
+ceiling beats the selected word by 5%.
+
+The candidate is not an idle histogram of the unchanged selected word. The
+published lever `{16: mass/16}` leaves idle mass at rank 51. Here that idle
+mass is moved into the local profile as extra rank-1 children. The published
+control that one extra rank-1 child lowers the ceiling does not say whether
+the five-percent gate survives the largest legal count.
+
+## What is established
+
+The pinned model has selected local mass 5586 and idle mass 1646. At grid
+`1e-15`:
+
+| profile | ceiling |
+| --- | --- |
+| selected word | `1690054109089/1000000000000000` |
+| rank-16 delivery plus 1646 rank-1 children | `285077936577/125000000000000` |
+
+Delivering the selected local mass as rank-16 children and spending all 1646 idle-mass units on extra rank-1 children still clears the five-percent ceiling gate.
+
+The ratio of those ceilings is `2280623492616/1690054109089`, about 1.349,
+against the gate `21/20`. One further rank-1 child makes local mass exceed
+the coverage law and is rejected. Ideal rank-16 delivery with no surcharge is
+the lever already printed by `levers.py`; it is not restated as a new ratio.
+
+## Reproduce
+
+Python 3.12, standard library only, from the repository root:
+
+```sh
+python3.12 -B scripts/research_package.py --package research/rank16-rank1-surcharge-screen
+```
+
+Expected marker: `PASS_RANK16_RANK1_SURCHARGE`.
+
+## Limits
+
+This does not construct a rank-16 decoder, price frames, restoration, or
+hosting, or change the halving guard. It does not repack an idle histogram at
+ranks up to 51; those favorable packings are the ceiling paper, #3811 and
+#3874. A charge the coverage law cannot express as rank-1 children is outside
+this screen. The selected baseline replay was not run in this partial checkout.
+
+## Open next questions
+
+Which sourced copy, frame or restoration histogram, outside extra rank-1
+children in this coverage law, pushes rank-16 delivery under the five-percent
+gate? The first step is to pin one such histogram and screen that exact
+profile. No such histogram is pinned in `levers.py`.
+
+## Credit
+
+Douglas Colkitt's ceiling model and lever table are the pinned inputs.
+Riquelme Soares (@hevlyo), with substantial AI assistance in the screen and
+write-up. Apache-2.0. No independent human review is claimed.

research/rank16-rank1-surcharge-screen/SOURCES.json

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+{
+  "schema_version": 1,
+  "base_commit": "20ecf2891d80b5acf18d980b2164fb44ea7faa90",
+  "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/complex-local-word-ceiling/levers.py",
+      "usage": "input",
+      "git_blob": "e6aee6ce1178f5b68b9ce893b2f5b7f80a143b59",
+      "sha256": "24c71fc5dce5e2d8f9fbd34d059fc9a1c8ad635d93b62102ccb41b03a7b38b9e"
+    }
+  ]
+}

research/rank16-rank1-surcharge-screen/TASK.json

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+{
+  "schema_version": 1,
+  "task_id": "complex-rank-shape-decoder",
+  "priority_revision": 6,
+  "base_commit": "20ecf2891d80b5acf18d980b2164fb44ea7faa90",
+  "original_card": {
+    "id": "complex-rank-shape-decoder",
+    "question": "Can a decoder deliver the local paid mass in fewer, larger-rank children (block frame climbs instead of rank-1 to rank-3 steps)?",
+    "starting_points": [
+      "docs/research/research-family-status.md",
+      "research/complex-local-word-ceiling/README.md",
+      "research/complex-decoder-field-extension-seed44/README.md",
+      "research/complex-frame-pair-decoders/README.md",
+      "research/selected-k8-unrestricted-ends/README.md",
+      "research/eisenstein-reduction-copy-floor/README.md"
+    ],
+    "methods": [
+      "Find one exact small decoding identity whose frame path climbs in blocks, and price its complete per-call profile.",
+      "Bound the best effective child rank achievable for one fixed support alphabet, including copies, frames and restoration."
+    ],
+    "acceptance_gate": "A per-call local profile, with all copied information, frames and restoration counted, whose ceiling exceeds the selected word's by at least 5%; masked or overcomplete supports must change an assumption of the eight-term all-pairs bound. 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. Ideal budget: rank-16 delivery is 2.31x (levers.py).",
+    "bottleneck_link": "Rank-1 children are about half of recursive cost; the selected word's effective child rank is about 3.9. Larger-rank delivery lowers recursive cost per unit of paid mass.",
+    "allowed_variations": [
+      "One masked, overcomplete or block decoder family with exact labels and supports.",
+      "A scoped lower bound on effective rank for one alphabet.",
+      "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": [
+      "Repacking idle remainders of an unchanged word (covered by the packing ceiling).",
+      "Repeating the eight-term all-pairs search inside its proved scope.",
+      "Only changing helper terminal subspaces and monotone frames within the fixed scalar word, entrances and cleanup contract already covered by #1995/#2013.",
+      "Searching below C=40 in the #2017 Eisenstein binary scalar-rectangle or fixed-support block-linear additive pairing model; specify a changed premise instead. This bound does not cover every complex decoder.",
+      "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": [
+      "rank shape",
+      "block climb",
+      "masked decoder",
+      "overcomplete",
+      "effective rank"
+    ]
+  },
+  "scope_status": "refined",
+  "actual_scope": "Does any legal extra rank-1 child count on top of rank-16 delivery of the selected local mass push the pinned ceiling under the five-percent gate?",
+  "scope_change_reason": "The drawn p104-side-correction experiment is already open for flag 0, and PR #4061 took the unclaimed helper 600/601 sign test from the same chooser seed. This package is the other half of the rank-shape first experiment: screen one candidate profile with ceiling.ceiling() and reject it if the ideal ceiling misses the five-percent gate. The candidate is not an idle histogram of the unchanged selected word. It delivers the selected local mass as rank-16 children and moves idle mass into extra rank-1 children. The published lever table stops at ideal idle, rank 51.",
+  "bottleneck_link": "Rank-16 delivery is the catalogue's named 2.31x lever. A rank-1 surcharge is the natural copy charge inside this coverage law. If the strongest legal surcharge still clears five percent, no rank-1 copy count inside the law can reject the lever.",
+  "budget_minutes": 60,
+  "stop_rule": "Stop at the largest legal rank-1 count. Do not search a decoder, change ceiling.py, or price a charge the coverage law cannot express.",
+  "outcome": "negative-result",
+  "evidence": "At grid 1e-15 the selected ceiling is 1690054109089/1000000000000000 and the full surcharge ceiling is 285077936577/125000000000000, ratio 2280623492616/1690054109089, which is above 21/20. Idle mass is 1646. One more rank-1 child is rejected by the coverage law.",
+  "author": "Riquelme Soares (@hevlyo)",
+  "ai_assistance": "Substantial AI assistance was used for the screen, the verifier and the write-up. No independent human review is claimed.",
+  "open_questions": [
+    {
+      "question": "Which sourced copy, frame or restoration histogram, outside extra rank-1 children in this coverage law, pushes rank-16 delivery under the five-percent gate?",
+      "why_it_matters": "The gate survives every legal rank-1 surcharge, including spending the entire idle mass. A rejection has to change the coverage law, the centre charge, the halving guard, or replace the rank-16 children.",
+      "first_step": "Pin one histogram whose mass is not a rank-1 child count and screen that exact profile with ceiling.ceiling().",
+      "blocked_by": "No such histogram is pinned in levers.py. The coverage law cannot express it as further rank-1 children."
+    }
+  ]
+}

research/rank16-rank1-surcharge-screen/VERIFY.json

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+{
+  "schema_version": 1,
+  "status": "ready",
+  "python": "3.12",
+  "requirements": [],
+  "inputs": [
+    "research/complex-local-word-ceiling/ceiling.py",
+    "research/complex-local-word-ceiling/levers.py"
+  ],
+  "commands": [
+    {
+      "argv": [
+        "{python}",
+        "-B",
+        "{package}/verify.py"
+      ],
+      "timeout_seconds": 120,
+      "checks": "Recomputes the selected ceiling and the rank-16 profile plus all 1646 legal rank-1 children at grid 1e-15, checks the five-percent gate, and rejects one further child."
+    }
+  ]
+}

research/rank16-rank1-surcharge-screen/verify.py

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+"""Five-percent screen of the strongest legal rank-1 surcharge on rank-16 delivery."""
+
+import hashlib
+import sys
+from fractions import Fraction as Q
+from pathlib import Path
+
+ROOT = Path(__file__).resolve().parents[2]
+sys.path.insert(0, str(ROOT / "research" / "complex-local-word-ceiling"))
+import ceiling as C  # noqa: E402
+
+PACKAGE = Path(__file__).resolve().parent
+WORD = {1: 2412, 2: 418, 3: 432, 4: 142, 5: 82, 8: 8}
+M, FAMILIES, STAGES, CENTRE = 73, 896, 9, 64
+GRID = Q(1, 10 ** 15)
+CEILING_SHA = "86a1432870b3b21d8454106ec9162fddc0471472d9214c590a1420f2426cedfc"
+BASE_HI = Q(1690054109089, 1000000000000000)
+FULL_HI = Q(285077936577, 125000000000000)
+LEMMA = (
+    "Delivering the selected local mass as rank-16 children and spending all "
+    "1646 idle-mass units on extra rank-1 children still clears the five-percent ceiling gate."
+)
+
+
+def require(ok, why):
+    if not ok:
+        raise SystemExit(why)
+
+
+def main():
+    ceiling_path = ROOT / "research" / "complex-local-word-ceiling" / "ceiling.py"
+    digest = hashlib.sha256(ceiling_path.read_bytes()).hexdigest()
+    require(digest == CEILING_SHA, "ceiling.py hash changed")
+    require(LEMMA in (PACKAGE / "README.md").read_text(encoding="utf-8"), "README dropped the lemma")
+    mass = sum(rank * Q(count) for rank, count in WORD.items())
+    require(mass == 5586, "selected local mass changed")
+    idle = C.model(WORD, M, FAMILIES, STAGES, CENTRE)["idle_mass"]
+    require(idle == 1646, "idle mass is not 1646")
+    base_hi = C.ceiling(WORD, M, FAMILIES, STAGES, CENTRE, grid=GRID)[1]
+    full = {16: mass / 16, 1: idle}
+    full_hi = C.ceiling(full, M, FAMILIES, STAGES, CENTRE, grid=GRID)[1]
+    require(base_hi == BASE_HI, "selected ceiling moved")
+    require(full_hi == FULL_HI, "surcharge ceiling moved")
+    require(full_hi > base_hi * Q(21, 20), "five-percent gate failed")
+    try:
+        C.model({16: mass / 16, 1: idle + 1}, M, FAMILIES, STAGES, CENTRE)
+    except ValueError as exc:
+        require("coverage law" in str(exc), "unexpected rejection")
+    else:
+        require(False, "one extra rank-1 child was accepted")
+    print("PASS_RANK16_RANK1_SURCHARGE")
+
+
+if __name__ == "__main__":
+    main()