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Director: priority revision 3 — aim effort at centre path, rank shape and coverage law (stacked on #1240) #1272

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Director: priority revision 3 — aim effort at centre path, rank shape and coverage law (stacked on #1240) #1272

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43 changes: 36 additions & 7 deletions autoresearch.md
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Expand Up @@ -97,9 +97,34 @@ starting points are historical evidence, not promises of unexplored territory.
## 2. Where effort is most useful

The October 13, 2026 assessment is that many local improvements leave the paid
recursive profile unchanged, or improve a nonbinding supplier. Stronger packing
still helps, but a large jump needs a changed mechanism or interface. Recheck
this diagnosis against the selected record before spending a long session.
recursive profile unchanged, or improve a nonbinding supplier. Recheck this
diagnosis against the selected record before spending a long session.

**Revision 3 diagnosis (pending review of #1240 and #1264).** On the binding complex side, a ≈ D/E:

- **D is small.** Each call has about 99.6 live families. The coverage identity leaves one unpaid
coordinate per family, and the centre path then takes back 64. Only about 35.6 of 7,232 paid
coordinates per call remain unpaid.
- **E comes from small children.** The effective child rank is about 3.9, and rank-1 children are
about half of the recursive cost.

[The packing ceiling](research/complex-local-word-ceiling/README.md) caps every hosting, owner or
idle repacking of the selected word at **+0.87%** (κ < 0.0016872). The open-claim census in #1264
finds no covered claim able to pass κ ≈ 0.0016873 by packing. Its leading claims sit on words with
*lower* caps than the selected word.

A target-scale gain must change the structure. Ideal one-at-a-time budgets (`levers.py`):

| Lever | Ideal multiplier |
|---|---:|
| Centre path free | 2.80× |
| Centre path shared by two calls | 1.90× |
| Rank-16 local children | 2.31× |
| Two unpaid coordinates per family | 3.77× |
| Centre free and rank-16 combined | 6.5× (κ cap ≈ 0.0109) |

These are favorable relaxations, not expected gains. Screen any changed local profile with
`ceiling.ceiling()` before building a network.

For a supplier with width `m`, role count `W`, and `n_r` children of rank `r`,
price the **whole completed construction**, including its additional charges:
Expand All @@ -126,13 +151,13 @@ probabilities; the catalogue is the machine-readable source for assignments.
| Track | Share | Useful outcome |
|---|---:|---|
| Bit mechanisms (`bit-mechanisms`) | 20% | A changed decoder/frame contract with a full paid budget |
| Complex mechanisms (`complex-mechanisms`) | 20% | A new decoding or helper-boundary mechanism |
| Recursive interfaces (`recursive-interfaces`) | 15% | Real eliminated work across a legal boundary |
| Complex mechanisms (`complex-mechanisms`) | 20% | A larger-rank decoder or helper inventory whose screened ceiling beats the selected word's |
| Recursive interfaces (`recursive-interfaces`) | 20% | A shared or smaller centre path, a changed coverage law, or other real eliminated boundary work |
| Adversarial audit (`adversarial-audit`) | 15% | A specific missing implication or exact counterexample |
| Independent verification/formalization (`independent-verification`) | 10% | A separately implemented check or scoped formal lemma |
| Verifier engineering (`verifier-engineering`) | 10% | Faster, reproducible checks with unchanged coverage |
| Verifier engineering (`verifier-engineering`) | 8% | Faster, reproducible checks with unchanged coverage |
| Consolidation (`consolidation`) | 5% | Evidence-backed overlap, attribution or navigation repair |
| Incumbent optimization (`incumbent-optimization`) | 5% | A genuinely new, fully priced incremental improvement |
| Incumbent optimization (`incumbent-optimization`) | 2% | A genuinely new, fully priced improvement, reported against its packing cap |

Before reopening a negative result, name the hypothesis you change. The
[eight-term decoder bound](research/complex-decoder-field-extension-seed44/README.md),
Expand Down Expand Up @@ -247,6 +272,10 @@ Do not run every historical replay just to change documentation. Do not run
artifact-regenerating suites concurrently in the same worktree. Cache immutable,
source-bound evidence only when coverage and invalidation remain explicit.

A new complex κ claim should report its local word's packing cap
(`research/complex-local-word-ceiling/ceiling.py`) and the fraction of it realized,
so reviewers can tell a packing gain from a structural gain.

Before submission, refresh the overlap check. Keep one focused PR with the task
card, precise delta, exact heads, commands, evidence, limitations and credit.
An independently corroborated or superseded contribution still deserves credit;
Expand Down
139 changes: 112 additions & 27 deletions docs/research/agent-task-catalog.json
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@@ -1,6 +1,6 @@
{
"schema_version": 1,
"priority_revision": 2,
"priority_revision": 3,
"priority_log": "docs/research/research-priority-log.md",
"assessed_on": "2026-10-13",
"status": "Research suggestions, not reservations or assertions that these questions are unclaimed. Check current main and live PRs.",
Expand Down Expand Up @@ -88,65 +88,71 @@
"weight": 20,
"tasks": [
{
"id": "complex-masked-decoder",
"question": "Can one specified masked or overcomplete decoder improve the complete moment budget?",
"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": [
"research/complex-local-word-ceiling/README.md",
"research/complex-decoder-field-extension-seed44/README.md",
"research/complex-frame-pair-decoders/README.md"
],
"methods": [
"Synthesize a decoder with exact coefficients and fully priced helper endpoints.",
"Bound the best possible budget for a fixed support alphabet before synthesis."
"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": "Change an assumption of the eight-term all-pairs bound and count all copied information, 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.",
"first_step": {
"command": [
"python3",
"-B",
"research/complex-decoder-field-extension-seed44/verify.py"
"research/complex-local-word-ceiling/verify.py"
],
"expected": "PASS_COMPLEX_DECODER_FIELD_EXTENSION_S44",
"inspect": "Locate the excluded classes: masked identities, at least nine terms, and deeper punctures.",
"scope": "Positive control / source-bound orientation only; this is not a new construction or full cold replay."
"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": "Choose one finite support alphabet and test exact decoding constraints before building a whole network.",
"bottleneck_link": "A cheaper fully realized decoder could increase deficit or lower recursive cost on the binding complex side.",
"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": [
"Select a specific masked or overcomplete family with exact labels and supports."
"One masked, overcomplete or block decoder family with exact labels and supports.",
"A scoped lower bound on effective rank for one alphabet."
],
"scope_change_triggers": [
"Repeating the exact eight-term all-pairs search inside its proved scope."
"Repacking idle remainders of an unchanged word (covered by the packing ceiling).",
"Repeating the eight-term all-pairs search inside its proved scope."
],
"overlap_terms": [
"rank shape",
"block climb",
"masked decoder",
"overcomplete",
"eight-term"
"effective rank"
]
},
{
"id": "complex-new-helper-inventory",
"question": "Can a new local cost interface change the deficit-to-recursive-cost ratio beyond current packing?",
"starting_points": [
"research/complex-local-word-ceiling/README.md",
"research/heterogeneous-owner-assembly/README.md",
"certificates/selected-result.json"
],
"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, not another mixture already covered by the frozen catalogue.",
"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 word with a lower ceiling is only a packing aid and must be labelled so.",
"first_step": {
"command": [
"python3",
"-B",
"scripts/research_baseline.py"
"research/complex-local-word-ceiling/verify.py"
],
"expected": "PASS_RESEARCH_BASELINE_BINDINGS_ONLY",
"inspect": "Read the frozen catalogue bound exclusions and select one genuinely different helper endpoint inventory.",
"scope": "Positive control / source-bound orientation only; this is not a new construction or full cold replay."
"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": "Write the complete optimistic child histogram and reject it immediately if even the relaxation has insufficient headroom.",
"bottleneck_link": "Helper inventory changes can improve the moment; repacking a covered cost interface cannot evade its scoped bound.",
"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."
],
Expand All @@ -163,8 +169,86 @@
},
{
"id": "recursive-interfaces",
"weight": 15,
"weight": 20,
"tasks": [
{
"id": "centre-path-sharing",
"question": "Can the 64-per-call centre path (eight rank-8 COPY/ERASE totals through the private temporary) be shared across calls or shrunk?",
"starting_points": [
"research/complex-local-word-ceiling/README.md",
"research/split-centres-global/proofs/PR386-BIT-GEOMETRY.txt",
"certificates/selected-result.json"
],
"methods": [
"Derive a fully charged favorable relaxation for sharing one centre path across k calls, including restoration, hosting and precision.",
"Prove a lower bound on copied information per call for the selected decoder contract."
],
"acceptance_gate": "Show the changed centre charge and copy profile per call with every added restoration or hosting cost charged, and its ceiling via ceiling.ceiling(centre=...).",
"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": "Write the per-call centre charge and copy children for sharing across k = 2 calls, charge the sharing overhead, and screen it; stop this route if even the ideal sharing gains under 10%. Ideal budgets: free 2.80x, shared by two 1.90x (levers.py).",
"bottleneck_link": "The centre path consumes 64 of about 99.6 unpaid coordinates per call, i.e. about 64% of the raw deficit.",
"allowed_variations": [
"One sharing pattern across a fixed number of calls.",
"One reduced copied-total contract for the existing decoder."
],
"scope_change_triggers": [
"Removing copies without a replacement contract for the decoder's copied totals."
],
"overlap_terms": [
"centre path",
"copied totals",
"private temporary",
"shared centre",
"batching"
]
},
{
"id": "coverage-law-change",
"question": "Can a template or call contract leave two or more unpaid coordinates per live family?",
"starting_points": [
"research/complex-local-word-ceiling/README.md",
"research/idle-axis-hosting/PROOF.md",
"certificates/selected-result.json"
],
"methods": [
"State a replacement for the coverage identity (mass = 72W + 64N) and the contract change that realizes it, with its implementation cost.",
"Find an obstruction: show which data-endpoint obligation forces exactly one unpaid coordinate in the current template."
],
"acceptance_gate": "An explicit replacement identity, verified on a small complete instance with dirty inputs, priced with ceiling.ceiling(unpaid=...).",
"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": "Explain where the single unpaid coordinate per family comes from in the hosted template; propose one change and price it. Ideal budget: two unpaid coordinates per family is 3.77x (levers.py).",
"bottleneck_link": "The deficit is one coordinate per family minus the centre charge; doubling unpaid coordinates per family scales it directly.",
"allowed_variations": [
"One template change or one endpoint-contract change."
],
"scope_change_triggers": [
"Counting a coordinate as unpaid while leaving it unadvanced in the data endpoint."
],
"overlap_terms": [
"coverage identity",
"unpaid coordinate",
"deficit law",
"W - 64N"
]
},
{
"id": "persistent-boundary",
"question": "Can a specified pair of consecutive calls eliminate a restoration that the next call reconstructs?",
Expand Down Expand Up @@ -396,7 +480,7 @@
},
{
"id": "verifier-engineering",
"weight": 10,
"weight": 8,
"tasks": [
{
"id": "replay-runtime",
Expand Down Expand Up @@ -554,20 +638,21 @@
},
{
"id": "incumbent-optimization",
"weight": 5,
"weight": 2,
"tasks": [
{
"id": "selected-packing",
"question": "Is there a genuinely unsearched, explicitly bounded improvement to the selected packing?",
"starting_points": [
"certificates/selected-result.json",
"research/heterogeneous-owner-assembly/README.md"
"research/heterogeneous-owner-assembly/README.md",
"research/complex-local-word-ceiling/README.md"
],
"methods": [
"Search a named unclaimed canonical candidate domain with a reproducible partition.",
"Prove a stronger scoped relaxation or exact optimum for one named residual subproblem."
],
"acceptance_gate": "Check live PR overlap first, price both suppliers and distinguish a search best from an optimum.",
"acceptance_gate": "Check live PR overlap first, price both suppliers and distinguish a search best from an optimum. Report the word's packing cap from ceiling.ceiling() and the fraction of it realized; label packing gains as such.",
"first_step": {
"command": [
"python3",
Expand Down
6 changes: 6 additions & 0 deletions docs/research/bottleneck-brief.md
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Expand Up @@ -22,6 +22,12 @@ limiting conversion `κ = a/(1+a)`, κ > .01 needs both effective primitive budg
above approximately `1/99`, with strict margins and all transfer obligations.
This describes the current construction, not a lower bound for multiplication.

**Revision 3 update (pending review of #1240/#1264).** On the binding complex side, packing any
screened local word is capped within about 0.9% of the record. The 64-per-call centre path uses about
64% of the raw deficit, and the effective child rank is about 3.9. See the lever budgets in
[the packing ceiling](../../research/complex-local-word-ceiling/README.md) and the
[priority log](research-priority-log.md).

## What a successful change must affect

The construction recursively replaces work of width `m` with children of ranks
Expand Down
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