# TODO — what to try next

> Public mirror edition: repository-internal working instructions were removed. See MIRROR.md.

This is the forward queue. Detailed results and failed steps belong in
[research/OUTCOMES.md](research/OUTCOMES.md); Git preserves revisions.
Each item names a question, first move and payoff or a concrete reopening
condition. Ledger lines retain the links needed to avoid repeating work.

Start with [research/AGENT-START.md](research/AGENT-START.md).
Before an attempt, read its ledger entries and their decisive arguments.
An ANSWERED specification can still contain an OPEN estimate; a failed
bound does not refute that estimate. Each new research note needs a ledger
block and a parity scope, then an outcome entry and generated indexes.

## Priority board — 2026-09-09

| Priority | Item | Next decision |
|---|---|---|
| 1 | C: twin-prime arithmetic | Check a source/structure match for D's corrected small-gcd moment target; A2's exact B is an independent alternative |
| 2 | W: manuscript source review | Check the remaining source dependencies, independently of the twin target |
| 3 | 9: variance identification | Price the weighted theorem transfer; a separate mathematical goal |
| Conditional | Z2, Z4, D, 0c | Reopen only with a changed input, a new mechanism, or a specific defect |
| Parked | Larger enumerations and other routes below | Name a decision the work can resolve before allocating time |

## THE TARGET

The target is infinitely many twin primes. A positive weighted count on
unbounded dyadic scales suffices; a uniform gap bound is stronger than the
consumer being pursued. Exact formulas and errors:
[research/RESEARCH-HANDOFF.md](research/RESEARCH-HANDOFF.md) section 3.

## Active arithmetic

**C. Estimate the missing arithmetic, with the complete payoff.**

The second dispatch is complete and independently reviewed. Use
[research/RESEARCH-EXECUTION.md](research/RESEARCH-EXECUTION.md) for its
current dispositions, candidate obligations and report contract. No worker
is assigned by this review. All B/D returns are present; A's truncation
and A2's repaired low Type I estimate are accepted. C's growing norm
obstruction and E's all-depth failure of two explicit tests are retained
at the corrected scope. D adds a fourth condition to the exact residual.

First candidate: at D's target sector, preserve the prime-power structure
and prove a moment saving greater than 7/200 over exponent 57/40,
including all separation costs. Start with the source/structure match in
[structured-dispersion-estimate.md](research/structured-dispersion-estimate.md)
and the handoff section 5. This controls only a local box if it succeeds;
the global complement stays unpaid. Repeating the generic moment or a
region scan has no new decision without a changed input.

Independent alternative: estimate the actual Type II plus band B of
[fixed-endpoint-discrepancy.md](research/fixed-endpoint-discrepancy.md).
The sufficient B>=-(C2-c0)x+o(x), fixed c0>0 on unbounded dyadic scales,
remains OPEN. The stronger D margin is B+2C2*M>=-4x/25+o(x), not an
equivalent restatement of that B bound. General logarithmic margins
and exact definitions remain in the handoff section 3.

B/C/E reopen on a matched rate, new consumer or precise correctness
concern; their failed tests do not rule out whole approaches. Check
novelty before new analysis or compute and validate candidates in the
same pass. The six-hour allowance was treated as consumed by the retained
censuses; this review allocates no new enumeration.

Ledger: Q-chen-fold-benchmark, Q-chen-signed-target, Q-chen-opportunity, Q-prime-detection-inputs, Q-bilinear-fold-first-attack, Q-polylog-fold-transfer, Q-shifted-prime-decomposition, Q-singleton-fiber-audit, Q-data-reuse-audit, Q-signed-divisor-grouping, Q-endpoint-target-audit, Q-endpoint-fourier, Q-coefficient-structure, Q-endpoint-pairing, Q-prime-band-completion, Q-prime-dispersion, Q-dispersion-range, Q-sparse-dispersion, Q-prime-power-dispersion, Q-residual-coverage, Q-structural-literature-audit, Q-grouped-divisor-moment, Q-research-handoff, Q-small-divisor-kernel, Q-kernel-sign-control, Q-chain-review-0906, Q-corner-correlation, Q-left-divisor-signs, Q-reachability-coverage, Q-determinant-corollary, Q-mobius-bv-derivation, Q-consumer-comparison, Q-corner-measurement, Q-twin-reduction, Q-corner-log-average, Q-signed-moment, Q-heath-brown-edges, Q-review-request-0906, Q-handoff-review-0906, Q-prime-band-transfer, Q-agent-start, Q-next-transfer-review, Q-corner-branch-diagnostic, Q-next-correlation-source-map, Q-round-review-0906, Q-cross-campaign-synthesis, Q-corner-coefficient-energy, Q-sharp-corner-transition, Q-transition-research-execution, Q-transition-energy-review-spec, Q-transition-source-match-spec, Q-transition-joint-budget-spec, Q-transition-energy-review, Q-transition-source-match, Q-transition-joint-budget, Q-transition-signed-estimate, Q-transition-round-review, Q-transition-round-audit, Q-cofactor-progression-transfer, Q-global-cutoff-averaging, Q-global-factor-signs, Q-global-smooth-majorant, Q-smooth-sieve-literature, Q-switching-negative-mass, Q-paired-factor-budget, Q-supported-coefficient-dickman, Q-joint-correction-source-audit, Q-moving-cutoff-parity, Q-research-execution, Q-shifted-prime-mobius-sums, Q-centered-discrepancy-measurement, Q-full-coefficient-average, Q-centered-discrepancy-estimate, Q-fold-arithmetic-bridge, Q-research-round-validation, Q-joint-factor-estimate, Q-structured-dispersion-estimate, Q-fixed-endpoint-discrepancy

## Independent mathematical work

**W. Review the consolidated bounds manuscript at source.**

Ledger: none

**9. Complete the variance identification transfer.**

Question: can the weighted form needed for the theta=2 replacement error
be derived from Harper's theorem with the correct range and tails?
First move: read the ledger's identification, smooth-AP and correction
notes, then write the (H_w) transfer and its accumulated error in full.
Payoff: a justified two-branch contribution; the three-branch type must
also be addressed before claiming the variance limit.

Keep the outstanding mirrored-pattern producer correction and re-embed
listed under maintenance below. Model convergence alone does not settle
the identification step. A larger Var(41) run has no current decision.

Ledger: Q-varE-limit, Q-redteam-0828-varE, Q-applied-0828-varE, Q-var41, Q-paper-iii-restructure, Q-lit-scourfield-2008, Q-varE-identification-0830, Q-recon-0830-smooth-aps, Q-verify-record-defects-0830, Q-redteam-0830-imports, Q-redteam-0830-slack

## Conditional routes — no automatic dispatch

**Z2. Anchored occupancy certificate.**

Can a new arithmetic input bound the scour count against the channel floor? Read
the capture identity and the ledger’s certificate failures before selecting an
input. Reopen only with a bound not obtained by assuming occupancy itself; payoff
is a certified positive count on the stated scales. The scored depth runs are not
a pending task.

Ledger: Q-redteam-0828-quadpoint, Q-capture-identity, Q-quadpoint-transplant, Q-quadpoint-prior-art, Q-applied-0828-quadpoint, Q-recon-0828-sieve, Q-recon-0828-rough, Q-parity-adversary, Q-roughpair-error, Q-roughpair-null, Q-X-upper-0829n, Q-parity-dstar-law-0829n, Q-quadpoint-blind-31607-0830, Q-quadpoint-c1c2-0830, Q-redteam-0830-zone, Q-redteam-0830-records, Q-derive-0904-r0-extension, Q-redteam-0904-r0-extension

**Z4. Anchored head and tail remainders.**

Can the anchored part be estimated without assuming its Hardy–Littlewood
prediction? First identify an input beyond the class ensemble; then price the
residual at the actual origin. Payoff is an anchored estimate, not another
derivation of the already-understood ensemble.

Ledger: Q-head-residual, Q-redteam-0828-census, Q-redteam-0828-head, Q-destroyer-census, Q-applied-0828-head, Q-applied-0828-census, Q-applied-0828-live, Q-zone-tail, Q-zone-tail-02, Q-tail-derivation-0830, Q-head-remainder-0830, Q-verify-record-defects-0830, Q-redteam-0830-slack

**Z5. Record-gap mechanism.**

Can a named new mechanism explain the finite-height shortfall with a falsifier
robust to the extrapolated tail? Read the existing null and prior-art records
first. Payoff is a calibrated record-process result; no direct twin-prime
implication is established. Do not rerun completed null comparisons.

Ledger: Q-record-deficit, Q-record-null2, Q-redteam-0828-litimports, Q-applied-0828-litimports, Q-applied-0828-registries, Q-record-mechanism-0830, Q-redteam-0830-records

**D. Fixed-base gap growth.**

Reopen only with a direct weighted-run or maxsum estimate that avoids the failed
fold composition. Coordinate with 0c. A theorem at all required rungs has a
conditional gap-growth payoff; the finite ladder does not provide it.

Ledger: Q-doubling-C2, Q-kstar-prereg, Q-doubling-bridge-0829n, Q-doubling-killrun-0830, Q-recon-0830-rec-killrun, Q-redteam-0830-imports, Q-redteam-0830-doubling

**0. Two-class exponent.**

Reopen only with a specific defect in the recorded remainder obstruction or an
estimate using changed inputs outside its proved scope. Read the REC and
CRT-planted-position arguments before making that distinction. Payoff is a
justified upper-bound improvement; no universal optimality claim is assumed.

Ledger: Q-rho2-bound, Q-redteam-0828-closures, Q-applied-0828-closures, Q-recon-0828-jacobsthal, Q-recon-0828-sieve, Q-recon-0828-covering, Q-recon-0828-farfields, Q-recon-0828-rough, Q-lit-siebert, Q-barrier-kappa2, Q-maximal-law-tpc, Q-rho-maximal-law, Q-theta-ladder, Q-gap-spectrum, Q-measure-g2-generic, Q-g2-provenance-x37, Q-tail-deficit-model, Q-recon-0829-farfields2, Q-recon-0829-escapes, Q-rml-proof-0829n, Q-usup-convention-0830, Q-rec-cheapest-0830, Q-recon-0830-rec-killrun, Q-rho-sup-z41-0830, Q-omega-floor-blind-0830, Q-redteam-0830-imports, Q-redteam-0830-floor-growth, Q-redteam-0830-rml, Q-redteam-0830-floor-sign, Q-derive-0904-L7-transfer, Q-recon-0904-sifting-limit-floor, Q-redteam-0904-floor-growth-2, Q-redteam-0904-item0, Q-redteam-0904-sifting-limit

**1d. Bounded-defect / Fekete formulation.**

The fixed-base option is coordinated under D. Reopen the all-bases form only with
a justified treatment of its sign condition. The tried finite-reach readers do not
settle that condition. Payoff must include a proved gap-ratio bound and its
quantifiers.

Ledger: Q-hsubpow-K, Q-redteam-0828-closures, Q-applied-0828-closures, Q-fekete-1d-defect47, Q-g2-falls-decision-rule, Q-hsub-reductions, Q-import-interp, Q-y2-recompute, Q-hsubpow-K-0829n, Q-delta-reader-0830, Q-redteam-0830-fekete

**0b. Fold multiplier.**

Reopen when there is a proof strategy for the required pair correlation that does
not re-assume the Zone Postulate. Read U-FRAME and the gate/import-thinning ledger
first. Payoff is the missing multiplier estimate, with its actual domain.

Ledger: Q-gate-multiplies, Q-import-thinning

**0c. Residue-deleted maxsum.**

Seek a direct maxsum estimate using information absent from the failed growth
laws. Read the copying/no-straddling hypotheses, scan-statistic source convention
and bridge cost first. Payoff requires an explicit transfer; this object alone
does not automatically bound the fold multiplier.

Ledger: Q-0c-holesweep, Q-0c0e-level-selection, Q-foldL-maxsum-direct, Q-import-chaining

**X. X-channel offset mechanism.**

Name a new offset mechanism and a falsifier after reading the cofactor-convolution
and rejected-candidate records. Payoff is an explanation of the residual constant
at a stated scope. The beta(37) ensemble is a conditional compute decision under
Z7, not a proof input by itself.

Ledger: Q-verify-cofactor-convolution, Q-xchan-at29-prereg, Q-xchan-at37-offset, Q-xchan-at37-score, Q-xchannel-at23, Q-xchannel-closedform, Q-xchannel-offset, Q-xchannel-triples

## Computation — allocate only for a decision

**A. Anchored ladder at the next named level.**

Before extending to @29, price the segmented calculation from the existing ladder
record and state the finite certificate it will decide. An all-level floor growing
without bound would itself require a twin-prime proof; do not infer it from a
larger table.

Ledger: Q-anchored-ladder, Q-anchored-unify, Q-history-dial, Q-anchored-ladder-17-0830, Q-redteam-0830-engine

**1. Larger exact tile census.**

Use the existing BigInt and segmentation cost analysis before proposing @43. The
recorded estimate is box-class and has no current proof consumer. Reopen only for
a pre-registered discriminating question and an explicitly allocated budget.

Ledger: Q-at43-bigint-0830, Q-redteam-0830-imports

**Z7. Shared compute queue.**

The handler must account for the campaign compute allowance, including prior
consumption. The 4–5 day research window is not permission for continuous
multi-day enumeration. The beta(37) ensemble and any box-class run remain
separately priced decisions. Reuse adopted producers; do not silently substitute
an inline record ladder.

Ledger: Q-zonegap-03-score

**6. Wrap-engine precision.**

First price a method that obtains the required T3/T4 precision from the existing
routing notes, such as a justified hybrid summation. The @17 computation is not
queued merely because a longer research window exists. Payoff is a finite
precision certificate.

Ledger: none

**2. Variance census at 41.**

Remain parked until a mathematical test changes the decision threshold in
var41-prereg. Retain its pre-registered bar and prediction. The existing cost and
indecisive payoff do not justify dispatch.

Ledger: Q-var41

**8. Buchstab transfer at usable depth.**

Reopen only with a new estimate that addresses the recorded dimension-2 ratio or
dimension-1 prime-comb count at the required sifting range. Read both completed
half-attempts and source corrections. Payoff is a transfer at the actual
certificate precision, not an order-of-magnitude comparison.

Ledger: Q-buchstab-transfer, Q-sharp-sieve-range, Q-comb-discrepancy, Q-redteam-0828-engine, Q-applied-0828-engine, Q-applied-0828-live, Q-u2-engine-depth, Q-buchstab-deep-0830, Q-comb-tail-0830, Q-redteam-0830-engine

## Integration, maintenance and owner decisions

**Z0. Review returned work before promotion.**

Open now: [research/review-request-0907.md](research/review-request-0907.md)
ranks the 2026-09-07 session's claims (the §6.2 demotion in the two-class
manuscript first) and lists what no reader outside that session has checked.
At each integration checkpoint, independently inspect new decisive arguments
and failed-step claims. Follow the acceptance checklist in
[research/RESEARCH-EXECUTION.md](research/RESEARCH-EXECUTION.md).
Payoff: a coherent current contract with unresolved claims still marked OPEN.
A green mechanical check is not mathematical review.

Ledger: Q-redteam-0828-census, Q-redteam-0828-quadpoint, Q-applied-0828-census, Q-applied-0828-quadpoint, Q-review-request-0907

Maintenance is a conditional queue, not a new claim that every old producer
has been repaired. Check its current state before editing:

- Apply the mirrored-pattern correction to research/history/staging/varE-theta2-step.js,
  then re-embed the affected entries; evidence is the Q-verify-record-defects-0830
  and Q-varE-identification-0830 records. Keep paper edits coordinated.
- Apply the documented convention correction to research/zone-tail-02.js
  and re-embed; first read Q-verify-record-defects-0830.
- Replace the inline record prefix in research/zonegap-01.js with its
  adopted producer, retaining the scored-run substitution checks.
- Complete the three over-budget output-custody records when their source
  logs and budget are available: custody-wave3, custody-overnight and
  custody-embed-migration. Do not invent embedded output.
- Manuscript work remains in paper/PAPERS.md and paper/proposals/PROPOSALS.md:
  source review, spine choice, theorem calibration, and the owner's reading
  of staircase-note and anchored-note. No external publication is authorized.
- Re-attestation and backup occur only on the owner's instruction, using
  attestation/README.md. No automation is created by this queue.

Other parked questions require a changed method or a decision they can resolve:
the c2-prime drift mechanism beyond the present ladder; Natal@5 grain and
covering constructions; the two-class Hensley–Richards source search in its
owning convention; double coverings; the mirror discrepancy salvage; the
deep-gap migration; and exact adversarial minima. Read their outcome and
question records before allocating work.