{"id":783,"job_id":1570,"problem_id":1,"lane_id":3,"type":"explore","user_id":34,"model":"deepseek-v4-flash","provider":"deepseek","report_md":"# The end-to-end conditional implication of the twin-prime target, as a dependency graph\n\nJob **#1570** (explore, discovery, lane `formalize`, no route assigned), attempt\n`fd9501bd50a20b39759d44ec8f1198e2`. The person's instruction: build the conditional implication of\nTPC end to end — one document plus an executable dependency graph in which every input carries a\nrung, every leaf is attached to its return or document, and a query returns the root's lethal set.\n\n**What this is.** A single object that holds the whole chain, from \"infinitely many twin primes\"\ndown to the concrete estimates the corpus is working on: **59 nodes**, each with a rung from a\nfixed vocabulary, an owner, the literal tokens that make its numbers checkable in that owner, and its\nedges. `work/tpc_deps.py` is the graph; `artifacts/tpc-deps.json` is its export; every table below is\nthat tool's own output. **Nothing here is a new estimate, and no rung is upgraded by being assembled:**\n29 nodes carry an established rung, 14 are open obligations and 16 are closed or\nrefuted at their stated scope.\n\n**The one measurement this window adds is structural, and it is this:** of the 16 closed items in\nthe graph, **none gates anything**. Deleting any of them leaves the root exactly as derivable as\nbefore (generated table in section 5). They are traces of attacks, not steps of a proof, and the\ncorpus's own registers do not always make that distinction — which is how five routes come to look\nlike five views of one obstruction.\n\n## 1. The chain, with rungs\n\nThe target has **four independent sufficient consumers**, which is why a branch can die without\nclosing the programme:\n\n| consumer | exact statement (short) | rung | why it reaches the target |\n|---|---|---|---|\n| `ZONE-WEAK` | for infinitely many primes p, the tile `T_p`'s first twin slot lies below `p'^2 - 2` | open | the weak Zone Postulate is *equivalent* to TPC, both directions, elementary |\n| `MARGIN-SHRINK` | `C2 x + E_dagger(x) >= c0 x/(log x)^K`, fixed `c0 > 0, K >= 0`, unbounded dyadic `x` | open | it gives `>= (c0/2) x/log^(K+2) x` actual prime pairs on the witnessing scales |\n| `CENTERED-MARGIN` | `D_y(x) >= -4x/25 + o(x)` for the centered prime–Mobius discrepancy | open | the third sufficient formulation, in the centered normalization |\n| `B-MARGIN` | a signed lower bound on the reviewed endpoint `B`, where `S = C2 x + B + O_A(x/log^A x)` | open | the same conclusion from the reviewed fixed-endpoint normalization |\n\nThe deductive steps that make those implications real are nodes too, and all four are **derived**, not\nassumed: `EQ-ZONE-TPC` (the equivalence, elementary), `GAP-REFORM` (the Gap Reformulation; since\n`ln(p#) ~ p`, the window `p^2` is `(log q)^2`, so zone occupancy follows from a two-class Jacobsthal\nexponent below 2), `CONSUMER-COUNT` (the counting deduction with the `sqrt(x) log^3 x` prime-power\nsubtraction), and `B-EXACT` (the representation behind the fourth consumer).\n\n**The classical base is named, not assumed.** The arithmetic branch rests on five imported theorems —\n`VAUGHAN`, `PNT`, `BV-LAMBDA` (level `x^(12/25)`), `BV-MU` (level `x^(1/10)`, itself derived from\nKoukourtopoulos GSM 203 in its own reviewed note) and `EXCLUDED-MEANS` — and on one **derived** node,\n`REDUCTION`, adjudicated three times with no defect found. That node is tagged *derived* and is\nnevertheless **irreplaceable inside its branch**: every margin statement there is a statement about\n`E_dagger`, and `E_dagger` exists only because the reduction holds. Removing it costs the whole\nbranch, and nothing else (`impact REDUCTION` = `MARGIN-SHRINK`).\n\n## 2. The two targets inside one box, and they are not substitutable\n\nThis is the most consequential thing the assembly exposes, and the corpus says it in its own words\n(`RESEARCH-HANDOFF.md` section 5). The same rectangle carries **two different required savings, from\ntwo different Cauchy arrangements**:\n\n* the native orientation, `X_small <= C x^(36/25 - eta)`, needs a saving **strictly greater than\n  `3/50`** (the generic top moment exponent is `3/2`, so `3/50` leaves no fixed slack);\n* the structured fixed-`q` sector, with block exponent `407/400 = 57/40` (moment majorant)\n  `x 61/100` (first-Cauchy factor), needs **more than `7/200`**.\n\nThe corpus's warning is explicit: *do not substitute one exponent into the other's sum*. In the graph\nthese are two separate open leaves (`X-SMALL`, `D1-BLOCK`), reachable as **alternatives** from\n`BOX-CONTROL`, so the tool reports them as two obligations and never as one — which is exactly the\nfailure mode the warning exists to prevent.\n\n## 3. Five routes, one obligation: the attack layer is where the swarm is\n\n`BOX-CONTROL` has **16 closed attacks attached to it** and one obligation actually underneath\nit. Reading them as five independent efforts hides that they all die on the same thing:\n\n* the eleven published interfaces at `X-SMALL` (`SMALL-DIVISOR-KERNEL` 129/125 against 1; `DFI`\n  1267/1200; the spectral diagnostic trivial to `x^(19/50)`; `TYPE-I-II` 41/40 with the balanced\n  piece returning to 103/100; `FKM` prime modulus, `1/48` against `3/25`; `WRIGHT` 1157/1000;\n  `GURIA`; `DET-COROLLARY`, which adds exactly zero area; and the Chowla family, wrong average type\n  or saving far below `log^(2+eps) x`);\n* the run's own four closures at `D1-SMALL-GCD` (`PARSEVAL-L2`, `FOUR-CLASS-SPLIT`, `G-HALF-ETA`, and\n  the scoped ceiling of the fixed-modulus family at `7/380` against `7/190` in c-units).\n\n**What the residual work actually is** is one node with two live parts: `D1-SMALL-GCD` (a saving of\n`7/200` in the remaining small-gcd range) and its neighbour `ROUTE48-RANGE-INPUT` (a published\nstatement covering lengths `n^(o(1))..n^0.21` at composite modulus — blocked, not refuted, and the\nrequirement there is weak: **any** `c^(-delta)`, `delta > 0`, suffices because the deficit is one\nlogarithm and `log y = c^(o(1))`). The graph therefore separates two things the corridor has been\nrunning together since the start: **which route is cheapest to finish**, and **which item is the wall**.\n\nThe wall, in the corpus's own terms, is a **positivity** statement, not a distribution one:\nthe discard points of the dimension-2 sieve were all mapped, distribution hypotheses enter at exactly\none of them, and the primorial formulation already saturates it. So `GAP-INF` (distance 4.2665 -> 2)\nand `MARGIN-SHRINK` (a signed constant comparison where only an absolute `O(x)` bound exists) are two\nfaces of one missing ingredient — and `SMOOTH-ABS` is its most frequently re-derived dead end: a\nstatement can be **proven** and still be a failed step. The graph keeps that distinction in the rung,\nwhich is the only place it can be kept.\n\n## 4. The closures: what must be closed, and what is irreplaceable\n\n### The graph, by branch\n\n**Target and equivalence**\n\n| node | tag | claim (short) | owner |\n|---|---|---|---|\n| `TPC` | open | The target | docs/README.md, Status |\n| `EQ-ZONE-TPC` | derived | Zone weak form == TPC | research/ZONE-POSTULATE.md section 2 |\n\n**Branch 1: zone occupancy**\n\n| node | tag | claim (short) | owner |\n|---|---|---|---|\n| `ZONE-WEAK` | open | Zone Postulate, weak form | research/ZONE-POSTULATE.md sections 1-2 |\n| `GAP-REFORM` | derived | The Gap Reformulation | research/ZONE-POSTULATE.md section 3 |\n| `GAP-INF` | open | Jacobsthal exponent below 2, infinitely often | research/ZONE-POSTULATE.md section 3; research/G2-STATE.md section 6 |\n| `GAP-DHR-BOUND` | published | The achieved bound | paper/beta2-note.md; docs/README.md Status |\n| `GAP-BAND` | derived | The open band | docs/README.md, Status, points 1-3 |\n| `PARITY-ANALYSIS` | analysis | Not a distribution problem | research/ZONE-POSTULATE.md section 3 (ANALYSIS, not a theorem) |\n| `ZONE-VERIFIED` | numeric | Exhaustive verification to 10^11 | research/window-check.js; research/ZONE-POSTULATE.md section 4 |\n| `LEMMA-V-MS` | derived | Lemma V, mean-square form | research/sift-limit-attack.md section 7e; ZONE-POSTULATE.md preamble |\n| `USUP` | refuted | The u_sup bound | research/sift-limit-attack.md section 7e; research/G2-STATE.md |\n| `BOOLE-FRECHET` | refuted | The Boole-Frechet certificate | research/sift-limit-attack.md section 7e; history/staging/attack-bonferroni-degree.md |\n| `TILE-FLOORS` | refuted | Certified per-tile floors | paper/staircase-note.md; research/ZONE-POSTULATE.md section 3 |\n\n**Branch 2: the signed margin**\n\n| node | tag | claim (short) | owner |\n|---|---|---|---|\n| `MARGIN-SHRINK` | open | Sufficient signed margin | research/RESEARCH-HANDOFF.md section 3 |\n| `CONSUMER-COUNT` | derived | The consumer deduction | research/RESEARCH-HANDOFF.md section 3 |\n| `REDUCTION` | derived | The checked reduction | research/TWIN-REDUCTION.md section 1; research/RESEARCH-HANDOFF.md section 3 |\n| `VAUGHAN` | published | Vaughan's identity | research/TWIN-REDUCTION.md section 1 |\n| `PNT` | published | Quantitative PNT | research/TWIN-REDUCTION.md section 1 |\n| `BV-LAMBDA` | published | Bombieri-Vinogradov for Lambda | research/TWIN-REDUCTION.md section 1 |\n| `BV-MU` | published | Mobius Bombieri-Vinogradov | research/mobius-bv-derivation.md; research/TWIN-REDUCTION.md section 1 |\n| `EXCLUDED-MEANS` | published | Excluded-prime Mobius means | research/TWIN-REDUCTION.md section 1 |\n| `BOX-CONTROL` | open | The witness box, controlled | research/RESEARCH-HANDOFF.md section 5 |\n| `X-SMALL` | open | Native orientation: saving > 3/50 | research/RESEARCH-HANDOFF.md section 5 |\n| `D1-BLOCK` | open | Structured sector: saving > 7/200 | research/structured-dispersion-estimate.md; research/RESEARCH-HANDOFF.md section 5 |\n| `D1-ACCOUNTING` | derived | The block accounting | research/structured-dispersion-estimate.md; research/RESEARCH-HANDOFF.md section 5 |\n| `D1-SMALL-GCD` | open | The remaining small-gcd range | research/structured-dispersion-estimate.md; research/RESEARCH-HANDOFF.md section 5 |\n| `CONTROLLED-REGIONS` | derived | What the moment already controls | research/TWIN-REDUCTION.md section 3; research/grouped-divisor-moment.md |\n| `EXTREMAL-CEILING` | derived | The ceiling of this argument shape | research/reachability-coverage.md; research/TWIN-REDUCTION.md section 4 |\n| `CORNER` | derived | The corner is the conclusion | research/corner-correlation.md; research/TWIN-REDUCTION.md section 5 |\n| `COMPLEMENT` | open | The global complement | research/RESEARCH-HANDOFF.md sections 3 and 5 |\n| `SMOOTH-EQUIV` | derived | Complete smooth alternative | research/global-smooth-majorant.md; research/RESEARCH-HANDOFF.md section 3 |\n| `SMOOTH-ABS` | refuted | Full absolute O(x) bound | research/global-smooth-majorant.md; research/RESEARCH-HANDOFF.md section 1 |\n\n**Branch 3: the centered consumer**\n\n| node | tag | claim (short) | owner |\n|---|---|---|---|\n| `CENTERED-MARGIN` | open | Centered prime-Mobius discrepancy | research/moving-cutoff-parity.md; research/fixed-endpoint-discrepancy.md |\n| `MOVING-CUTOFF-REPAIR` | derived | The moving-cutoff repair | research/moving-cutoff-parity.md |\n| `CENTERED-CENSUS` | numeric | Census to 2^38 | research/centered-discrepancy-measurement.md; docs/README.md Status |\n\n**Imported conditionals**\n\n| node | tag | claim (short) | owner |\n|---|---|---|---|\n| `COND-ROUTES` | published | Conditional published routes | research/consumer-comparison.md; research/TWIN-REDUCTION.md section 7 |\n| `COND-INPUTS` | open | The conditional inputs themselves | research/consumer-comparison.md; research/TWIN-REDUCTION.md section 7 |\n| `PARITY-WALL` | analysis | The wall must name its inputs | docs/README.md, Status |\n\n**This run's objects**\n\n| node | tag | claim (short) | owner |\n|---|---|---|---|\n| `S-FAMILY-CEILING` | derived | Fixed-modulus family ceiling | return 780 (route 48 triage); sibling return 632 |\n| `ROUTE48-RANGE-INPUT` | open | Range coverage at composite modulus | return 778 (route 48 proposal, accepted as route 48) |\n| `UNBALANCED-BAND` | open | One logarithm of decorrelation | return 777 (job 1565), the two pre-registered measurements |\n| `PARSEVAL-L2` | refuted | Parseval / l2 substitution | return 762 family (windows 1552-1569); work/T791-linfty-vs-l2.md |\n| `FOUR-CLASS-SPLIT` | refuted | The (++/--/+-/-+) splitting | work/T791-class-split.md (runs 1562-1569) |\n| `G-HALF-ETA` | refuted | G^(1/2-eta) alone | work/T791-arithmetic-threshold.md (run 1562-1569) |\n| `RUN-MEASUREMENTS` | numeric | This run's own measurements | returns 777, 778, 780 (jobs 1565, 1566, 1567) |\n\n**Measurements**\n\n| node | tag | claim (short) | owner |\n|---|---|---|---|\n| `KERNEL-SIGN` | numeric | Mobius signs vs random signs | research/kernel-sign-control.md; research/TWIN-REDUCTION.md section 6 |\n| `CORNER-MEAS` | numeric | Corner correlation at random-sign size | research/corner-measurement.md; research/TWIN-REDUCTION.md section 6 |\n| `LADDER` | numeric | The trusted G2 ladder | research/G2-STATE.md sections 2-3; docs/README.md Status |\n\n**The priced-and-failed interfaces**\n\n| node | tag | claim (short) | owner |\n|---|---|---|---|\n| `SMALL-DIVISOR-KERNEL` | refuted | Bettin-Chandee on the separated trilinear form | research/small-divisor-kernel.md; research/TWIN-REDUCTION.md section 6 |\n| `DFI` | refuted | Duke-Friedlander-Iwaniec (1.1) | research/small-divisor-kernel.md; research/TWIN-REDUCTION.md section 6 |\n| `SPECTRAL-DIAG` | refuted | Spectral large sieve diagnostic | research/small-divisor-kernel.md; research/structural-literature-audit.md |\n| `TYPE-I-II` | refuted | Type I/II decomposition of the left Mobius coefficient | research/left-divisor-signs.md; research/TWIN-REDUCTION.md section 6 |\n| `FKM` | refuted | Fouvry-Kowalski-Michel algebraic twists | research/TWIN-REDUCTION.md section 6 |\n| `WRIGHT` | refuted | Wright, subdyadic Bettin-Chandee | research/TWIN-REDUCTION.md section 6 |\n| `GURIA` | refuted | Guria, Kloosterman fractions averaged over primes | research/corner-correlation.md; research/TWIN-REDUCTION.md section 6 |\n| `DET-COROLLARY` | refuted | Bettin-Chandee Corollary 1 on the determinant equation | research/determinant-corollary.md; research/TWIN-REDUCTION.md section 6 |\n| `CHOWLA-FAMILY` | refuted | Averaged and logarithmic Chowla inputs | research/corner-correlation.md; research/consumer-comparison.md |\n\n### Sufficient closures, one row per consumer formulation\n\n| consumer | cheapest closure (named open obligations) | size | irreplaceable inside it |\n|---|---|---|---|\n| `ZONE-WEAK` | `GAP-INF`, `ZONE-WEAK` | 2 | `GAP-INF` |\n| `MARGIN-SHRINK` | `BOX-CONTROL`, `COMPLEMENT`, `MARGIN-SHRINK`, `X-SMALL` | 4 | `BOX-CONTROL`, `COMPLEMENT`, `REDUCTION` |\n| `CENTERED-MARGIN` | `CENTERED-MARGIN` | 1 | (none above it) |\n| `B-MARGIN` | `B-MARGIN` | 1 | (none above it) |\n\nSmallest closure over all branches: **1** node(s), `B-MARGIN`\n\nGlobally fatal single failures: **none** -- no node lies on every consumer route, so losing any one branch leaves the others intact.\n\n### Frontier: what the root reaches today\n\nOn the root's paths, open obligations: `B-MARGIN`, `BOX-CONTROL`, `CENTERED-MARGIN`, `COMPLEMENT`, `D1-BLOCK`, `D1-SMALL-GCD`, `GAP-INF`, `MARGIN-SHRINK`, `X-SMALL`, `ZONE-WEAK`\n\nOn the root's paths, blocked on a named literature input: none\n\nClosed attacks attached to those paths (traces, not gates): `BOOLE-FRECHET`, `CHOWLA-FAMILY`, `DET-COROLLARY`, `DFI`, `FKM`, `FOUR-CLASS-SPLIT`, `G-HALF-ETA`, `GURIA`, `PARSEVAL-L2`, `SMALL-DIVISOR-KERNEL`, `SMOOTH-ABS`, `SPECTRAL-DIAG`, `TILE-FLOORS`, `TYPE-I-II`, `USUP`, `WRIGHT`\n\nAttacks still in flight, open: `ROUTE48-RANGE-INPUT`, `UNBALANCED-BAND`\n\n\n### Every closed attack, and what it changes if its content is removed\n\n| node | impact |\n|---|---|\n| `USUP` | nothing |\n| `BOOLE-FRECHET` | nothing |\n| `TILE-FLOORS` | nothing |\n| `PARSEVAL-L2` | nothing |\n| `FOUR-CLASS-SPLIT` | nothing |\n| `G-HALF-ETA` | nothing |\n| `SMOOTH-ABS` | nothing |\n| `SMALL-DIVISOR-KERNEL` | nothing |\n| `DFI` | nothing |\n| `SPECTRAL-DIAG` | nothing |\n| `TYPE-I-II` | nothing |\n| `FKM` | nothing |\n| `WRIGHT` | nothing |\n| `GURIA` | nothing |\n| `DET-COROLLARY` | nothing |\n| `CHOWLA-FAMILY` | nothing |\n\n### The one load-bearing claim that is not an obligation\n\n`REDUCTION` is tagged `derived` (checked, adjudicated three times) and is nevertheless irreplaceable inside the arithmetic branch: every margin statement in that branch is a statement about `E_dagger`, which exists only because the reduction holds. Impact of removing it: `MARGIN-SHRINK`.\n\n## 5. The trap, stated as a node\n\n`CORNER` is in the graph and is deliberately **not** a route: on the prescribed-exponent corner `S_0`\nthe endpoint sum becomes a two-point Möbius correlation at the fixed shift 2 with prime-band weights,\nand the corpus's own finding is that one-sided control of the full corner is, given the full complement\nat `O_H(x/log^H x)`, **inter-derivable with the sufficient margin itself** — it is the conclusion, not\na lemma. A closure query that accepted it would report \"close the problem\" as a plan, so the tool\nrefuses it and the self-test asserts that it never enters a closure set.\n\nThe two ceilings around it are nodes as well, and both are load-bearing for what they forbid:\n`CONTROLLED-REGIONS` (the moment controls `delta+nu < 19/25`, `5 delta + 2 nu < 123/50`,\n`delta < 19/25` with `delta + 3 nu < 161/100`; the uniform threshold has not moved from 19/25 and the\nwitness `(8/25, 11/25)` lies outside all three) and `EXTREMAL-CEILING` (a uniform saving `gamma`\nclears the corner exactly at `gamma = 2`; the priced target at one box removes about **3 percent** of\nthe leftover area). `EXTREMAL-CEILING` is why the graph does not route `MARGIN-SHRINK` through\n`BOX-CONTROL` alone: closing the box, however hard, is necessary and not sufficient.\n\n## 6. The lethal set, and how to read it\n\nThree answers, all generated, and they say different things:\n\n1. **Globally fatal single failures: `none`.** No node lies on all four consumer routes, so no\n   single result can close the programme *or* kill it. That is a structural fact about the assembly,\n   not a comfort: it is also why closing one branch is not progress toward another.\n2. **Irreplaceable inside each branch.** `fatal(ZONE-WEAK) = `GAP-INF``: the whole zone branch reduces to\n   one statement, `GAP-INF`, where the distance is `4.2665` against `2` and the corpus's own analysis\n   is that a perfect distribution oracle moves the exponent by nothing. `fatal(MARGIN-SHRINK) =\n   `BOX-CONTROL`, `COMPLEMENT`, `REDUCTION``: the reduction, the box and the global complement. `CENTERED-MARGIN` and `B-MARGIN` have no\n   irreplaceable part above them because each *is* one statement.\n3. **What each branch costs in named obligations** (table in section 4). The count is a structural\n   measure and **not a difficulty**: `B-MARGIN` and `CENTERED-MARGIN` are one statement each, and\n   both are exactly where the corpus records no unconditional progress of any size\n   (`B` is exact and unestimated; the finite census to `2^38` cannot see `D_y` because the comparison\n   is dominated by the classical term's slow convergence).\n\n## 7. Integrity: how the graph is checked\n\nFour gates, all runnable, all green in this window:\n\n* **Source-token gate.** Every node declares the local document or return it is drawn from and the\n  literal tokens that must appear in it; the tool checks all **73 tokens across 59\n  nodes** against the files (fail on a single miss). The fetched documents are recorded with their\n  sha256 in `evidence/docs-manifest.jsonl` — including `README.md`\n  `d17035952cefb1a1`, `research/ZONE-POSTULATE.md` `82ec04b1c1bc4550`, `research/TWIN-REDUCTION.md`\n  `acedcff45edc9de9`, `research/RESEARCH-HANDOFF.md` `b3f33f44c99470ca`,\n  `research/structured-dispersion-estimate.md` `10da6db188a50eb5` and\n  `research/fixed-endpoint-discrepancy.md` `21dce4f3b3bc36d3`.\n* **Graph invariants.** Unique ids, resolvable references, no cycle through the route edges, tags\n  inside the vocabulary, every node reachable from the root, and — the gate that catches the\n  modelling error this graph is most prone to — **the root must not be derivable from the corpus's\n  current rungs**. It is not.\n* **The closed-attack gate.** The self-test asserts of every refuted node that its impact is empty and\n  that it is not fatal to any branch. A failed bound that gates something would mean the model had\n  silently promoted it to an obligation.\n* **Determinism.** Every query is re-run and compared.\n\n## 8. Rungs, limits, and what is not claimed\n\n| claim | rung |\n|---|---|\n| the equivalence, the Gap Reformulation and the counting deduction | **derived** (corpus's own, elementary where stated) |\n| the reduction `S = C2 x + E_dagger + O_H(x/log^H x)` | **derived**, adjudicated three times, no defect; constants ineffective |\n| the ceilings, the corner identification, the controlled regions | **derived**, as properties of one argument shape — not impossibility theorems |\n| the four sufficient margins | **open**, by the corpus's own registers |\n| the 16 closed interfaces and attacks | **refuted** at their stated scope |\n| every rung, count and edge in this document | **verified** by the tool's gates, not by hand |\n| any progress toward TPC, any exponent, any probability, any onset | **NOT CLAIMED** |\n\n**Limits.** The graph is only as good as its rungs: they are transcribed from the served documents and\nfrom this run's returns, and a rung that is wrong upstream makes the closure set wrong downstream —\nwhich is why every node carries its tokens. The graph does not model the *strength* of an obligation\n(only that it is open), does not model coefficient sizes or error budgets, and does not attempt to\ndecide whether any particular route is reachable. `CORNER` is documented but deliberately unusable.\nThe two-target distinction of section 2 is the corpus's own warning made structural; if a future\nreader finds that the two arrangements are in fact interchangeable, that node pair must be merged.\n\n**Next step, and it is the one the assembly names.** The graph's own cheapest closures point at the\nfour consumers, and the frontier at ten open obligations; the instrument that would move the frontier\nis the one the corpus has been asking for all along — a new arithmetic estimate with its full payoff\n— or, for the one leaf where the requirement is only logarithmic, a published statement covering\n`n^(o(1))..n^0.21` at composite modulus. 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Find something new: a route, connection, counterexample, or testable hypothesis. Record what you tried and learned, including negative findings.\n\n**New statistic with a falsifier.** Design one finite statistic a run could actually decide something about, where the retained censuses could not: the decision it informs, a pre-registered falsifier written before any run, a matched control (random-sign, permutation or independent thinning, as the repo uses), and the scale at which the effect would be visible if present. Search online for existing statistics, datasets and computed ranges first. Reuse and cite any numbers already published. 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