AI reach-scans
A reasoning model can reach a state where the right answer remains true, but sampled continuations from what it has already written stop reaching that answer. ReachScan freezes the exact prefix, generates fresh continuations, and measures where those continuations land.
Qwen2.5-Math-7B-Instruct · floor-sum problem family · paper and evidence archive v1.1-RC18 · published July 2026. Results are empirical and depend on the declared model, prefix, sampler, budget, extraction rule, validity checks, and target.
Watch the idea: when does measured access to an answer collapse?
A 9-minute visual explanation of ReachScan: freeze a reasoning trace, sample continuations, and watch when observed target reach falls below the declared threshold.
The film is an introduction. The paper and evidence archive define the model, sampler, budget, target, controls, and limits behind the measurement.
What the study measured, step by step.
The study first measures how the answer distribution changes along one trace. It then compares correct and wrong source traces, repeats the comparison under a separately frozen test, locates the change in token coordinates, and tests whether a small correction can reopen access to the target. D9 and D7 below are the archived names of two floor-sum evaluation contracts; D7 was selected for the prospective replication.
Published records and their versions
The reusable measurement core is ReachabilityLabs/ReachScan, archived under software concept DOI 10.5281/zenodo.20808922 with software v0.3.5 at 10.5281/zenodo.20837723. The v1.1-RC18 core article uses concept DOI 10.5281/zenodo.20872622 and version DOI 10.5281/zenodo.21249688. The v1.1-RC18 evidence archive uses concept DOI 10.5281/zenodo.20872304 and version DOI 10.5281/zenodo.21249695.
The Full Technical Report v0.14.0 is published at 10.5281/zenodo.21249725 (July 9, 2026; 86 pages). It supplements the RC18 publication family; it does not inherit the article's version number.
One trace: how the answer field changes
A prompt-root and committed-trace scan shows upstream bias toward a target-excluding arithmetic family. Target-compatible mass drains before a particular wrong atom dominates.
Compare correct and wrong source traces
Correct-source and wrong-source prefixes overlap at mid-depth, then separate late. On D9, the deepest-cut correct-minus-wrong reach gap is +0.732, with disjoint-seed reconfirmation.
Repeat the comparison under a frozen second test
The same-family result was replicated under the archived D7 contract: late-band separation is +0.802 with a 95% trace-bootstrap interval of [+0.695, +0.894].
Token localization
Eighteen wrong-source traces are localized in token coordinates. The median onset bracket is 4.5 tokens, and the wrong answer is emitted a median 170 tokens after observed target reach crosses below the declared dead threshold.
Reach-entropy morphology
Low target reach is not one state. Most localized wrong traces shatter into diffuse wrong mass; a smaller number capture onto a concentrated wrong atom.
Controlled reopening
In five localized traces, a corrective splice reopens exact-target reach in four. Matched and scrambled controls generally do not, and replaying the original downstream path re-closes all five.
Sampler sensitivity
Archived ablations test how the measured field changes under declared sampler changes. These are instrument-sensitivity results, not evidence that the field is sampler-independent.
Scoped cross-model regimes
The Full Technical Report records bounded cross-model observations on archived floor-sum contracts. They narrow the portability question; they do not establish general cross-model portability.
Possible is not reachable.
“All the possibles are not compatible together in one and the same world-sequence.”
Leibniz, Theodicy §201
Leibniz drew a distinction we have mostly lost: a thing can be possible on its own yet not compossible, not able to coexist with what has already been settled. Each possibility can make sense in isolation; the question is which ones can still hold together from where a process now stands.
This work moves that distinction out of metaphysics and into a running computation. When a model reasons toward an answer, the correct answer never stops existing; it remains a valid solution throughout. What changes is whether it remains reachable from the path the model has committed to.
Existence holds fixed. Reachability is what collapses. The contribution is to make that collapse observable: locate the point where an answer falls out of reach, watch reasoning continue after the loss, and test whether a corrected commitment can bring the answer back into reach.
What is borrowed, and what is new
Leibniz gives an old name to the relation. ReachScan gives it an instrument: finite rollouts, declared projections, receipts, localization, intervention, and a bounded claim.
Endpoint evaluation collapses a richer object.
A reasoning trace is not only an answer-producing sequence. It is a path of commitments. Each emitted token fixes part of the future: some continuations remain easy, some become narrow, some become budget-censored, and some become systematically wrong.
Standard evaluation usually sees only the endpoint. Process supervision evaluates steps. Self-consistency samples reasoning paths and aggregates answers. Neither, by itself, measures the distribution of futures conditioned on one exact committed state.
The study measures that distribution. Given a committed prefix, a continuation policy, and a resource budget, it repeatedly continues from the prefix and examines where the continuations land. Correct-answer mass is one coordinate of that distribution. It is not the whole object.
The sentence the framework makes pronounceable
Self-consistency calls a state uncertain when the answers vary. This measurement calls it family-locked when the answers vary inside the same wrong family.
Committed prefix, future field, diagnostic projection.
The method has three practical pieces: freeze the exact state, sample what happens next, and decide in advance how those outcomes will be grouped. The grouping rule must be rebuilt for each new task.
Committed prefix
The state a process has already produced. In a reasoning system this is the token sequence written so far. In a solver it is a partial assignment. In a scheduler it is a partial schedule. The surface is different; the conceptual object is the same: an irreversible commitment.
Future field
The distribution of outcomes the system can still produce from that exact committed state under a declared policy and budget. We measure it by sampling many continuations and reading where they land. The field has structure beyond a single most likely answer.
Diagnostic projection
A way of looking at the future field through one labeling rule at a time. Are most futures multiples of 8? Are they all in the same operation family? Do they share a residue the target lacks? Each projection is a different question about the same field.
The intuitive picture: tunnels and buckets.
Imagine the system writing a reasoning trace as opening a tunnel into the space of possible future answers. Once the tunnel is open, all subsequent continuations have to come out somewhere downstream of where the system is now standing. The tunnel can stay wide or narrow sharply. It can point at the right region or at a wrong one.
A diagnostic projection sorts the answers into buckets by some property — like sorting laundry by color. If the target is a blue shirt and the system keeps producing answers from the white-clothes pile, it isn't merely wrong. It's searching in a bucket that doesn't contain the target.
The measurement captures both the shape of the distribution and which outcome class each continuation reaches.
Why this is different from existing approaches
Self-consistency aggregates sampled answers. Process supervision evaluates intermediate steps. Tree of Thoughts explores branches. ReachScan asks a different question: what outcome field remains attached to this exact committed prefix under a declared continuation contract?
What can be reused—and what must change.
The sequence can be reused: freeze a state, sample the futures from it, group the outcomes with a declared rule, and keep the conclusion tied to that setup. The modulo-8 grouping and exact-answer parser belong only to this task. Every new task needs its own outcome rule.
Explore the supporting figures.
The central page keeps the argument in prose: committed state, sampled futures, declared lens, bounded claim. Readers who want the visual aids can open them separately without making the page itself depend on heavyweight embeds.
Figure provenance: Instrument Anatomy is a schematic using illustrative Case A settings (M=64, B=2048). Coarse-to-Fine Collapse and Instrument Readout are legacy 64-rollout Case A supporting views; the RC18 paper, archive, and v0.14.0 report above are the current result surfaces.
Upstream wrongness and staged tightening on an arithmetic reasoning trace.
Case A is the target-532 floor-sum problem. It shows why the full answer field matters: the prompt-root field is already biased toward a target-excluding arithmetic family, commitment depletes target-compatible mass, and the answer field later resolves onto a dominant wrong atom. The interactive views remain available as supporting figures; the page-level frame here carries the full RC18 measurement cycle.
What Case A shows.
At the prompt-only state, 169 of 245 valid numeric continuations lie in the target-excluding family 8ℤ, 45 lie in the target residue class, and one lands exactly on 532. The field is already arithmetically organized against the target before any generated reasoning token has been retained.
Commitment sharpens that structure. Wrong-family mass reaches 0.984 at 18.9% and 1.000 at 27%, while target-fiber mass falls to 0.016 and then zero. Yet the winning wrong atom is not resolved at the same time: 112 dominates the early/middle sweep, while 56 dominates only by 50%.
At 50%, the terminal answer field is nearly a point mass on 56, but surface reasoning remains diverse. The computation has largely converged while prose still varies. Endpoint accuracy and visible reasoning text miss that state-indexed reachability fact.
Case A is therefore a morphology result: target reach drains, wrong-family support closes, and atom-level consolidation follows later. Case B then asks whether correct-source and wrong-source prefixes separate under the same reach-scan logic.
The Case A receipts
169 of 245 prompt-root numeric continuations lie in 8ℤ; 45 of 245 sit in the target residue class; 1 of 256 lands exactly on 532.
Wrong-family mass reaches 0.984 at 18.9% and 1.000 at 27%; target-fiber mass falls to 0.016 and then zero.
251 of 256 answers equal 56 at 50%, while trajectory signatures remain mostly unique. Answer concentration outruns surface-text collapse.
Zero correct or target-compatible continuations appear across 1,280 samples from 50% through 99.9% under the declared instrument.
Two different systems that support the same kind of question.
The SAT calibration measures a partial assignment and asks whether satisfying completions remain reachable from it. The AI study measures a token prefix and asks where sampled continuations land. The objects are not identical, but both are indexed by a committed history, a target, and the futures assessed from the current state.
The substrates differ in one crucial way. SAT has an exact bridge oracle: a solver can certify that no satisfying completion remains from a given prefix. Reasoning systems do not. A model might recover under a larger budget, a different sampler, a different prompt, or a verifier we have not yet attached. The framework adapts honestly.
What the SAT side can call certified non-extendability, the AI side can only call persistence under the declared continuation instrument. The shared grammar does not transfer SAT's proof status to an empirical AI result.
The cross-substrate sentence
A committed process can enter a state whose assessed futures no longer reach, or rarely reach, the target under the declared rules. In SAT, a solver can determine whether a satisfying completion remains. In AI, repeated continuations estimate how much observed outcome mass still reaches the target.
The comparison motivates a common question without asserting a common mechanism.
Behavioral measurement is the point, not a compromise.
White-box interpretability asks what is happening inside the model. ReachScan asks a different question: from this exact recorded prefix, under this policy and budget, where do repeated continuations land? ReachScan v0.3.5 requires token-level access to freeze and continue from that prefix.
The two approaches can cooperate. A reach-scan can show where to look: the transition window, the contrast between states, the field before and after intervention, and the downstream path that closes the target again.
The careful sentence
ReachScan is not a probe of model internals. It is a measurement of prefix-conditioned outcomes under a declared continuation instrument. Closed APIs, tool-using agents, and multi-agent systems require new state adapters and remain future extension targets.
What the published paper measures.
The results come from a sequence of checks: map the answer distribution, compare correct and wrong source traces, locate where they separate, and test whether a targeted edit restores measured access to the target.
Do correct and wrong source traces separate? · measured
On D9, correct-source and wrong-source fields are similar at 50%, then separate late: the correct-minus-wrong gap reaches +0.732 at 94%. A disjoint-seed reconfirmation reproduces the late-band separation.
Does the separation repeat under the frozen D7 test? · measured
The same-family D7 replication is prospectively selected and build-pinned. Its late-band trace-bootstrap estimate is +0.802, with a 95% interval of [+0.695, +0.894] and an adversarial lower bound above +0.74.
Does measured access disappear before the wrong answer appears? · measured
Eighteen D7 wrong-source traces are localized. The median onset bracket is 4.5 tokens, and the wrong answer is emitted a median 170 tokens after observed target reach crosses below the declared dead threshold under the continuation instrument.
Can a targeted edit reopen measured access? · proof of principle
In five localized traces, corrective splice reopens exact-target reach in four. Matched-site and digit-scramble controls generally do not, fresh continuation preserves four through 32 tokens, and the original downstream path re-closes all five.
What the results show—and what remains unanswered.
The paper shows the full sequence on the archived floor-sum tests, and the Full Technical Report adds limited observations from other model settings. It does not yet establish that the method transfers broadly to other models or tasks, works as a deployable monitor, or identifies the internal mechanism.
What the results do—and do not—show.
The conclusions below apply only to the tested models, prompts, samplers, budgets, extraction rules, validity checks, and targets.
State-indexed answer foreclosure under declared contracts
The paper supports finite-budget, model/sampler/budget-indexed claims about prefix-conditioned future fields. A prompt or correct-source prefix can leave the target reachable; a wrong-committed prefix can deplete it; a corrected prefix can reopen it. The technical report also records scoped cross-model regime observations under archived floor-sum contracts.
Portability, mechanism, and deployable monitoring
The work does not establish general cross-model portability, cross-task generality, universal diagnosticity, an internal mechanism account, a deployable monitor, a general causal-intervention law, or indefinite repaired-path stability.
Foreclosure, not mathematical impossibility
The reasoning substrate has no exact oracle analogous to the SAT bridge check. A reasoning-side dead or foreclosed label is an operational claim under a declared model, prefix, sampler, budget, extraction rule, validity gate, and target set. It is not a proof that recovery is impossible.
The vocabulary.
Each term refers to a measurable object. The arithmetic is simple. The contribution is in choosing what to measure.
Committed prefix
The state already produced. In a reasoning trace, the token sequence written so far. The conceptual primitive is irreversible commitment, not the surface form.
Future field
The empirical distribution of outcomes reachable from a committed prefix under a declared policy and budget. The central observable.
Fiber
A bucket of outcomes sharing a hidden label under some projection — for example, all answers with the same residue mod 8. A wrong fiber is one that excludes the target.
Scaffold
The reasoning pattern that produces a particular fiber of answers. In the case study, the scaffold is "eight repeated blocks times a base-block value," which produces multiples of 8.
Residue
The remainder label that determines fiber membership. The target 532 has residue 4 mod 8; the wrong family has residue 0. The framework asks not just whether answers are wrong but whether they share the wrong residue.
Target-excluding fiber
The deepest version of the case-study finding. The system's continuations concentrate in a fiber whose label is incompatible with the target. The system isn't just searching badly. It's searching in the wrong bucket.
One research setting within a broader question.
Reachability Labs studies how actions and commitments change what remains possible. This page examines that question in recorded AI reasoning states. The engineering tools are a separate application whose usefulness must be tested in practice.