Live figures
Hypnos is a research harness, a program whose loop has run since August 11, 2026, with pauses between runs: three small open AI models on a home rack read a growing notebook of mathematics, one or two entries at a time, and write one-line candidate ideas. Claude Opus 5, a frontier model made by Anthropic and the harness's judge, reads a sample of those lines and writes the few worth a closer look into the notebook as new entries. In sessions that the owner, the person who runs Hypnos, starts by hand, frontier models derive and check new work; this layer is built to shape what the sessions read, and whether it saves them any effort is untested.
The list holds the most recent kept entries this site has received, up to 50, newest first. Their titles and summaries are written for this site by Gemma 4 26B, one of the three small models, for readers who are not mathematicians, so they leave the mathematical objects out. They are shown as written.
Under each title is the name the judge gave the entry, its identifier inside the notebook. The judge's description of the entry and the small model's line it came from are private, like the rest of the notebook. For the latest entry kept from a pair of entries, a page of its own names the two entries it was written from.
A kept entry is the judge's write-up of a small model's line it found worth a closer look: in its own words, at a median of eleven times the line's length, filed in the notebook with links to the entries the line was about, where it can be drawn into later pairs. It is not a checked result: every kept entry enters at the lowest of four trust levels, and nothing in the running harness raises it.
Of the four mathematics manuscripts frontier models wrote in those sessions, only the unfolded-zeros paper (Claude Fable 5.1, Anthropic) follows a chain of entries that begins with a small model's line kept this way, a recall of Kadec's 1/4 theorem on August 12, 2026, and ends in a theorem the paper says answers the question the notebook posed; where each paper's question came from is on the explanation page.
Each entry shows the date it was kept and its kind, the type the judge gave it.
The latest figures reached this site on ; new figures arrive about every ten minutes. At that update the judge had kept 863 entries in all since August 11, 2026.
50 kept entries shown
If a mathematical operator mirrors itself in a specific way, its energy levels must always come in pairs. This idea asks if such a symmetry could force the zeros of certain functions to always appear in even counts.
The judge's name for the entry: kramers-parity-closes-the-minus-arm-given-multiplicity-faith
When dealing with certain odd-numbered grids, can we always find a minimum distance of one between a specific mathematical object and its target? This gap might act as a buffer to distinguish true patterns from mere noise.
The judge's name for the entry: odd-n-minus-arm-margin-is-one
Does removing the influence of the prime number two prevent a specific mathematical pattern from shifting when we blur the data? It asks if this single prime acts as a stubborn anchor that keeps a certain signature stable despite smoothing.
The judge's name for the entry: heat-flow-signature-invariance-after-removing-p2
In a specific mathematical setting, does a collection of functions eventually stop adding new information, or does it keep expanding? This asks if a certain way of measuring gaps between functions hits a hard ceiling due to its unique algebraic structure.
The judge's name for the entry: function-field-nb-gram-rank-saturation
Does a hidden starting point in how we align data points change the final score? If the way we shift a sequence is unrecorded, comparing the accuracy of two different models might be like comparing two rulers with different zero marks.
The judge's name for the entry: pair-correlation-fitness-inherits-the-unfolding-fork
Does an optimization process stop improving because it has already hit a structural limit? This idea asks if adding more complexity to the mathematical model fails to change the result because the solution is already trapped within a fixed, unchanging shape.
The judge's name for the entry: dnn-plateau-as-gram-rank-saturation
Can the way a physical system's properties flip when mirrored depend entirely on whether the strip's width is even or odd? This idea asks if a specific mathematical pattern emerges from how individual components are combined.
The judge's name for the entry: spin-flip-tensor-power-as-kramers-witness
Does the mathematical behavior of a thin strip of magnetic atoms depend on whether its width is an even or odd number? Specifically, does the strip's internal symmetry flip between two distinct types based on this simple parity?
The judge's name for the entry: ising-antiunitary-sign-follows-strip-parity
Does the width of a narrow magnetic strip dictate whether a specific type of symmetry - a mirror-like flip that reverses magnetic spins - can exist? The idea asks if this mathematical property shifts between being possible or impossible depending on whether the strip's width is even or odd.
The judge's name for the entry: strip-kramers-arm-is-spin-flip-parity-selective
Can we distinguish between a growing trend and a fixed offset when measuring the fluctuations of the Riemann zeta function? The idea asks if the data is too limited to tell if the pattern is truly growing or just shifted.
The judge's name for the entry: selberg-offset-as-determinacy-witness
When a small bump on a surface shrinks toward an edge, how fast does the system's fundamental vibration frequency change? The idea asks if this speed depends only on the bump's shape and the edge's properties, regardless of the bump's initial size.
The judge's name for the entry: splitting-exponent-set-by-bump-geometry-not-match-count
Does a specific way of classifying quantum systems become meaningless far away from their center? If certain mathematical laws coincide in the bulk, then a tool designed to tell them apart might be looking at a blank screen.
The judge's name for the entry: az-class-bulk-laws-may-coincide-making-the-screen-vacuous
When tracking the lowest value of a shifting system, does the path form a smooth valley or a sharp, pointed cusp? If it is a cusp, the typical way of measuring its curvature might just be a mathematical illusion.
The judge's name for the entry: lambda-min-cusp-breaks-the-curvature-sign-reading
odd-dim-defect-floor-two-sin-pi-over-2nNo summary is shown for this entry.
No title from the small model is shown; the heading is the judge's name for the entry.
Could a specific symmetry, involving both flipping all magnetic spins and complex conjugation, explain why certain mathematical models produce pairs of complex numbers instead of simple real values?
The judge's name for the entry: ising-strip-spin-flip-conjugation-is-the-antilinear-commutan
Does changing a single number in a mathematical recipe affect the density of its resulting pattern in the same way that it shifts the pattern's underlying structure?
The judge's name for the entry: local-factor-influence-ranking-tracks-sampling-density-respo
Does a specific number emerge from the underlying structure of prime numbers, or is it just a fixed byproduct of the mathematical tools used to measure them?
The judge's name for the entry: cstar1-plateau-input-side-decoy-beurling-atomic
Does a specialized instrument actually detect individual mathematical signatures, or is it merely seeing a single combined signal? The question asks if the device can tell different components apart when they are no longer identical.
The judge's name for the entry: class-number-one-voids-the-epstein-separation-basis
Does the number two drive the most influence in certain number patterns, or does its influence only appear when we add up all its powers? The idea asks if the most important contribution comes from a single step or a cumulative sum.
The judge's name for the entry: k-one-place-weight-peaks-at-p-seven
In a one-dimensional chain of magnetic atoms, does a specific field strength cause the two most influential energy states to become perfectly balanced in magnitude, effectively erasing the system's primary preference?
The judge's name for the entry: w-one-modulus-gap-closes-at-theta-pi-half
Does a mathematical pattern appear to vanish simply because the digital grid aligns perfectly with the wave's rhythm? This asks if a perceived zero result is a genuine property or just a trick of the grid's geometry.
The judge's name for the entry: commensurate-aperture-zeroes-pw-commutator-residual
If particles are held in place by a force, does checking the local curvature of their energy landscape actually prove they are at a stable resting point, or could they still be sliding toward a different position?
The judge's name for the entry: log-gas-probe-needs-stationarity-not-psd
At a specific tipping point in a system of generalized prime numbers, can one tool detect a breakdown in symmetry while another tool still sees everything as perfectly balanced?
The judge's name for the entry: beurling-instrument-discordance-at-the-three-halves-threshol
Can a calculation using smooth curves match a calculation using discrete prime numbers? This idea asks if a specific mathematical component can be measured through two different lenses without losing accuracy to the infinite tail of the calculation.
The judge's name for the entry: arch-term-x-space-versus-r-space-quadrature
Does a certain numerical value stay frozen because it is trapped between specific milestones set by prime numbers, much like a hiker stuck on a flat plateau between two mountain peaks?
The judge's name for the entry: prime-log-admission-thresholds-pin-the-certificate-plateau
Can we measure the size difference between two types of symmetry? The calculation fails for odd-numbered dimensions because one type of symmetry physically cannot exist there, making the comparison impossible.
The judge's name for the entry: antiunitary-price-undefined-at-odd-n
When simplifying complex physical models, does a specific mathematical shortcut only work if the underlying interaction matrix can be inverted? It asks if a rare exception exists where the shortcut works even when the required symmetry is broken.
The judge's name for the entry: generator-route-equivalence-needs-r-invertible
When a mathematical landscape changes, does its lowest point curve smoothly like a bowl, or does it form a sharp, pointed kink where two different paths meet?
The judge's name for the entry: lambda-min-kink-versus-curvature-at-self-dual-point
Could the way magnetic spins fluctuate in a narrow strip be described by a simple, fixed set of values that never changes, regardless of how strongly the magnets pull on each other?
The judge's name for the entry: ising-strip-generator-is-conjugated-spin-sum
Does a specific mathematical constraint, which requires all values to be non-negative, become irrelevant at a certain complexity level? If these constraints are inactive, the solution behaves as if the non-negativity requirement never existed.
The judge's name for the entry: dnn-nonnegativity-duals-inactive-at-rung-16
A mathematical optimization process keeps hitting the same value regardless of its complexity. Does this constant result depend entirely on the individual data points on the diagonal, or do the connections between them actually matter?
The judge's name for the entry: diagonal-tensor-ablation-of-dnn-plateau
counting-consistency-vacuous-when-counting-function-is-inputNo summary is shown for this entry.
No title from the small model is shown; the heading is the judge's name for the entry.
When calculating properties of a physical model, different mathematical paths might lead to different symmetry results. Does the choice of calculation route create a false signature that isn't actually a fundamental property of the system itself?
The judge's name for the entry: antiunitary-screen-splits-along-generator-route
A specific way of building symmetry-based transformations might only ever see one side of a coin. Can a mathematical tool designed to reflect objects ever reach the hidden, antisymmetric side that behaves like a negative mirror?
The judge's name for the entry: eigenbasis-conjugation-screen-cannot-reach-the-minus-arm
Could two mathematical rules that usually agree only match up at a single, accidental moment? This asks if a specific setup allows two different ways of measuring change to coincide at one special angle even when they are fundamentally different everywhere else.
The judge's name for the entry: generator-route-agreement-pointwise-vs-identical
If a mathematical object is built from a fixed core and a shifting shape, does that rigid structure prevent the two ways of measuring its growth from ever matching?
The judge's name for the entry: strip-factorization-decides-generator-route
If a mathematical system possesses a specific type of internal mirror symmetry, does that symmetry carry over to the physical world it describes, forcing every energy level to be doubled?
The judge's name for the entry: gns-reconstruction-of-a-minus-arm-witness
aperture-price-hides-the-pinned-feature-scaleNo summary is shown for this entry.
No title from the small model is shown; the heading is the judge's name for the entry.
Does a specific mathematical tool provide a genuine fingerprint of an object, or is it merely repeating a fixed pattern? The question asks if a constant reading is a true property of the system or just a glitch in the measuring device.
The judge's name for the entry: beurling-negative-control-for-certificate-flatness
When certain number patterns become more complex, their associated functions might lose the perfect symmetry that keeps their zeros on a single line, potentially creating stray points that drift away from the center.
The judge's name for the entry: epstein-class-number-signal-is-off-line-zeros
When comparing the fluctuations of prime numbers to random matrix models, the math requires matching a continuous value to a discrete set of objects. Does the comparison use a rounded integer, or a smooth mathematical formula that accepts any number?
The judge's name for the entry: cue-comparator-noninteger-matched-dimension
If a specific mathematical operator governs a magnetic system, its inherent symmetry might force its energy levels to appear in identical pairs, potentially meaning the system's characteristic zeros must always occur with even multiplicity.
The judge's name for the entry: kramers-doubling-screens-the-lee-yang-carrier
When a small change in a physical system's shape is made, does the resulting change in its vibration frequency follow that same shrinking pattern, or is the connection driven by something deeper than just the size of the change?
The judge's name for the entry: m-function-exhibit-decay-tracks-input-base
In a grid of magnetic spins with an odd width, does a specific mathematical symmetry force the system's energy states to perfectly balance each other out, causing certain sums of these states to vanish?
The judge's name for the entry: odd-width-strip-odd-traces-vanish
Can a specific mathematical transformation be split into a simple rotation and a fixed scaling factor that does not change as the rotation angle shifts?
The judge's name for the entry: strip-factorization-is-the-polar-decomposition
Does the way large numbers are composed of small prime factors carry enough information to reveal the truth about the Riemann Hypothesis, the famous unsolved puzzle regarding the distribution of prime numbers?
The judge's name for the entry: dickman-discrepancy-is-an-rh-sensitive-depth-functional
When a mathematical landscape shifts, does its lowest point curve smoothly like a bowl or form a sharp, jagged point like a mountain peak? The answer depends on whether the starting state is unique or shared by multiple paths.
The judge's name for the entry: weil-lambda-min-may-kink-at-t-zero
Does changing the starting point of a sequence of points change whether they form a stable mathematical basis? The idea asks if certain mathematical tests fail simply because the points were shifted, rather than because the underlying structure changed.
The judge's name for the entry: unfolding-offset-shift-is-a-unitary-modulation
Can the locations where a specific mathematical curve loses its smoothness reveal the exact positions of prime numbers and their powers? The idea asks if these prime-based jumps are the only points where the curve's behavior changes abruptly.
The judge's name for the entry: weil-band-nonsmoothness-only-at-prime-logs
Does a statistical similarity between two different physical models arise because the models are actually identical, or is it just a coincidence of the specific data being viewed? This ambiguity makes it impossible to tell which model is truly at work.
The judge's name for the entry: az-class-c-d-bulk-law-degeneracy-check
No kept entry matches that search and kind.