Code: every program on the site

130 programs, 4 of them tools.

• audit.py — one published deletion audit's estimator read root by root against a target known exactly: where its answer comes from, when it lands on the wrong side of one half, and what a statement built on its resamples can and cannot say when the target is not identified. Cited on RULER.
• band.py — at a fixed rank, which depths of flattening make the least-height polynomial beat every product of factors x^d - 1, and the single product that takes over past them. Cited on FLATTEN.
• binding.py — what the ring's multiplication keeps of a code, what its addition breaks, and where a superposition's count has to live. Cited on BINDING.
• bonacci.py — which scalings and floor divisions extend continuously to the completion of the trailing d-bonacci numeration. Cited on READING.
• borrow.py — which moves that lower a depth keep a program's halting decidable: a move that clears a place whole, or one that divides once. Cited on MACHINE.
• bridges.py — where growth meets open number theory: the primes a world grown along a fixed alphabet ever opens, the phoenix that lives on the least move, the atoms of the odd part of lambda and the least odd number that is never one, and the rudder that steers the lock. Cited on BRIDGES, GROWTH.
• budget.py — what omitting a place frees at a global constraint. Cited on BUDGET.
• carrier.py — what a place over another prime does to a place's door: how deep a carrier's jump of the count reaches down a ladder, what it moves the door to there, and the ramified quadratic place over 2 read through it, whose width is a function of delta mod 8. Cited on CLOCK.
• cascade.py — whether the greedy walk over a number ring must lock: the escape as a conjunction of carrier ladders, the budget that pins each ladder's ceiling, where the ladders die, and why a small-prime sieve's expected count does not see the level they die at. Cited on CASCADE, GROWTH.
• ceiling.py — evaluations whose Bayes-optimal score is derived, not estimated: an integer read through a proper set of its residue channels and asked one question about its size or its order. Cited on RULER.
• cell_exact.py — LB_s >= G2(sort P) at m = 2 and m = 3, at every real partition, by an exact case split. Cited on SIZE.
• census.py — the admission census: which items a greedy walk strands, read off the menu's prices with no walk run. Cited on CLOCK.
• cgreedy.py — a policy between greed and freedom over Z: the c-greedy walk, which takes any lambda-raising multiplier m <= c m_0, m_0 the least one, and the dam that holds its support finite at every c. Cited on IMAGE.
• chains.py — what a chain of on-line units pays: the inset law, the threshold-miss law, the matching law, and the led stream spent in one hop. Cited on REDUNDANT.
• checksum.py — the Internet checksum read one prime at a time. Cited on COORDINATES.
• clock.py — what one place charges a growth walk: the tick ladder of a place of a Dedekind ring with finite residue field, read as the orbit of one map, with one overshoot and one number beside it. Cited on CLOCK.
• clocks.py — the clock machine over a growing supply of windows: one zero-test per register runs Minsky's machine on every unbounded supply with no saved window, one zero-test over every register leaves a finite automaton reading a word the supply writes, and a trip that tells coprimality from old windows waits out their lcm. Cited on SUPPLY.
• cofactor.py — at an odd prime, the departure of a field holding zeta_(p^N) is p^(N-1) times the level of that root's cofactor, capped at the bend, and it can sit below p^M. Cited on OBSERVATORY.
• collide.py — when two pairs of menus weigh every temperature alike, and what a menu must carry for the product to factor two ways. Cited on COLLIDE.
• collision.py — a substrate of primes grown on the collisions a labelled set of integers presents, read off the primorial tower's own chain of unresolved differences. Cited on LEARNER.
• column.py — the closed form of a place's lambda column, where it holds, what a number ring's norm does not fix of it, and which index its price is. Cited on CLOCK.
• comparators.py — what a comparator costs a signed-digit reader: the maps whose images are tiles, the absolute value's digit-set clause, and max and min inside a unit and on its output. Cited on REDUNDANT.
• comparison.py — what a multiply-only machine buys when its tests compare depths: one linear form decides, two forms can run Minsky (differences at three places), and at exactly two places the ratios 1:1 and alpha:beta run FRACTRAN. Cited on MACHINE.
• conductor.py — what the conductor of a complex cubic field hands its quadratic resolvent, read as a module under conjugation, and what that module decides about the triples of triple.py. Cited on TRIPLE.
• coordinates.py — which coordinate system on the integers reads which operation, and what kind of wall each one pays. Cited on COORDINATES.
• coverage_cap.py — how many points of a degree triangle one residue class can hold. Cited on TORSION.
• crt.py — residue arithmetic on Z/N for N a product of coprime prime powers, with the primorial rungs Z/p_k# as the canonical family. Cited on TOWER. A tool.
• cubic.py — complex cubic fields read through binary cubic forms: the ring of integers, the prime places, a class group checked against the analytic class number formula, and the class of a degree-1 place. Cited on TRIPLE. A tool.
• cubrace.py — the race between the F_2 place and the column of norm 3 read at a cubic field, where cubtop.py's bound cannot decide it. Cited on THERMAL.
• cubtop.py — does the place with residue field F_2 top the thermal place spectrum over every cubic field that has one? Cited on THERMAL.
• dam.py — a slack max(ct, t log2(ln t) / 8) is dammed from every seed; the covering's exponent L_J divides 2 lcm(1..J) <= 2 4^(J-1). Cited on IMAGE.
• delays.py — the delay of an on-line unit, read by one entry point: pass a unit's box, as its width rate (the sup of its gradient's L1 norm over the box) and its range, or its pieces, or a chain, at a signed digit system, and read its lead, its delay L* and its lookahead. Cited on REDUNDANT. A tool.
• dial.py — the block clock: how many runaways a greedy walk keeps when items share a notch in blocks, and what decides which blocks run. Cited on CLOCK.
• door.py — the door identity: a number ring's place reads the state through one p-adic valuation, so its block clock ticks in COUNTS, and what that does to the chain inside a block. Cited on CLOCK.
• dual.py — the leading end of base b: what a reader of an integer's sign, exponent and first t digits computes, and how it mirrors the trailing end. Cited on DUAL.
• element.py — where one greedy walk goes when a move must be principal: the ring of a curve over F_2 read as a supply MATRIX over its class group, the one minimal rider every class summons, what the rider does to the chain of clock holders, the limit the walk converges to, and the arithmetic deciding which of its coordinates are unbounded. Cited on ELEMENT, IMAGE.
• element_ring.py — the element world over a number ring: whether the supply matrix still prices every move once degrees become norms, what the ring must hand the walker beyond it, and whether the curve walk's one runaway survives a ring whose ladder does not double. Cited on ELEMENT, IMAGE.
• envelope.py — where the record run's own slack sits, and what every run from the void owes at each prime power. Cited on IMAGE.
• erring_cells.py — the cell tent bound: each cell pair errs at least the larger of its two one-boundary tent integrals, and over nondecreasing widths that bound puts the error at least (1 - o(1))/(2 log m), and the sorted bound that would carry it to every partition, if true, is sharp on a grid; the per-shift bound LB3 holds it where the tents fail. Cited on SIZE.
• erring_label.py — a monotone size label that addition keeps up to an error: the least error at each reach. Cited on SIZE.
• erring_lower.py — the lower side of kappa_m: a width bound under the continuum error, and the exponential widths that meet it up to a constant. Cited on SIZE.
• erring_widths.py — does a width profile growing with position err locally below rounding's quarter? Cited on SIZE.
• erring_zones.py — the continuum error of a cut set, the scaling limits of the growing-width profiles, and the zone construction at reachable m. Cited on SIZE.
• estimators.py — standard Bayes-error estimators scored against an exact Bayes error, on the threshold family of ceiling.py. Cited on RULER.
• faces.py — where on the Newton polytope two factorizations of one menu product part, and what a face reads there. Cited on COLLIDE.
• fates.py — which atoms the marginal optimum hands the empty set: the abandonment condition at equal masses, its failure in both directions off them, the death of every predicate on one atom's own numbers, and the finite key that decides an atom's fate exactly. Cited on SETS.
• fieldtop.py — which place tops the thermal place spectrum over a number field: quadratic fields, the abelian fields K(m, d) inside Q(zeta_m), and the cyclic fields of degree 4 and 8 with one place of residue field F_2. Cited on THERMAL.
• fingerprint.py — one real number reads a residue tuple up to sign. Cited on FINGERPRINT.
• flatten.py — the least height of an integer polynomial forced to vanish to a given order at 1: the exact chart, where products of x^g - 1 attain it and where they do not, and the inverse dial read as the shortest integer-tap filter that kills polynomial signals. Cited on FLATTEN.
• floor.py — the private zone: a floor under every producer of x y feeding z·U, and the threshold-miss pair priced by it. Cited on REDUNDANT.
• floors.py — what each growth fate needs of the ground it grows on: a bare order, a cancellative monoid with a weight, or unique factorization. Cited on THERMAL.
• flush.py — a redundant output alphabet on the trailing Ostrowski numeration: which maps a bottom-up reader then computes, and what reading the integers costs over reading their completion. Cited on FLUSH.
• forecast.py — the straddle-cover reader scored on forecasting its stream: a density forecast collapses to a length loss, a side forecast makes the best reader depend on the stream, and a reader can depart from the stream-free optimum only at a REVERSAL. Cited on LEARNER.
• forget.py — when a state provably no longer holds a datum, how that grade moves when the datum is coarsened, and which forgettings survive the demand that the state keep computing a function. Cited on FORGET.
• free_image.py — the set of limits a growth demand reaches under EVERY policy it admits, over Z and over F_2[x]: five demands, five forms, one chain, and the one image the ring can reach. Cited on IMAGE.
• gaplaw.py — the anchored gap along a geometric walk, in closed form: where the certificate's size profile stops moving, and what the least positive value of the anchored box is from there on. Cited on SETS.
• gates.py — what gates on words decide about a tuple of units, and what the decision costs. Cited on GATES.
• ghosts.py — a seed whose walk picks as many ghosts as a set of witness primes allows: the ghosts up to x are the witnesses' records. Cited on GROWTH.
• growth.py — a modulus grown by the cheapest move a demand admits: the three fates, the wall mortality stops at, the prime the dynamics demand locks onto, and the two facts about -1 that price the prime 2. Cited on CASCADE, GROWTH, IMAGE.
• halfsize.py — how many dimensions a polynomial with n terms can span and still factor. Cited on COLLIDE.
• headroom.py — what a probe learns of a grown state by offering it moves: the headroom xi(M) = W(lambda(M))/M, what a move spends of it and what it opens, the closure underneath, what it costs to tell apart two states the reading merges, and the density of the probe's blind classes. Cited on HEADROOM.
• hulls.py — a producer with a hull per string: does x y feed z·U past the threshold-miss law? Cited on REDUNDANT.
• image.py — the set of limits a greedy growth walk reaches when its ties are all followed: a union of orbits of the colour-preserving permutations, a finite count over an imaginary quadratic ring where the walk locks, the continuum over a curve over F_2 with a rational place besides the one removed (the ideal world at limit.py's corner), and the lock's rider as what erases a choice rather than what adds one. Cited on IMAGE.
• lattice.py — the sum head's tree of hulls on its lattice: does x + y feed z·U past its budget? Cited on REDUNDANT.
• learner.py — a reader of a continued-fraction stream commits intervals of the straddle cover; the intervals holding what it knows have a least member, so the best reader reads nothing from the stream. Cited on LEARNER.
• lid.py — when a greedy walk over a number ring has locked for good: the lid a block's last mover puts on every later price, and the one condition, checkable at a single state, under which it never lifts. Cited on CLOCK, GROWTH.
• limit.py — where one greedy growth walk goes: the pricing schedule a walk over F_2[x] or a curve over F_2 is an instance of, the chain its clock moves form, the one deep coordinate that chain leaves, the support beside it, the ceiling on the deep coordinate's degree, and the rules that can stop the support from widening. Cited on ELEMENT, IMAGE, LIMIT.
• lira.py — a published per-example membership audit scored against the exact posterior: the probability it states converges to its Gaussian limit rather than to the truth, and whether its membership call survives is a side criterion read cell by cell. Cited on RULER.
• logic.py — the logic a squarefree ring's own polynomials carry. Cited on LOGIC.
• lossdensity.py — the density of the cubic fields where the F_2 place loses the top: one number for both signatures, read as a probability under the product of the local splitting laws. Cited on THERMAL.
• machine.py — the growth apparatus read as a machine: a state M, moves that multiply it, and the reads a program may make before it moves. What a program can decide about its own halting depends only on which read it holds. Cited on MACHINE.
• manystream.py — the least lookahead of a smooth map of several signed-digit streams, read against the affine criterion. Cited on REDUNDANT.
• members.py — what the least-height polynomials are made of where products of x^d - 1 lose: the factor they carry that is not cyclotomic, the construction that rebuilds them from a pure product, and whether the inverse dial's break is the same phenomenon. Cited on FLATTEN.
• memory.py — what a grown world can know of its own genesis: the evidence a state, a dated state, a watched path and a probe each carry about the generator that grew it, fate by fate. Cited on MEMORY.
• mixing.py — two factorizations at twelve terms where no block divides a block across, and the lemma that pins them. Cited on COLLIDE.
• module_law.py — what one tick of lambda costs at one place of a ring, and what that price decides about the greedy walk over a number ring. Cited on CASCADE, ELEMENT, GROWTH.
• naming.py — which primes divide the Euler characteristic of a set. Cited on NAMING.
• ostrowski.py — the trailing Ostrowski numeration read as a numeration of the circle, and what that decides for every affine integer map and every floor division, at every irrational alpha. Cited on OSTROWSKI.
• pentanomial.py — five terms: a seed with a factor cyclotomic in a monomial carries it negative, a free seed can be mixed, and a seed free of every negative torsion zero is a question about one variable. Cited on COLLIDE.
• piecewise.py — the least lookahead of a map of one signed-digit stream that is smooth on finitely many pieces: the three clauses that decide it, the segment lemma sorting the slopes a piece may carry, and the radius around a curve within which no table of chords reads lower. Cited on REDUNDANT.
• poles.py — the pole units read by the many-stream theorem, and the law that sets their lookahead: the square root, the reciprocal and the divider, whose lookahead can be negative. Cited on REDUNDANT.
• precision.py — how many digits of the unit u = p/pi^e fix the jump set of a field holding zeta_p, and what the digit cells weigh. Cited on OBSERVATORY.
• principal.py — where a quadratic field's first principal split prime sits, and why principal split primes run short of their share at small p. Cited on PRINCIPAL, TRIPLE.
• quadrinomial.py — a four-term 0/1 polynomial that factors into two non-monomial factors carries a binomial factor, and off a line every factor vanishes on roots of unity. Cited on COLLIDE.
• quadtop.py — the place with residue field F_2 tops the thermal place spectrum over every quadratic field that has one. Cited on THERMAL.
• quarantine.py — which grown worlds can hide their route at every temperature, and what the answer needs of the menus. Cited on COLLIDE, FORGET.
• quarter.py — over 2, the wild departure of a field holding i read off the cofactor of i - 1: the lam <= e at which some field holds i are exactly the even ones below e, and the cofactor readout of the odd primes holds at 2 with lam in place of l. Cited on OBSERVATORY.
• race.py — which place of a number ring's block runs: the race inside a block, the unit its places share, and the void ties a ring's menu stages. Cited on CLOCK, IMAGE.
• rank2.py — the rank-2 flattening lattice: its least height, its second minimum, and the gap between them. Cited on FLATTEN.
• rates.py — what a digit-by-digit reader pays at the continued-fraction numeration, where the scale of a digit varies from stream to stream. Cited on RATES.
• rationed.py — a reader of the straddle cover paid a fixed income of rank per step: the income decides how deep it reads, and the policy decides only which of the incomparable members at that depth it holds. Cited on LEARNER.
• reading.py — which maps a digit-by-digit reader computes at bounded lookahead, what the numeration's tiles charge for it, and which place pays for a wall. Cited on DUAL, READING.
• readout.py — what a similarity lets a reader read exactly, and why the prime a collision grower takes is the tower's agreement plus one. Cited on LEARNER.
• realrace.py — cubrace.py's race read at the totally real cubic fields: whether the F_2 place loses the top over one with d_K <= 3000, and the least where it does. Cited on THERMAL.
• redundant.py — what a signed-digit reader of integers computes at bounded lookahead, and exactly how much lookahead it needs. Cited on REDUNDANT.
• relative.py — the jump set read off the cofactor of the root of unity, coefficient by coefficient: Pagano's relative reading, and the points past it. Cited on OBSERVATORY.
• rider.py — the lid when every move must be principal: what a greedy walk over a number ring pays once it has locked, when each move buys a core together with the minimal rider that makes it an element. Cited on ELEMENT.
• rns_compare.py — a published residue comparison method, implemented from its pseudocode and priced against the size wall. Cited on SIZE.
• rooted.py — whether a seed's negative factor vanishes at a point of roots of unity. Cited on COLLIDE.
• rung.py — the weight of every point of a field's jump set but the first is the highest landing of one class of units: the jump set is the staircase of the class maxima. Cited on OBSERVATORY.
• seat.py — where a complex cubic field's degree-1 places sit against the squares of its class group: the two fibers of degree-1 places, the prime-power term each one carries, and the least partially split place. Cited on TRIPLE.
• selfreport.py — what a deletion auditor can say about the stability of their own answer without the truth, and the proof that no such statement is right at every size. Cited on RULER.
• sensor.py — what element-coprimality reads of an imaginary quadratic ring: the class sequence of the gcd, and nothing finer. Cited on ELEMENT.
• sets.py — set-valued prediction scored against its exact optimum: what coverage can and cannot rank, the certificate that brackets the marginal optimum, when that certificate is the optimum, and an exact solver for the cells no enumeration reaches. Cited on RULER, SETS.
• shifts.py — a digit shift of the trailing Ostrowski numeration read as a change of numeration, and the one criterion that decides where every map linear in the digits reads. Cited on SHIFTS.
• shortfall.py — where the trivial class's shortfall at degree 3 lives: the principal degree-1 places of a complex cubic field read across cuts, across discriminants, and prime by prime. Cited on TRIPLE.
• sign.py — what the sign of a signed-digit string costs: the least automaton that reads it, why no lookahead short of the whole string decides it, and how comparison and the free comparator read the same boxes. Cited on REDUNDANT.
• size.py — what a residue window cannot read about size, and what the cheapest exact read of size costs. Cited on COORDINATES, SIZE. A tool.
• sizeless.py — growth with size taken out of the cost: what the divisibility order alone can author, and what only the ordering of the integers by size supplies. Cited on GROWTH.
• slack.py — a slack polynomial in the tide escapes the dam, and its square reaches breadth; the tide ceiling tau(P) is at least beta(P). Cited on IMAGE.
• spectrum.py — the critical point of the thermal dynamics column at every finite place: over Z, over F_2[x] and over Z[sqrt(-5)]. Cited on THERMAL.
• sprawl.py — the dynamics demand over F_2[x]: why it never locks, why it opens at most one place of each degree, and the walk from the void in closed form. Cited on GROWTH.
• staircase.py — the jump set is the staircase of the class maxima in every field holding zeta_p, however many p-power roots of unity it holds. Cited on OBSERVATORY.
• standing.py — the standing-move dichotomy: when a greedy walk must lock, what coordinate prices the lock over Z, and how one schema reads the three fates of growth. Cited on GROWTH.
• statements.py — a stated uncertainty read as a law: the sign of what it omits, the two ratios its coverage is a function of, and what an auditor can see of the omission from inside. Cited on RULER.
• stop.py — where a bounded ladder stops a greedy walk, and whether the two numbers a place hands a walk, the sup and the tail, decide it. Cited on CLOCK.
• storey.py — the next storey of the cyclotomic tower over a ramified field, read off the last point of its jump set, and what one radical storey does to the p^m-power defects of zeta_p. Cited on OBSERVATORY.
• supply.py — the element machine over a growing supply of windows: on a bounded supply it is a finite automaton reading its supply, on an unbounded one universal, with base extension or without it; over the supplies that follow a word v over {2, 3} by an unbounded tail opening past 3, base extension hands one program every v, and so decides whether it is a palindrome, which no one bare program does. Cited on SUPPLY.
• swaps.py — how an optimum that abandons an atom turns into one that serves it: the two mass bounds, the level-excess identity, and the exchange every serving optimum is, with the arithmetic that can forbid the simple ones. Cited on SETS.
• tame.py — at an odd prime, where a class of units lands past the bend, read off one coefficient level of the Eisenstein polynomial, and what that makes of a head's width. Cited on CLOCK, OBSERVATORY.
• thermal.py — the greedy growth walks at finite temperature: what the three fates keep when the least move is softened into a Boltzmann choice, over Z and over F_2[x]. Cited on THERMAL.
• torsion.py — which torsion a plane curve over F_p holds, counted by its monomials and by its degree. Cited on TORSION.
• tower_growth.py — how lambda grows along the primorial rungs: the density of transparent rungs, the ledger of lambda's jumps, and the serial law that each jump raises one base. Cited on TOWER.
• tower_rungs.py — the primorial rungs one by one: the table, the transparency criterion, the fate rule, the birthday formula, the residue code's distance, the Hamming spectrum, the escape law and the unitary spectrum. Cited on TOWER.
• track.py — does a run escape under the least slack the dam allows? Cited on IMAGE.
• triangle.py — the digits of an Eisenstein polynomial's coefficients and the digits of the unit p/pi^e: a unitriangular map, level by level, at every prime, and the designer that runs it backwards. Cited on OBSERVATORY.
• triple.py — what a cubic field's split primes carry: the triple of classes over a totally split prime, the subgroup those triples fill, and the class of the one degree-1 place over a partially split prime. Cited on PRINCIPAL, TRIPLE.
• weld.py — the second point of a field's jump set, read off the digits: Pagano's jump set and the landing readouts are one invariant. Cited on CLOCK, OBSERVATORY.
• wild.py — at p = 2, where a class of units lands past the bend: the tame formula at every class but the top one, and the top class, whose least landing is a head's width, read off the departure of the Eisenstein polynomial from one fixed design. Cited on CLOCK, OBSERVATORY.
• winner.py — which places a greedy walk from the void seats, read off its first winner: is the winner-kind trichotomy the winner's lone path, and is the catch of a ramified place a question of characteristic? Cited on CLOCK.