Slop Dealer
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Books
Music
Videos
Essays and fiction notes
- 7,648 Cracks in the Coca Codo Sinclair Dam
- A Life Sentence for Zhou Yongkang
- Asteroid Mining Starts With Assay
- Bacteria in the Copper Heap
- Cross-Laminated Timber and CO2-Cured Concrete
- Fine Wine and Shotguns in Stockholm
- Fourteen Grievances and a Submarine Pact
- How ability slots work in Wavefall
- How Cinderwake gets rebuilt
- How people find safe paths in Wavefall
- Ice and Frozen Volatiles in the Moon's Permanently Shadowed Craters
- Law is a weapon in Cinderwake
- Lithium and Uranium from Desalination Plant Brine
- Living signs in Kethan Valley
- Lunar Oxygen in Cryogenic Propellant Depots
- Lunar Regolith as Ore: Mare Ilmenite and Highland Anorthosite
- Lunar Relay and Navigation Satellites: Lunar Pathfinder and Moonlight
- Magic works like weather in The Landing
- Nine Days After the Bund Speech
- Nine Missiles After the Songshan Landing
- Ninety-Nine Years on Hambantota
- One Hour Before the Anniversary
- Polymetallic Nodules on the Deep Seafloor
- Red Health Codes for the Henan Depositors
- Scale Wars essays
- Seismic Surveys of the Deep Continental Crust
- Sintered Regolith Roads and Machines in Lunar Dust
- Six Months Across America in 1988
- Sixty-Two Cases and Four Clean Wins
- Superhot Geothermal Wells at Krafla and Reykjanes, Iceland
- Sydney becomes a LitRPG map
- The Circuit Breaker That Lasted Four Days
- The Emperor Has Some Clothes
- The Girl Found After the Search Stopped
- The Graveyard Reef hides the base
- The Great Hall Declaration of February 25
- The Natural Hydrogen Well at Bourakebougou, Mali
- The Pilot Who Held Up His Email
- The Rose Garden Line and the Bunkers
- The Score Wired Described in October 2018
- The Thursday Fire in Urumqi
- The Village Factories the State Did Not Plan
- The White Sphere Over Myrtle Beach
- Three Hundred Days Inside the Grid
- Twelve Days Out of Libya
- Vertical Farms and the Price of Electricity
- Water Where the Fuel Should Have Been
- Why Cinderwake starts broken
- Why Homebush works as a map
- Why the ship can't solve everything
- Why this site exists
Research overview and programs
- Adders, counters and the heap law
- Cipher S-boxes, χ, and quantum gate counts
- Direct sums, wedges and the p14 frontier
- Exact answers in open problems
- Formal verification and machine-checked proof
- Further results
- Symmetry, state encodings and search gauges
- The full register
- The Papers
- The quadratic hull and its defects
- The Research Institute
- The SHA-256 record and exact synthesis
- What rank-one constraints can express
Research papers
- A census of one-block affine data-split pins for c0c2 hull repair
- A conditional arithmetic total of 17,841 for JSC-11
- A conjectural lower bound for the multiplicative complexity of T2
- A conjectured rank-two bilinear custom gate for the p14 bridge
- A counterexample to the laminar multiplication-tree normal form
- A degree bound for determined coordinates in odd-multiplicity F₂-R1CS systems
- A lower bound for the multiplicative complexity of the AES S-box
- A lower bound for the multiplicative complexity of χₙ⁻¹
- A lower bound on chained products for the period-two p14 target
- A lower bound on multiplicative complexity of 2x2 matrix multiplication over F2
- A lower bound on the Toffoli count of exact NCT networks implementing χ₅
- A minimal three-row quadratic constraint system for the inverse-or-default gadget
- A multiplicative complexity lower bound for 28 q-rank-6 edges
- A polar rank 8 separator in the JSC-12 K1x even dual coset
- A profile for quadratic pinning and defect structure
- A projected full-heap construction for truncated addition
- A soundness condition for subset-UNSAT certificates under symmetry breaking
- A strict flag characterization of rank-tight acyclic full-domain XAGs
- A structural characterization of the c0c2 quadratic defect
- A twelve-wedge prefix obstruction for the period-two carry law in p14 circuits
- A wedge-span obstruction for the exact Cartesian period-two carry law
- Affine equivalence classes of minimum-rank eight carry-state encodings
- Affine rank of product-output functions and fixed-XOR optimization in the leader
- An eight-product acyclic XAG for the low four bits of x₀+x₁+x₂+x₃
- An eight-product circuit for the low four bits of four four-bit numbers
- An exact conservation law for gauges in GF(2) forest systems
- An impossibility result for affine third factors of the named JSC-12 witness
- An impossibility result for two-witness AND4 in the affine-C model
- An impossibility theorem for deterministic state-only lifts of the c0c2 quadratic hull
- An impossibility theorem for four-input AND in two-witness relational R1CS
- An impossibility theorem for pinning the three-input AND under quadratic systems
- An impossibility theorem for the normalized two-witness selector for AND₄
- An impossibility theorem for the χ₀₁ catalyst and the full-domain p7 tile
- An upper bound on the multiplicative complexity of a three-column interior adder tile
- An upper bound on the multiplicative complexity of the natural (S,S+R) component
- Automorphism group structure of 7-universal tournaments on 13 vertices
- Basis-free lower bound on the multiplicative complexity of GF(2^k) multiplication
- BLAKE3 and ARX redeployment limits from banked addition assets
- Bounds and search limits on the constant-weight code size A(13,4,5)
- Bounds on strict width-nine complexity E_9
- Bounds on the multiplicative complexity of multi-operand addition
- Bounds on the multiplicative complexity of the injected-carry family
- Bounds on the strict width-nine cost E_9
- Classification of One-Word XOR-Mask Transports for Four-Word Addition
- Classification of relations implemented by single-row R1CS over F_p
- Classification of the identity-C fixed-point consumer on toy Boolean graphs
- Closure of all 68 p7-eligible directed edges under the rank-tight affine-code model
- Closure of flat Joint Semantic-Carry systems at every row budget
- Closure of redundant-carry seam route for natural prefixes
- Closure of the maximal standalone-wedge family for the period-two carry law
- Closure of the ordered acyclic A*B=C catalyst class at p6
- Complete witness-width classification of Boolean functions on F₂⁴
- Conditional arithmetic for nonlinear Maj gauge closure
- Contraction censuses and lifting obstructions for CW(112,36)
- Copy-locality of target-bearing products at the rank-tight boundary over GF(2)
- Correcting two truncated-addition cells
- Counterexamples to four former addition laws
- Decomposability of the extremal top form in acyclic XOR–AND circuits
- Deficit law lower bound for all-quadratic spaces
- Degree distribution of the two-column C7 transducer nonlinear quotient
- Direct-sum additivity barrier for extension-field batching over F₂ᵐ
- Direct-sum theorems and lower bounds for unrestricted multiplicative complexity
- Discard-tax principle for heap optimality with discarded top digits
- Domination of tensor slice rank floors for systems of quadratic forms
- Elimination of stationary additive carry/raw phases with terminal syndrome-only checks
- Empirical limits of single-counterexample CEGIS exact synthesis
- Equality of multiplicative and quadratic complexity for 3-spaces on at most 5 variables
- Estimated SHA-256 R1CS constraint reduction via XOR3 and MAJ3 gadgets
- Exact additivity of two-copy block sharing in leader pairs
- Exact B2 circuit size and machine-checkable certificate for 5-input MOD3,1
- Exact B2 circuit size of MOD3 on 6 inputs and solver scaling wall
- Exact catalyst dimension in a rank-tight XAG
- Exact characterization of additive quadruples destroyed by one AND gate
- Exact complexity of the canonical heap-prefix class
- Exact constant-weight code bound A(11,4,5) = 66 via verified SAT
- Exact costs of strict syntactic equivariance for widths 3, 5, and 7
- Exact fibre cardinality of the two-round SHA-256 edge-relaxed relation
- Exact finite-horizon minimisation of natural SHA carry states
- Exact gate-state duality and 1-Lipschitz potential bounds for multiplicative complexity
- Exact GL(2,2) symmetry quotient for catalyst parameterization
- Exact joint multiplicative complexity of chi_n and its square
- Exact Kummer endpoint valuation and boundary-alias count for FullAdd
- Exact multilinear separator degree of the Boolean AND graph
- Exact multiplicative complexity of 2×2 unsigned integer multiplier
- Exact multiplicative complexity of 5-by-3 addition and six addition floors
- Exact multiplicative complexity of 7-variable majority
- Exact multiplicative complexity of a Fano 3-space at n = 8 and floor census at n = 4
- Exact multiplicative complexity of a ten-input schedule tile
- Exact multiplicative complexity of A_{4,3} and constant-added addition F_{3,K}
- Exact multiplicative complexity of all 16 optimal 4-bit S-box classes and standard ciphers
- Exact multiplicative complexity of all powers of the width-four chi map
- Exact multiplicative complexity of carry-calculus and threshold functions
- Exact multiplicative complexity of chi_5^2
- Exact multiplicative complexity of direct sums of monomial Boolean functions
- Exact multiplicative complexity of GF(16) inversion and bounds for GF(32)
- Exact multiplicative complexity of odd inverse chi
- Exact Multiplicative Complexity of Parallel Counters and Multi-Operand Compressors
- Exact multiplicative complexity of small modular additions
- Exact multiplicative complexity of the forward χ mapping
- Exact multiplicative complexity of the resolved-carry family K_m
- Exact multiplicative complexity of the schedule tile
- Exact multiplicative complexity of the two-column C7 carry transducer
- Exact multiplicative complexity of two exposed-sum ripple chains
- Exact Multiplicative Complexity of x1x2x3 ⊕ y1y2y3y4
- Exact multiplicative complexity of χ₅⁻¹ and S_Ascon⁻¹
- Exact nonlinear cost of an eight-state controller under affine relabeling
- Exact number of quadratic equations for a unique common zero in GF(2)^32
- Exact quadratic cover number of an OR-chain lift of a width-k clause over F2
- Exact quadratic multiplicative complexity of GF(2^4) multiplication and polymul_4
- Exact R1CS complexity of XOR3 and MAJ3 gadgets
- Exact R1CS Row Counts and Allocation-Independent Lower Bounds for Basic Gadgets
- Exact restriction loss conservation law for multiplicative complexity
- Exact scans of published p8 factors for three maximal mixed p14 skeletons
- Exact shear symmetry of multiplicative complexity in constant addition
- Exact sizes of small single-output median networks
- Exact unrestricted multiplicative complexity of 3-term binary polynomial multiplication
- Exact unrestricted multiplicative complexity of binary GF(8) multiplication
- Exact-UNSAT of Phase B in the natural P10 missing-plane model
- Exclusion of 19- and 20-vector Kochen-Specker sets in C^6
- Exhaustion of the 3-gate full-domain start on the Toffoli acyclic p7 route
- Exhaustion of the t = 5 Two-Phase Route for 22-Variable Symmetric Functions
- Failure of Keccak-family score reduction via inverse-χ exactness
- Failure of SMS standalone LRAT certificate verification for Kochen-Specker n = 18
- Finite classification of the primary-affine pairing-one localization component
- Finite-horizon Nerode minimisation of the 22-state carry transducer
- Fixed-interface factor-component contraction on the 22,215-row leader
- Formal verification of end-to-end output equality for XAGs in Lean
- Formal verification of large cryptographic circuits via cone-local proofs
- Formula for canonical constant-heap complexity H_n(K)
- Full linear rank of multiplicative rows in the SHA-256 leader circuit
- Full-domain replay for candidate XAG validity
- Functional census and degree bounds for the two-row cyclic model
- Gate-class dimension increment per C7 column
- Impossibility of Constant Absorption by Memoryless Scalar Carry Codes
- Impossibility of helper-free IsZero over finite fields with |F| ≥ 4
- Impossibility of p7 realizations for rank-tight q-rank-7 edges under G = W
- Impossibility of rank-tight p5 realizations for q-rank-5 edges
- Impossibility of realizing AND4 with three witnesses and three product rows
- Ineffectiveness of 3-tensor slice rank for multiplicative complexity bounds
- Infeasibility of K12 score reduction via banked rowwise chi5 replacements
- Injected carry is exactly the flagship one-gate gap
- Invertibility of odd rotation sums in F2[x]/((x+1)^{2^r})
- Is the projected-heap upper bound always exact?
- Iterate structure, degree, and attributions for the Keccak chi mapping
- Kummer endpoint and boundary-alias formulas
- Limitations and obstructions in R1CS gadget arithmetization over F_p
- Limits of plain CDCL with cardinality totalizers for Turán numbers ex(n, K_4^(3))
- Limits of SHA-256 row reduction from banked component certificates
- Linear fresh-defect growth in the natural five-code relaxed relation
- Linear fresh-defect growth in the strongest natural five-code relaxed SHA relation
- Machine-checked lower bound t(7) > 12 via fourteen amalgam cubes
- Matroid invariants of the quadratic hull of a Boolean relation
- Maximum row degree bound for 16×17 Zarankiewicz extremal matrices
- Method limit of cube-and-conquer without algebraic reduction
- Minimum degree bounds for (J4, J8; N)-graphs at orders 30 and 31
- Model dependence of finite-field multiplication complexity over GF(4) and GF(8)
- Model transfer barriers for finite-field multiplication complexity
- Multiplicative complexity bounds for 2x2 matrix multiplication over GF(2)
- Multiplicative complexity bounds for chi_5^2
- Multiplicative complexity bounds for chi_6^2 and chi_7^2
- Multiplicative complexity bounds for the injected-carry family J_m
- Multiplicative complexity bracket for GF(2^4) multiplication
- Multiplicative complexity lower bounds and brackets for chi_6^2 and chi_7^2
- Multiplicative complexity of cascaded k:2 carry-save compressor slices
- Multiplicative complexity of four-operand addition
- Multiplicative complexity of independent copies of 2×2 matrix multiplication over GF(2)
- Multiplicative complexity of modular addition of up to eight operands
- Multiplicative complexity of Pascal and averaging-algebra state-feature classes
- Multiplicative complexity of the three-product carry cell
- Necessary carrier sequence and connected-leakage bounds for hypothetical p14
- Non-existence of 18-vector Kochen-Specker sets in dimension 6
- Nonexistence of 19-vector Kochen-Specker sets in C^6 and the lower bound m_6 ≥ 20
- Nonexistence of 20-vector Kochen-Specker sets in C^6 and minimality of m_6 = 21
- Nonexistence of small low-witness AND4 cells
- On gate savings under repeated period doubling
- On the exact consecutive-Maj edge identity and rank-32 gauge growth
- On the full-word gauge of the consecutive-Maj identity
- On the functional direct-sum additivity of M₂ over GF(2)
- On the miss rate of cubic rejection rules for exact K00 same-input H2 invalid points
- On the multiplicative complexity of adding K unsigned n-bit integers
- On the multiplicative complexity of the 26-input Cartesian period-two law
- On the natural stationary p7 route targeting 21,738
- On the quadratic hull of carry relations under state-only catalyst lifts
- On the soundness of the verifier-level Phase-Trellis P5 model
- On the static quadratic hull as a general SAT preprocessor
- On the support-cage test for degree-eight p7-eligible edges
- On the zero sets of products of affine forms on F₂³
- Open status and catalogue corrections for resolution hardness h_11
- Open Status of the NIST 21-vs-22 Question for Degree-22 Symmetric Functions
- Orbit and comodule anatomy of obtained J_3 witnesses
- Packing floors on quadratic multiplicative complexity for linear spaces of quadratics
- Partial degree-cube search wall for Zarankiewicz number z(16,17;3)
- Piecewise cubic separation of JSC-12 cases in the flip-support subspace
- Pinning obstructions and the one-missing-direction empirical wall
- Proof-system mismatch for the circulant weighing matrix cell CW(112,36)
- Quadratic hull closure for the canonical Z-difference counter interface
- Quadratic hull closure of the Z-counter transition relation
- Quadratic-hull screens of two-column SHA-256 seed allocations
- R1CS lower bound for modular addition via quadratic degree bound
- Rank-one-target deficiency of stationary full covers on GF(2)⁵
- Reduction of named p14 census residual to 221 cells
- Refutation of five candidate multiplicative complexity lower-bound conjectures
- Refutation of stationary additive raw/state phases by a three-column divergent carry path
- Refutation of the general carry-bond tensor floor
- Refutation of the Maj Edge Phase -1,024 Candidate
- Refutation of the universal carry-bond tensor lower bound
- Refutation of three proposed multiplicative complexity laws
- Residue-class parity theorem for circulant weighing matrices
- Resolution tax τ_4 in its smallest open form
- Restriction conservation law for multiplicative complexity under exact restriction
- Row complexity of n-bit range checks and u32 addition in R1CS
- Search scale barrier for unrestricted 6-AND XAG decision of M_2(F_2)
- Search wall for the smallest 7-universal tournament at order 13
- SHA-256 compilation record and status of conditional sub-22,215 alternatives
- Sharpness of the 5/8 law and multiplicative complexity of n-bit addition
- Shortest-path and LP-dual formulation of multiplicative complexity via semantic gate states
- Simultaneous and cyclic witness definitions in the Lean 4.28 kernel
- Solver wall in SAT-based exact median network synthesis
- Solver-Free Multiplicative Complexity Lower Bounds from Degree and Walsh Floors
- Sparse exact synthesis of a 69,862-variable allocator
- Status of the FCNS reduction chain for uniform lower bounds
- Strict syntactic-equivariant inverse-χ costs at widths 3, 5, and 7
- Structural constraints on the slack gate in seven-wedge one-slack p14 orbits
- Symmetry and exact small-width complexity of constant-addition shears
- The 37-wall atlas of failed proof routes and scope limits
- The Boolean ramification polytope common evaluation conjecture
- The degree-(d) hull of Boolean relations with few forbidden points
- The exact digit-sum law for full K-operand addition
- The exact width-two law for truncated multi-operand addition
- The false path 8 -> 0 -> 0 in the natural five-code Ghost-P5 quadratic hull
- The k-window law for joint multiplicative complexity of Chi iterates
- The kernel of the Boolean product-residue map on separable signal cuts
- The live p14 frontier and its doubly conditional row saving
- The Mirwald–Schnorr 3-form transfer gap and n = 6 enumeration barrier
- The mixed-image tax and rank-tight copy-locality
- The p8 top-form obstruction for the exact three-column boundary tile
- The packing filtration lower bound and master identity for multiplicative complexity
- The packing lemma lower bound for multiplicative complexity
- The separated-product theorem over any field under square closure
- The universal one-gate bracket for three-operand addition
- The verified 22,215-row SHA-256 bill remains unchanged
- Three sound whole-function multiplicative complexity lower-bound floors
- Two necessary conditions on Kochen-Specker orthogonality graphs
- Unification of Additive Line Multiplicative Complexity via Greedy Column-Heap Recursion
- Uniqueness of (J4,J7;26)-graphs with minimum degree at least 9
- Universal screen refutation of the JSC one-catalyst class
- Universal wrong row-0 assignments in Toffoli-lift cyclic p6 modules
- Unsoundness of the fixed Ghost-P5 ITER19 allocation and K0 trellis adapter
- Verified structural obstructions for universal tournaments
- Verified width-three constructions for nine and ten operands
- Verifier-level audit of finite phase-trellis relations
- Vertex-deletion averaging ladder for the Turán (3,4)-problem
- Witness power, degree collapse, and allocation walls over large prime fields
- Wrong Fixed Points in Rank 5/5 Deterministic Quadratic-Atlas Charts