This directory holds one HTML file per public research record. The searchable catalog is the research library. Research library.
- A structural-gap family of order X / sqrt(log X)
- Additional filters on the parity-cubic `3r` index-six defect
- Almost all prime depth values are structural gaps
- Asymptotic skeleton of Type A/B ancestry shadows
- Automated WS-CAND-003 results — 2026-08-14
- bb.kernel
- Binary defects on the full external-nonresidue factor cycle
- Binary-prime completed layers collapse to one-dimensional power intervals
- Binary-r rescue after one exact greedy denominator
- Binary-r rescue as a signed divisor collision
- C1 conditioned-fiber collapse on the `{3,11,13}` residual family
- C1 Escape Core Theorems
- C1 Partial Theorems Toward DSC-P — corrected
- C1 Pullback Cardinality Bound
- C1 Theorem — Single-Active Pullback Escape
- C1: single-active Class-C attack
- C2 Theorem — Two-Active-Layer Escape
- Candidate-independent trap-fiber bounds
- CC.kernel
- Character-shield obstruction completeness
- Class-C active-core census through k = 1500
- Class-C residual core: coordinated primary formulation
- Classification of Jacobi-saturated Type A/B layers
- Classification of universal square-lift signature shadowing
- CN Theorem — Finite Active-Core Escape
- CN-shared analyzer report
- CN-shared certificate — 2026-08-15
- CN-Shared Theorem — Lift-Room, Tight Clusters, and Admissible Escape
- Complete classification of the depth-1 Type A/B shadow component
- Complete classification of Type A/B multiplicative coset saturation
- Complete dichotomy for prime Type A/B minimal depths
- Composite successor `3r`: exact index-six defect classification
- Composite successor `3r`: index-four defect elimination
- Composite successor `3r`: parity-constrained signed-box theorem
- Consecutive binary-selector probe
- Constructive counterexample to universal Direct-Shadow Completeness
- Constructive nonuniversal square-lift certificate results
- Coprime fab certificates force an external hard-class nonresidue
- Coprime fab certificates reduce to one divisor congruence
- Counterexample to naive hit-on-cycle / least-entry conjectures
- Counting bounds for the Type A/B minimal-depth spectrum
- Counting the source-1 structural-gap semigroup
- Cryptology control lemmas for WS-CAND-003
- Cryptology research track for WS-CAND-003
- Cubic-log sieve bound from q=3,7,11,23 Type-II filters
- Cubic-surface form of the gcd-square rescue
- Current research frontier
- Dimension-two sieve from the exact q=3 and q=7 strong/Type-II filters
- Direct-Shadow Completeness attack through k = 1000
- Direct-Shadow Completeness attack through k = 1200
- Direct-Shadow Completeness attack through k = 1500
- Direct-Shadow Completeness counterexample — primitive q=3 triple cover
- Direct-Shadow Completeness: candidatewise finite attack
- Direct-shadow smoothness theorem
- Divisor-child ancestry theorem for Type A/B shadowing
- DSC-P Fragment — Coprime Active Cores
- Dual descent system behind sufficient fab certificates
- Dyachenko ED2 lattice repair audit
- Dyadic trap lattice automated regression results
- Dyadic trap-coset and shadow lattice
- Erdős-Straus Type A/B automated research harness
- Erdős-Straus — Wall
- Even-index FAB defects expose every quadratic-nonresidue factor
- Exact `2p+1` factor filter
- Exact `4p+1` factor filter
- Exact `p+4` factor rescue
- Exact `r=11` binary rescue classification for Mordell-hard primes
- Exact ancestry rigidity for quotients 21 and 29
- Exact anchor-row domination inside the C1 residual core
- Exact classification of multiplicative-ancestry shadows
- Exact fixed-k=7 filter for Mordell-hard primes
- Exact index-6 FAB Kneser defect classification
- Exact index-six normal form for the combined FAB targets
- Exact q=11 filter for Mordell-hard primes in the strong/Type-II corridor
- Exact q=23 filter for Mordell-hard primes in the strong/Type-II corridor
- Exact q=7 filter for Mordell-hard primes in the strong/Type-II corridor
- Exact r=7 binary rescue for Mordell-hard primes
- Exact reduced-parameter domain
- Exact survivor density and hazard for the Type A/B sieve
- Exact two-target divisor-square criterion
- Exact two-target filter at the composite shift `k=15`
- Exact two-target filter at the prime shift `k=19`
- Exact two-target signed-box equivalence for prime Erdős--Straus
- Exponent-lattice formulation of square-completed ancestry shadows
- External-nonresidue factor cycle
- External-nonresidue m=1 character synchronization
- External-nonresidue shield certificates carry a synchronized nonresidue triple
- External-nonresidue shield-ratio census through `p <= 10^7`
- External-nonresidue × hard-shield fixed-k probe
- Fiber shadow kernel: a sharper local elimination theorem
- Findings index
- Findings library
- Finite shift corridor for the classical strong/Type-II conjecture
- Finite square-completion census through 50,000,000
- First exact shifted-factor filters for Mordell-hard primes
- Five-halves sieve bound from the exact q=3, q=7, and q=11 Type-II filters
- Fixed-k fab certificates are signed divisor products
- Fixed-k fab criterion collapses to one divisor of N²
- Full fiber-kernel and bounded-selector replay through k = 1200
- Full local quadratic signature quotient of Type A/B traps
- Full quadratic-signature coset for Type A/B traps
- Full quadratic-signature shield through k = 1200
- Full-stabilizer compression of FAB Kneser defects
- GCD-square reformulation of coprime fab rescue
- General odd-prime-shift ancestry rigidity — corrected scope
- Genus-theoretic identification of the square-lift defect quotient
- Hard-class union shadows and the five-of-nine C1 3-adic fiber theorem
- How grades are decided
- Hunt seeds
- Infinite exact-depth structural gap families
- Infinite squarefree factor-lift families at every ancestry quotient
- Kneser defect theorem for external binary-r rescue
- Kneser defect theorem for the fixed-k FAB divisor box
- Large-prime defect forcing by CRT starvation
- Mersenne shadow lattice: an infinite exact family of impossible Type A/B minimal depths
- Mersenne-prime backbone inside the Type A/B depth spectrum
- Mirror character obstruction for fixed-k fab rescue
- Mixed-box obstruction in exact square-lift shadowing
- Multiplicative reciprocity defect quotient for Type A/B square lifts
- Multiplicative semigroup shadow families from saturated Type A/B sources
- Multiplicative trap quotient
- Multiplicative Type A/B trap coset
- Multiplicative-coset and Jacobi shields survive square completion
- Normalized Type-II signed-divisor target
- Odd-prime-shift ancestry rigidity above the small-ancestor window
- Prime-child ancestry shadows
- Prime-child shadow automated regression results
- Prime-depth backbone projection
- Prime-extension shadow family for square-completed Type-II layers
- Prime-index hierarchy for FAB Kneser defects
- Prime-index spectrum of the square-completed Type-II layers
- Prime-modulus backbone and unbounded depth for the square-completed Type-II layers
- Prime-modulus backbone of the Type A/B depth spectrum
- Prime-power shadow kernel
- Prime-power stabilizer dichotomy: only powers of two are periodic
- Prime-power Type A/B trap dichotomy
- Prime-shift Kneser dichotomy for the classical strong/Type-II corridor
- Primitive sextic defect chains and the neighbor-square recurrence
- Prior-art audit — recent claimed Erdős–Straus proofs
- Prior-art calibration for the square-completed Type-II route
- Prior-art matrix for WS-CAND-003
- Proof ledger
- Proper Jacobi ancestor theorem for higher Type A/B signature codimension
- Provenance correction: the completed square layer is the classical strong/Type-II route
- Public Erdős–Straus hunt
- Pure-dyadic first denominators are universally obstructed on the hard-prime lane
- q=3 Fiber Injectivity and Three-Layer Minimum
- q=3 Next-Digit Normal Form
- q=3 Pointwise Absorption
- q=3 Pullbacks Are Singleton
- q=3 Strong Absorption
- q=3 Weak-Ancestor Redundancy
- Quadratic cycle core for the Type A/B character shield
- Quadratic trap signature and character shield
- Quadratic-character prior-art note
- Quadratic-field bridge for the square-lift core
- Quantitative counting in the Type A/B exact-depth spectrum
- Quantitative infinite-coinfinite spectrum for square-completed Type-II depth
- Quotient-13 shadow rigidity
- Quotient-17 shadow rigidity
- Quotient-21 shadow rigidity
- Quotient-29 shadow rigidity
- Quotient-9 shadow rigidity
- Reciprocity defect quotient for square-lift signature shadows
- Reciprocity tower automated regression results
- Reciprocity tower shadows
- Research proportions — Type A/B program
- Safe-prime shifts q = 23 mod 24 carry a forced nine-class Type-II obstruction
- Secret Oasis expedition — 2026-08-14
- Shadow semigroups from the three Jacobi-saturated bases
- Shadow-cover geometry behind Direct-Shadow Completeness
- Shifted nonresidue transfer and the `p+4` mirror filter
- Shifted-factor descent for the post-DSC Erdős–Straus wall
- Single-active Class-A local escape
- Single-active first-shell collapse — retracted proof attempt
- Single-active hard-class quotient collapse through k = 100,000
- Small-selector hypothesis for residual Type A/B fiber kernels
- Square-completed López layer equals a symmetric signed divisor box
- Square-completed trap complement: global inversion and exact mixed-parameter count
- Square-completed Type-II trap geometry: López A/B are the two boundary orthants
- Square-lift core after quadratic character saturation
- Square-lift quadratic-signature shadow theorem
- Square-lift reciprocity and infinite ancestor-shadow families
- Square-lift towers in the character residual core
- Squarefree factor-lift shadows and an infinite quotient-nine family
- Squarefree semiprime layers always contain genuinely new mixed Type-II residues
- Squarefree-lift localization of the Type A/B character residual
- Stabilizer-extension shadow theorem for square-completed Type-II layers
- Standard Type II as the square-divisor completion of López Type A
- The composite rescue core
- The Type A/B depth-spectrum diamond
- The Type A/B minimal-depth spectrum
- The Type A/B minimal-depth spectrum is infinite and co-infinite
- The Type A/B reciprocity matrix
- Two-divisibility constructor for the fab master equation
- Two-target Kneser collapse for external nonresidue shifts
- Type A/B shadow ancestry: formal working lemmas
- Type A/B shadow pullbacks as a structured odd-covering problem
- Type A/B trap quotient factorization
- Type I cannot rescue a hard-prime `q=7` Type-II miss
- Type-I companion to the exact `q=11` filter
- Type-II root geometry: López A/B are the comparable-root cases
- Unbounded defect forcing from prescribed external nonresidue load
- Unbounded strong sufficient certificates and the fixed-k divisor-ratio box
- Unique-active valuation excess is a first prime-power lift
- Universal reduced escape for a unique active fixed-negative row
- Universal square-lift shadow classification
- WS-CAND-001 — Authority cannot confer truth
- WS-CAND-002 — Justified outward decimal rendering
- WS-CAND-003 cryptology results — 2026-08-14
- WS-CAND-003: Erdős-Straus Type A/B witness depth and congruence shadow structure
- Zero-product atom decomposition of square-lift multiplicative defects
- {2,3,5,7}-smooth forced factors cannot produce a Type-II hit