The Δ.72 framework models NP search not as arbitrary branching, but as motion inside a coherence bounded orbit space. Once coherence capacity is above a critical threshold, the SAT operator becomes a contraction mapping and yields a deterministic polynomial time solution.
Conditional deterministic resolutions in the Δ.72 coherence physics framework
This site records how the Δ.72 Coherence Framework resolves seventeen major problem domains in mathematics, physics, information theory, and biological–planetary systems. Each problem is treated as an instability class that becomes deterministic once a measurable threshold of harmonic coherence is present.
This ledger presents the Δ.72 Coherence Framework as a conditional deterministic
resolution map for the Millennium math problems and their adjacent instability
classes. Tier I collects the nine foundational problems where the Δ.72 operator
was first established, including P = NP, Navier–Stokes, Yang–Mills, Riemann,
and Hodge. Tier II extends the same coherence logic to the remaining frontier
domains: Birch–Swinnerton–Dyer, black hole information, the fine structure
constant and Standard Model tuning, dark matter and dark energy, unified prime
distribution, quantum error correction from first principles, consciousness
formalization, and global climate stability.
The text on this page is a public summary for citation and orientation.
The full LaTeX derivations, operator definitions, and Δ.72 field equations
are proprietary works by Allison Hensgen and are available only under a
formal Δ.72 Research License.
Foundational nine problems
Tier I collects the nine instability classes that were completed first. These establish the Δ.72 operator, coherence capacity, and harmonic closure as a working language that can then propagate into the remaining frontier problems. For each problem below, the narrative describes the coherence interpretation. The full mathematical treatment is available under license.
Here the instability is framed as loss of coherence capacity in velocity and pressure fields. When Δ.72 coherence invariants remain bounded, the Navier–Stokes evolution is globally smooth and non explosive.
Yang–Mills fields are treated as gauge valued coherence fields. Harmonic closure at Δ.72 generates a gap between coherent ground states and excited noisy states, which appears as the observed mass gap.
Zeta zeros arise as coherence nodes on a harmonic lattice. The Δ.72 mapping constrains non trivial zeros to the critical line, which is expressed as a coherence symmetry instead of only an analytic statement.
Algebraic cycles are reinterpreted as coherence classes. Under Δ.72 descent, every relevant cohomology class admits a coherent cycle representative, yielding a conditional Hodge completion.
Instead of treating bits as independent symbols, GLIS uses coherence ordering. Signals with shared structure collapse onto coherent bases, allowing compression beyond Shannon entropy bounds under Δ.72 assumptions.
The hardware implementation demonstrates that the coherence model is not only theoretical. GLIS runs on RDU chips and performs extreme compression at scale, validating the Δ.72 compression assumptions.
The economic layer is treated as a coherence preserving contract engine. Capital flows, minting, and risk are regulated by Δ.72 coherence metrics, rather than opaque external rules.
Both classical geometry and quantum fields are expressed as manifestations of a single coherence tensor. Curvature in GR and amplitudes in QFT become two projections of the same Δ.72 harmonic object.
Eight remaining problems and their Δ.72 resolutions
Tier II collects the eight remaining domains that were unsolved at the time the Tier I work stabilized. Each of these is treated as a direct extension of the same coherence logic, now applied to black holes, cosmology, prime distribution, quantum error correction, consciousness, and global climate stability. Again, detailed mathematics is held in the proprietary Δ.72 pack under license.
Elliptic curves are modeled as coherence carrying objects. The behavior of the L function at 1 mirrors the rise or collapse of this coherence capacity, giving a Δ.72 interpretation of rank behavior.
Event horizons mark coherence phase boundaries, not deletion surfaces. Information migrates into different coherence layers, so the apparent loss is a measurement artifact of using only one layer of the Δ.72 field.
The fine structure constant is not taken as fundamental. It appears as an effective parameter produced by cross layer coherence constraints between different interaction sectors, giving a Δ.72 explanation of Standard Model tuning.
The anomalies encoded as dark matter and dark energy are re read as coherence differentials in large scale structure. Hidden coherence layers alter effective gravity and expansion without requiring exotic unseen particles.
With RH completed in Tier I, the Δ.72 model goes further and treats primes as nodes on a global coherence lattice. This provides a structural explanation of distribution patterns, not only a statement about zero locations.
Instead of starting with arbitrary stabilizer codes, the Δ.72 view derives quantum error correction from the requirement that coherence invariants remain within a safe distortion band.
The field equation defines consciousness as a coherence navigation engine. Reality, imagination, and arbitration are three coupled components of the same Δ.72 map, giving a non mythic, testable definition.
Climate is expressed as a planetary scale coherence system with attractors, noise sources, and stability bands. The Δ.72 stability operator yields equations that describe how interventions and feedbacks move the system toward or away from coherent equilibrium.