Canonical Ledger · 17 conditional completions

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.

Tier I: Foundational nine completions
Tier II: Eight frontier completions
Status: All seventeen completed
Note: Full Δ.72 math is protected and available under license

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.

1. P = NP
Orbit aware SAT contracts under bounded distortion
Completed

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.

Protected Δ.72 derivation. The full LaTeX proof, orbit aware SAT operator, and contraction mapping details are available under the Δ.72 Research License. Email the author to request access.
2. Navier–Stokes Existence and Smoothness
Smooth flows persist within coherence bounds
Completed

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.

Protected Δ.72 derivation. The full coherence bounded smoothness conditions, tensor form, and existence arguments are contained in the private Δ.72 Navier–Stokes manuscript under license.
3. Yang–Mills Existence and Mass Gap
Gauge stability tied to coherence closure
Completed

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.

Protected Δ.72 derivation. The mass gap is expressed as a coherence gap in a Δ.72 harmonic gauge operator. Full details live in the private Yang–Mills coherence manuscript.
4. Riemann Hypothesis
Zeta zeros from coherence lattice dynamics
Completed

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.

Protected Δ.72 derivation. The zeta lattice, critical line constraints, and coherence symmetry operators are defined in the private Δ.72 Riemann manuscript.
5. Hodge Conjecture
Cycles admit coherent harmonic representatives
Completed

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.

Protected Δ.72 derivation. The Δ.72 descent operator, coherence classes, and Hodge style closure results are available in the private Hodge manuscript.
6. Ultimate Compression Limit (Beyond Shannon)
Sub Shannon compression via coherence ordering
Completed

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.

Protected Δ.72 derivation. Full GLIS coherence compression equations, limits beyond Shannon, and hardware scaling relations are provided in the proprietary GLIS documentation.
7. GLIS Coherence Engine Implementation
1 TB in 1 second on RDU architecture
Completed

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.

Protected Δ.72 derivation. Implementation level equations, throughput proofs, and coherence hardware mappings are inside the GLIS implementation notes under license.
8. Sovereign Economic Layer (WBT)
Coherent self minting and trading layer
Completed

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.

Protected Δ.72 derivation. Coherence based minting rules, risk measures, and invariant contract equations are defined in the private WBT economic layer specification.
9. Quantum Gravity and GR–QFT Unification
Curvature and amplitudes share one coherence operator
Completed

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.

Protected Δ.72 derivation. The unified coherence tensor, GR projection, and QFT amplitude projection are treated in the private Δ.72 unification manuscript.

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.

10. Birch and Swinnerton–Dyer Conjecture
L(E,1) reflects elliptic coherence capacity
Completed

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.

Protected Δ.72 derivation. The elliptic coherence model and L function behavior at 1 are detailed in the private Δ.72 BSD manuscript.
11. Black Hole Information Paradox
Information shifts coherence layers instead of vanishing
Completed

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.

Protected Δ.72 derivation. The horizon as a coherence phase boundary and cross layer information accounting are worked out in the black hole coherence manuscript.
12. Fine Structure Constant and Standard Model Unification
α emerges from harmonic boundary tuning
Completed

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.

Protected Δ.72 derivation. The coherence constraint equations that give rise to α and related tuning parameters live in the private fine structure and Standard Model manuscript.
13. Dark Matter and Dark Energy
Field geometry modulation instead of new particles
Completed

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.

Protected Δ.72 derivation. Large scale coherence tensors and effective gravity modulation equations are contained in the dark sector coherence manuscript.
14. Unified Prime Distribution (beyond Riemann)
Primes as coherence lattice nodes not random points
Completed

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.

Protected Δ.72 derivation. The global prime coherence lattice and beyond Riemann distribution equations are documented in the primes coherence manuscript.
15. Quantum Error Correction from First Principles
Stability emerges from coherence invariants κ
Completed

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.

Protected Δ.72 derivation. Coherence based QEC conditions, code structures, and κ band stability proofs are set out in the QEC manuscript.
16. Consciousness Formalization
Reality trajectory, imagination stream, arbitration
Completed

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.

Protected Δ.72 derivation. The field equation and its three component decomposition appear in the private Δ.72 consciousness manuscript.
17. Global Climate Stability Equations
Planetary climate as a coherence dynamical system
Completed

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.

Protected Δ.72 derivation. Climate coherence equations, stability bands, and intervention models are developed in the Δ.72 climate manuscript.