The papers form one tower over the executable model. Each layer states a hypothesis, proves finite theorems under displayed premises, and hands a conclusion upward only after the next layer proves that premise on the same model process. The common target is the executable-model hypothesis: one simple local repair and memory law on the carrier architecture whose continuing observers have the observed 3+1-dimensional quantum-field description and a common classical-gravity limit, with stable matter as localized topological defects of native overlap transport. The completion program orders the open joins and their stopping rules; the basis states the closure hypothesis behind it, and the model directory holds the executable construction. Every paper carries the same tower panel and a section stating its own hypothesis, what it proves, the open join it needs from the model and what would refute it.
| Layer | Hypothesis | Papers |
|---|---|---|
| 0. Closure and agreement | One history reads itself into existence; agreement defines the public world; state selection and response endogeneity are additional adopted principles | Flagship |
| 1. Repair mathematics | Local agreement repair reaches global consistency; nonzero cycle holonomy is the residue local repair cannot remove | Reality as a Consensus Protocol, Observable normal forms, Finite event algebras |
| 2. Carrier and repair law | Federated twelve-port icosahedral carriers with native C/E seam repair are the substrate | Twelve-Port Icosahedral Carriers and Native Seam Repair |
| 3. Executable observer | Observers are continuing native processes that prepare, read, retain and act on records | An Executable Observer for Observer Patch Holography, Observers Are All You Need |
| 4. Clocks and fields | Modular flow supplies local clocks; native repair supplies the field generator | Construction paper, Recovering Observer Spacetime and Einstein Dynamics |
| 5. Gauge structure and matter | Gauge structure is the transport of overlap data; stable massive matter is a localized defect whose boundary holonomy admitted repairs cannot erase | Standard Model Gauge Structure, Particles as Localized Topological Defects of Native Overlap Transport |
| 6. Gravity | Einstein dynamics is the coarse response of the same process | Recovering Observer Spacetime and Einstein Dynamics, de Sitter time-advance sign |
| 7. Cosmology and tests | The same process fixes vacuum, dark sector, primordial response and black-hole records, and passes prospective tests | Cosmology papers, fine-structure diagnostic, Koide identity, Yang–Mills identification |
- Established on stated domains: the finite repair, normal-form and holonomy-frustration theorems; the forced classical seam rule and the classified record laws; the rank-three slow-response band; finite executions of one continuing observer with complete outputs, overlapping observers on one process, event clocks and checkpoint continuation; a continuing C/E finite-buffer observer with counted record exports and an exact stationary source/complete-record reference (finite campaign); the positive continuum screen generator of spectral dimension two; the compact Lie type of the complete response under its premises; the conditional null-balance and tensor-completion implication.
- Conditional on declared inputs: the smooth 1+3 scalar description (declared radial extension), the candidate modular clocks (declared reference and controls), the one-generation matter representation and Higgs channels (declared spin lift and exterior module), the cosmological branches.
- Open joins: a physical clock and energy normalization; a native defect sector with a protecting invariant, its maintenance energy and transport; an interacting chiral 3+1 field description from native records; a responsive geometry realizing the Einstein premises; independent prospective tests.
- Negative results on the tested law: the native double-load defect is transient; the static radial product fails the null-balance comparison; passive repair has no wave sector; the tested uncalibrated family and mass laws miss the charged hierarchy; no nontrivial source-only charge commutes with every complete C/E branch; real native operations cannot implement the nontrivial modular action of the constructed reference on its full support algebra; no measured particle spectrum is derived.
The tower is a construction target, not a claim that every layer is realized. The following map identifies the result to assess in each paper and the inputs that cannot be inferred from its place in the tower. The papers give the hypotheses, proofs, evidence and comparison with prior work; standard results used in a new interface remain standard results.
| Paper | Achieved contribution | Retained inputs or open physical identification |
|---|---|---|
| Flagship synthesis | A common specification, selected conditional results, negative controls and ordered completion tests | The synthesis constructs no common realized Standard Model and gravity theory; closure, state selection and response endogeneity have distinct logical content |
| Executable observer | Finite record-controlled operations, complete outcome laws, continuing observer/reference constructions and scoped error bounds | Supplied coherent services, preparations, actions, clocks and physical units retain their individual contracts |
| Consensus protocol | Protected-observation normal forms, accepted repair, provenance and quantitative finite/refinement interfaces | Termination, confluence, scheduler and protected-record hypotheses must hold on the actual source; Newman's theorem is an imported ingredient |
| Observers and records | Finite record, entropy, capacity and instrument constructions with explicit composition boundaries | Quantum algebra, reference, energy calibration and field actions are premises where supplied; familiar quantum and thermal identities do not alone select a physical source |
| Spacetime and Einstein dynamics | Finite causal/count interfaces, null tomography, tensor completion and same-metric obstruction tests | The geometric/stress/entropy balance and common physical clock require a source realization; the static radial product fails the tested null balance |
| Gauge structure | Compact Lie-type selection under complete-response/endogeneity premises and a specified matter/tensor witness | Complete source currents, physical chirality, matter selection, global form and field dynamics remain separate obligations |
| Particle defects | Tests and obstructions for native defect, maintenance-energy and family candidates | No stable physical particle sector or measured mass spectrum follows from the failed candidates or supplied representation |
| Carrier and seam repair | Exact carrier incidence, classical seam rule, record-law classification and rank-three response | The selected architecture, response menu and physical spatial/refinement interpretation remain explicit |
| Finite event algebra | A checked projection-event API, expectation range/uniqueness results and measurement/CHSH adapters | The underlying finite quantum algebra is supplied; the contribution is formalization and interface design, not a new quantum probability law |
| Observation-determined normal forms | Observable reconstruction, stability/receipt and refinement certificates with necessity counterexamples | Each quantitative estimate retains its stated error-bound witnesses and domain hypotheses; it assumes no physical interpretation |
| de Sitter capacity | Finite entropy, capacity-transfer, shock-normalization and spectrum identities | Horizon-area, capacity, mass and dynamical-shock identifications are conditional |
| Fine-structure fixed point | Interval-certified roots of declared maps and independent reconstruction of the credited entangled-pair scalar | Target-independent map selection, common coupling normalization and Thomson identification require physical derivations; the measured-payload endpoint misses the measured coupling |
| Koide circulant identity | Positive-chamber algebra and a conditional finite tracial balance | Balance was target informed; the phase and physical charged-family/mass attachment are not derived |
| Yang--Mills gap identification | Finite repair floors, rate comparisons and failed interacting transfer tests | Physical gap transfer and the four-dimensional continuum certificate contain the unresolved Yang--Mills construction |
| Vacuum and structure formation | Finite ensemble/vacuum interfaces and native-density comparison boundaries | A selected physical vacuum, cosmological source and scale are not supplied by the finite conditional constructions |
| Finite-source cosmology | Conditional source spectra, radial-identification criteria and exact finite population controls | The physical source, primordial embedding, scale and transfer map remain required |
| Candidate inflation-free branch | Exact record-density expansion on a declared population and conditional tilt/flatness criteria | The population, expansion profile and generator density are supplied; an inflation replacement is a target, not an achieved result |
| Photon--baryon transfer | A common convention and conditional transfer interface reproducing standard Boltzmann transport | Geometry, photon/collision physics, masses and recombination are imported; no new transport dynamics or source spectrum is derived on the standard branch |
| Dark sector | Conditional charge/saturation/profile identities and explicit retrospective comparisons | Collar stress, abundance and universal coupling need physical realization; the deep law uses stated scaling/composition premises and fitted acceleration scale |
| Black-hole ledger | Finite record-channel identities and declared crossing-count scaling | The horizon-entropy coefficient, thermality and physical information-return mechanism are not established |
| Data and likelihood contracts | Explicit comparison classes, data contracts and independently replayed retrospective values | Exposure, calibration and supplied cosmology remain visible; a posterior comparison is not a derivation of its source model |
- Model results enter the model directory first, with their own claim rows owned by the protocol records there. The construction paper states them in its next revision.
- Library papers receive errata, correctness fixes and links to the premise map. New results go to the model or to a companion paper.
- The flagship changes zero-sum: a stronger result replaces a weaker one within the 60-page ceiling.
- A new paper release follows the owner's approval of a recorded model milestone. Deposited releases retain their original bytes.
These papers left the active set. Their sources, claim rows and last built PDFs remain in paper/archive/, and every deposited release keeps its bytes.
| Paper | Main content |
|---|---|
| Paradise as Fixed-Point Consensus | An interpretation of continuation, justice and repair of observer records. |
| OPH as a String-Vacuum Selector | A vacuum-selection sieve and the exact rank-zero obstruction of the five-coordinate comparison map on the 71-dimensional one-Higgs Bouchard–Donagi moduli space. |
| Thinking as Patch-Net Fixed-Point Search | A model of cognition as fixed-point search, with audited descent, Hopfield and equilibrium-propagation proof boundaries. |