{ "schema": "fieldflux-research-catalog/v1", "updated": "2026-10-02", "purpose": "Public relational index for Fieldflux preprints, founder reflections, and field notes. Relations are editorial/navigation metadata unless explicitly described otherwise.", "collections": [ { "id": "publications", "label": "Preprints & Publications", "href": "research.html", "description": "Citable technical results organized by research series." }, { "id": "notebook", "label": "Research Notebook", "href": "notebook.html", "description": "Founder reflections and field notes preserving questions, distinctions, methods, failures, and bridges between programs." } ], "themes": [ { "id": "health-foundations", "label": "Health & foundations", "description": "What health is, what makes a system itself, and what must be preserved across scale.", "landing_page": "research-theme-health-foundations.html" }, { "id": "invariance-identity", "label": "Invariance & identity", "description": "What remains the same through change, quotient, transformation, or representation.", "landing_page": "research-theme-invariance-identity.html" }, { "id": "boundary-measurement", "label": "Boundary & measurement", "description": "How boundary exchange becomes observable, reconstructable, and physically meaningful.", "landing_page": "research-theme-boundary-measurement.html" }, { "id": "formalization-proof", "label": "Formalization & proof", "description": "Machine-checkable structure, admissibility, closure, gauge structure, and proof authority.", "landing_page": "research-theme-formalization-proof.html" }, { "id": "evidence-validation", "label": "Evidence & validation", "description": "Failure tests, controls, calibration, empirical support, and the boundary of warranted claim.", "landing_page": "research-theme-evidence-validation.html" }, { "id": "relational-organization", "label": "Relational organization", "description": "Relations, multiplicity, compression, comparability, ownership, and organization across states.", "landing_page": "research-theme-relational-organization.html" }, { "id": "continuation-stability", "label": "Continuation & stability", "description": "Persistence, regularity, restart, dynamic stability, and the anatomy of breakdown.", "landing_page": "research-theme-continuation-stability.html" }, { "id": "representation-reconstruction", "label": "Representation & reconstruction", "description": "What descriptions retain, discard, reconstruct, or obstruct when states move between representations.", "landing_page": "research-theme-representation-reconstruction.html" } ], "relation_types": [ { "id": "continues", "label": "continues", "description": "The later work continues the same declared series or technical program." }, { "id": "companion", "label": "companion", "description": "The works are explicitly framed as companion explanations or notes." }, { "id": "context", "label": "context", "description": "One work supplies conceptual or interpretive context for the other." }, { "id": "example", "label": "explicit example", "description": "A work is explicitly used as an example in the connected reflection." }, { "id": "shared_question", "label": "shared question", "description": "The works address a common question without implying formal dependence." }, { "id": "measurement_bridge", "label": "measurement bridge", "description": "The connection carries a formal or conceptual question toward observability, evidence, or engineering." } ], "series": [ { "id": "navier-stokes", "label": "Navier–Stokes Continuation", "domain": "Fluid dynamics", "description": "Continuation geometry, regularity escape, spectral transfer, and endpoint rigidity.", "landing_page": "research-series-navier-stokes.html", "sequence_size": 3, "published_count": 3, "current_status": "Current published sequence: 3 papers" }, { "id": "schwarzschild-qg", "label": "Schwarzschild Quantum Gravity", "domain": "Quantum gravity", "description": "A self-consistent Einstein–real-scalar quantum sector from operator selection through BV/BRST, regulated quantization, and relational gravity.", "landing_page": "research-series-schwarzschild-quantum-gravity.html", "sequence_size": 8, "published_count": 8, "current_status": "Current published sequence: 8 papers" }, { "id": "gaussian", "label": "Gaussian Physical States and Celestial Representation", "domain": "Mathematical physics", "description": "An ongoing series studying how physical information survives successive changes of mathematical representation, from constrained Gaussian gauge-field states through radiative multiparticle structure, source-aware celestial decomposition, and the further spectral and dynamical questions opened by those constructions.", "landing_page": "research-series-gaussian.html", "published_count": 6, "current_status": "Ongoing series; Papers I–VI published; further papers in development", "paper6_current_result": "Paper VI proves all-label injectivity of the intrinsic cross-ratio and full signed principal-series transforms on the intrinsic physical source range, while retaining the explicit conditional status of the retained bounded completion. It closes this source-uniqueness stage and hands the resulting carrier forward to later papers in the series." }, { "id": "relational-biology", "label": "Relational / Systems Biology", "domain": "Systems biology", "description": "Relational state, fate, comparability, developmental organization, and morphogenetic direction across biological carriers.", "landing_page": "research-series-relational-systems-biology.html", "sequence_size": 2, "published_count": 2, "current_status": "Ongoing series" } ], "routes": [ { "id": "health-question", "title": "What can remain invariant across scale or representation?", "description": "A cross-domain route from the health question into biological comparability and source-aware representation.", "items": [ "note-question", "note-fixedness", "bio2", "gps4", "gps5", "gps6" ] }, { "id": "boundary-to-evidence", "title": "How does a boundary become a warranted measurement?", "description": "From the boundary primitive through observability, certification, reconstruction, and deliberate failure.", "items": [ "note-boundary", "note-living-boundary", "note-observable", "note-certification", "note-residual", "note-failure" ] }, { "id": "relational-identity", "title": "Where does identity live when relations carry the information?", "description": "A route through relational measurement, cell fate, developmental organization, and quantum ownership.", "items": [ "note-one-plus-one", "bio1", "bio2", "sqg8" ] }, { "id": "continuation", "title": "What does persistence look like near breakdown?", "description": "The fixedness question specialized into the Navier–Stokes continuation program.", "items": [ "note-fixedness", "ns1", "ns2", "ns3" ] }, { "id": "gaussian-representation", "title": "What survives as a physical state changes representation?", "description": "The Gaussian series from current-zero completion to radiative and celestial representation.", "items": [ "gps1", "gps2", "gps3", "gps4", "gps5", "gps6" ] }, { "id": "quantum-ownership", "title": "How does a quantum sector own its dynamics, gauge structure, and geometry?", "description": "The Schwarzschild program from self-consistent matter into master-action ownership, BRST, quantum obstruction, and relational gravity.", "items": [ "sqg4", "sqg5", "sqg6", "sqg7", "sqg8" ] } ], "items": [ { "id": "note-question", "collection": "notebook", "subtype": "founder_reflection", "title": "The Question Behind Our Research", "href": "question-behind-our-research.html", "date": "2026-10-02", "summary": "Why biology, fluid dynamics, mathematical physics, formal proof, and measurement engineering keep meeting inside one long-running question about a scale-agnostic definition of health.", "primary_theme": "health-foundations", "themes": [ "health-foundations", "invariance-identity", "relational-organization", "boundary-measurement" ], "domains": [ "Foundations", "Measurement science" ], "order": 1 }, { "id": "note-boundary", "collection": "notebook", "subtype": "reflection", "title": "The boundary comes first", "href": "boundary-comes-first.html", "summary": "Why measurement begins with the edge that makes an aggregate distinguishable, and how a maintained gradient connects boundary to health.", "primary_theme": "health-foundations", "themes": [ "health-foundations", "boundary-measurement" ], "domains": [ "Foundations", "Measurement science" ], "order": 2 }, { "id": "note-fixedness", "collection": "notebook", "subtype": "reflection", "title": "Fixedness", "href": "fixedness.html", "summary": "What must remain invariant for a changing system to remain itself, and how measurement keeps hold of identity through transformation.", "primary_theme": "invariance-identity", "themes": [ "invariance-identity", "health-foundations", "representation-reconstruction" ], "domains": [ "Foundations", "Measurement science" ], "order": 3 }, { "id": "note-algebra-ai", "collection": "notebook", "subtype": "reflection", "title": "Algebra before AI", "href": "algebra-before-ai.html", "summary": "Why formal structure, admissibility, and claim authority have to exist before learned inference is allowed to act.", "primary_theme": "formalization-proof", "themes": [ "formalization-proof", "evidence-validation", "boundary-measurement" ], "domains": [ "Formal methods", "Measurement science" ], "order": 4 }, { "id": "note-living-boundary", "collection": "notebook", "subtype": "reflection", "title": "Reading the living boundary", "href": "living-boundary.html", "summary": "A relational account of gradients, exchange, laminarity, reconstruction, and what an instrument can learn from a living surface.", "primary_theme": "boundary-measurement", "themes": [ "boundary-measurement", "representation-reconstruction", "evidence-validation" ], "domains": [ "Measurement science" ], "order": 5 }, { "id": "note-residual", "collection": "notebook", "subtype": "reflection", "title": "Residue and residual", "href": "residue-and-residual.html", "summary": "Two different remainders: what a living boundary retains, and what remains after a model has been tested against a law.", "primary_theme": "representation-reconstruction", "themes": [ "representation-reconstruction", "boundary-measurement", "evidence-validation" ], "domains": [ "Measurement science" ], "order": 6 }, { "id": "note-one-plus-one", "collection": "notebook", "subtype": "reflection", "title": "1 + 1 = 2", "href": "one-plus-one.html", "summary": "A reflection on relational measurement, compression, identity, and what arithmetic hides when relationships carry the information.", "primary_theme": "relational-organization", "themes": [ "relational-organization", "invariance-identity" ], "domains": [ "Foundations", "Measurement science" ], "order": 7 }, { "id": "note-what-new", "collection": "notebook", "subtype": "field_note", "title": "What is genuinely new, precisely.", "href": "what-is-new.html", "summary": "A proof-checked living algebra of physical observables, situated carefully against the fields nearest to it.", "primary_theme": "formalization-proof", "themes": [ "formalization-proof", "boundary-measurement" ], "domains": [ "Formal methods", "Measurement science" ], "order": 8 }, { "id": "note-certification", "collection": "notebook", "subtype": "field_note", "title": "A boundary-observable certification algebra", "href": "certification-algebra.html", "summary": "How mathematical freedom is progressively admitted through physical consistency, closure, witness, and evidentiary maturity.", "primary_theme": "formalization-proof", "themes": [ "formalization-proof", "evidence-validation", "boundary-measurement" ], "domains": [ "Formal methods", "Measurement science" ], "order": 9 }, { "id": "note-temperament", "collection": "notebook", "subtype": "field_note", "title": "The temperament of a bespoke algebra", "href": "temperament.html", "summary": "What repeated behavior under proof reveals about the character of a mathematical object built for measurement.", "primary_theme": "invariance-identity", "themes": [ "invariance-identity", "formalization-proof", "relational-organization" ], "domains": [ "Formal methods", "Foundations" ], "order": 10 }, { "id": "note-observable", "collection": "notebook", "subtype": "field_note", "title": "The making of an observable", "href": "making-of-an-observable.html", "summary": "How calibration, reconstruction, residual analysis, transport preservation, and claim maturity turn a signal into an observable.", "primary_theme": "boundary-measurement", "themes": [ "boundary-measurement", "evidence-validation", "representation-reconstruction" ], "domains": [ "Measurement science" ], "order": 11 }, { "id": "note-failure", "collection": "notebook", "subtype": "field_note", "title": "How we try to make the signal fail", "href": "make-the-signal-fail.html", "summary": "Why deliberate deletion, failure tests, and longitudinal challenge belong inside the evidence chain before a relationship is allowed to count.", "primary_theme": "evidence-validation", "themes": [ "evidence-validation", "boundary-measurement" ], "domains": [ "Measurement science", "Empirical validation" ], "order": 12 }, { "id": "ns1", "collection": "publications", "subtype": "preprint", "series": "navier-stokes", "order": 1, "date": "2026-09-13", "title": "Continuation Anatomy of Periodic Navier–Stokes Breakdown", "subtitle": "A machine-checked H² theory of finite-energy regularity escape.", "href": "research-continuation-anatomy-navier-stokes.html", "pdf": "research-continuation-anatomy-navier-stokes.pdf", "doi": "10.5281/zenodo.22737978", "summary": "Finite maximality is resolved into bounded kinetic energy, eventual H² divergence, escape beyond every fixed Fourier cutoff, positive-scale regularity, and collapse of uniform continuation reserve.", "primary_theme": "continuation-stability", "themes": [ "continuation-stability", "formalization-proof", "invariance-identity" ], "domains": [ "Fluid dynamics", "Formal methods" ] }, { "id": "ns2", "collection": "publications", "subtype": "preprint", "series": "navier-stokes", "order": 2, "date": "2026-09-14", "title": "Critical Regularity Anatomy of Periodic Navier–Stokes Breakdown", "subtitle": "Spectral transfer, terminal nonlinear H² work, and simultaneous failure of nonendpoint continuation controls.", "href": "research-critical-regularity-navier-stokes.html", "pdf": "research-critical-regularity-navier-stokes.pdf", "doi": "10.5281/zenodo.22754459", "summary": "The continuation anatomy is sharpened through finite-annulus spectral budgets, unbounded terminal nonlinear H² work, and simultaneous failure of nonendpoint continuation regimes.", "primary_theme": "continuation-stability", "themes": [ "continuation-stability", "formalization-proof" ], "domains": [ "Fluid dynamics", "Formal methods" ] }, { "id": "ns3", "collection": "publications", "subtype": "preprint", "series": "navier-stokes", "order": 3, "date": "2026-09-24", "title": "Endpoint Rigidity in Periodic Navier–Stokes Flow", "subtitle": "Terminal magnification, intrinsic restart, and analytic rigidity at the L∞t L³x boundary.", "href": "research-endpoint-rigidity-periodic-navier-stokes-flow.html", "pdf": "research-endpoint-rigidity-periodic-navier-stokes-flow.pdf", "doi": "10.5281/zenodo.22943388", "summary": "Bounded terminal L³ forces global continuation, while finite maximal time forces infinite terminal L³ limsup through magnification, restart, backward identification, and rigidity.", "primary_theme": "continuation-stability", "themes": [ "continuation-stability", "invariance-identity", "representation-reconstruction" ], "domains": [ "Fluid dynamics", "Formal methods" ] }, { "id": "sqg1", "collection": "publications", "subtype": "preprint", "series": "schwarzschild-qg", "order": 1, "date": "2026-09-16", "title": "Critical Schwarzschild Scalar Dynamics", "subtitle": "A machine-checked operator theory of terminal self-adjoint laws and Friedrichs selection.", "href": "research-critical-schwarzschild-scalar-dynamics.html", "pdf": "research-critical-schwarzschild-scalar-dynamics.pdf", "doi": "10.5281/zenodo.22800860", "summary": "A Hardy-critical radial operator with a genuine family of self-adjoint terminal laws is reduced by a ground-state form to the Friedrichs-selected no-log realization.", "primary_theme": "representation-reconstruction", "themes": [ "representation-reconstruction", "formalization-proof", "continuation-stability" ], "domains": [ "Quantum gravity", "Mathematical physics", "Formal methods" ] }, { "id": "sqg2", "collection": "publications", "subtype": "preprint", "series": "schwarzschild-qg", "order": 2, "date": "2026-09-17", "title": "Friedrichs-Selected Schwarzschild Quantum Dynamics", "subtitle": "A machine-checked continuum Fock theory and real-scalar physical Cauchy evolution.", "href": "research-friedrichs-selected-schwarzschild-quantum-dynamics.html", "pdf": "research-friedrichs-selected-schwarzschild-quantum-dynamics.pdf", "doi": "10.5281/zenodo.22805014", "summary": "Friedrichs selection is propagated into positive one-particle frequency, continuum bosonic Fock dynamics, and an independently action-derived physical Cauchy theory.", "primary_theme": "representation-reconstruction", "themes": [ "representation-reconstruction", "formalization-proof", "continuation-stability" ], "domains": [ "Quantum gravity", "Mathematical physics", "Formal methods" ] }, { "id": "sqg3", "collection": "publications", "subtype": "preprint", "series": "schwarzschild-qg", "order": 3, "date": "2026-09-17", "title": "Friedrichs-Selected Schwarzschild Quantum Matter", "subtitle": "A machine-checked real-scalar stress theory, physical-clock coherence, and regulator-independent sources.", "href": "research-friedrichs-selected-schwarzschild-quantum-matter.html", "pdf": "research-friedrichs-selected-schwarzschild-quantum-matter.pdf", "doi": "10.5281/zenodo.22819417", "summary": "The selected scalar is promoted from quantum dynamics to local spacetime matter through action-derived stress, coherent Fock moments, regulator removal, and explicit quantum sources.", "primary_theme": "boundary-measurement", "themes": [ "boundary-measurement", "representation-reconstruction", "formalization-proof" ], "domains": [ "Quantum gravity", "Mathematical physics", "Formal methods" ] }, { "id": "sqg4", "collection": "publications", "subtype": "preprint", "series": "schwarzschild-qg", "order": 4, "date": "2026-09-18", "title": "A Self-Consistent Einstein–Scalar Quantum Sector", "subtitle": "Friedrichs selection, native quantum evolution, and exact gravitational matter.", "href": "research-self-consistent-einstein-scalar-quantum-sector.html", "pdf": "research-self-consistent-einstein-scalar-quantum-sector.pdf", "doi": "10.5281/zenodo.22834305", "summary": "The changed nonlinear geometry owns its own selected quantum law, Fock/Cauchy dynamics, conserved stress, and exact quantum-source branches satisfying Einstein's equation on that same geometry.", "primary_theme": "invariance-identity", "themes": [ "invariance-identity", "formalization-proof", "representation-reconstruction" ], "domains": [ "Quantum gravity", "Mathematical physics", "Formal methods" ] }, { "id": "sqg5", "collection": "publications", "subtype": "preprint", "series": "schwarzschild-qg", "order": 5, "date": "2026-09-18", "title": "Master-Action Ownership of a Self-Consistent Einstein–Scalar Quantum Sector", "subtitle": "Symmetric-projective BV closure, Palatini descent, and quantum Ward/source exchange.", "href": "research-master-action-ownership-self-consistent-einstein-scalar-quantum-sector.html", "pdf": "research-master-action-ownership-self-consistent-einstein-scalar-quantum-sector.pdf", "doi": "10.5281/zenodo.22846743", "summary": "The completed Einstein–scalar sector is traced upstream to an intrinsic symmetric/projective Palatini BV theory whose classical projection binds back to the same native action, source, and clock.", "primary_theme": "formalization-proof", "themes": [ "formalization-proof", "invariance-identity", "relational-organization" ], "domains": [ "Quantum gravity", "Formal methods" ] }, { "id": "sqg6", "collection": "publications", "subtype": "preprint", "series": "schwarzschild-qg", "order": 6, "date": "2026-09-20", "title": "Quantum Gauge Structure of a Self-Consistent Einstein–Scalar Sector", "subtitle": "Operator BRST representation, a retracted physical Hilbert sector, and projective gauge reduction.", "href": "research-quantum-gauge-structure-self-consistent-einstein-scalar-sector.html", "pdf": "research-quantum-gauge-structure-self-consistent-einstein-scalar-sector.pdf", "doi": "10.5281/zenodo.22859436", "summary": "A square-zero BRST charge realizes physical cohomology, embeds the native scalar Fock space faithfully, descends native evolution, and removes the Palatini projective quartet cohomologically.", "primary_theme": "formalization-proof", "themes": [ "formalization-proof", "invariance-identity", "representation-reconstruction" ], "domains": [ "Quantum gravity", "Formal methods" ] }, { "id": "sqg7", "collection": "publications", "subtype": "preprint", "series": "schwarzschild-qg", "order": 7, "date": "2026-09-22", "title": "Regulated Palatini BV Quantization of a Self-Consistent Einstein–Scalar Sector", "subtitle": "Quantum-master obstructions, finite Gaussian BV pushforwards, and restricted physical cohomology.", "href": "research-regulated-palatini-bv-quantization-self-consistent-einstein-scalar-sector.html", "pdf": "research-regulated-palatini-bv-quantization-self-consistent-einstein-scalar-sector.pdf", "doi": "10.5281/zenodo.22904031", "summary": "Finite BV regulators support genuine quantum complexes, while Gaussian refinement exposes a first-shell Hamiltonian descent obstruction and canonically leaves a greatest compatible restricted physical complex.", "primary_theme": "formalization-proof", "themes": [ "formalization-proof", "evidence-validation", "representation-reconstruction" ], "domains": [ "Quantum gravity", "Formal methods" ] }, { "id": "sqg8", "collection": "publications", "subtype": "preprint", "series": "schwarzschild-qg", "order": 8, "date": "2026-09-23", "title": "Relational Quantum Gravity in a Self-Consistent Einstein–Scalar Sector", "subtitle": "Independent physical and gravitational quotients, nonlinear Einstein realization, and intrinsic gauge rigidity.", "href": "research-relational-quantum-gravity-self-consistent-einstein-scalar-sector.html", "pdf": "research-relational-quantum-gravity-self-consistent-einstein-scalar-sector.pdf", "doi": "10.5281/zenodo.22939782", "summary": "Physical-owner and gravity-visible equivalence relations are globally incomparable, while intrinsic curvature data rigidly recover the source parameter and represented geometry class on the fixed nonlinear family.", "primary_theme": "relational-organization", "themes": [ "relational-organization", "invariance-identity", "representation-reconstruction" ], "domains": [ "Quantum gravity", "Mathematical physics" ] }, { "id": "gps1", "collection": "publications", "subtype": "preprint", "series": "gaussian", "order": 1, "date": "2026-09-17", "title": "Closed Matter-Current Constraints and Gaussian Physical Moduli", "subtitle": "Bounded-particle exclusion and all-orders Fock structure in a machine-checked gauge-field model.", "href": "research-closed-matter-current-gaussian-physical-moduli.html", "pdf": "research-closed-matter-current-gaussian-physical-moduli.pdf", "doi": "10.5281/zenodo.22818292", "summary": "Every nonzero joint closed-current state extends beyond every finite particle cutoff while the same kernel contains an injectively parametrized positive-orthant Gaussian family.", "primary_theme": "representation-reconstruction", "themes": [ "representation-reconstruction", "formalization-proof", "invariance-identity" ], "domains": [ "Mathematical physics", "Formal methods" ] }, { "id": "gps2", "collection": "publications", "subtype": "preprint", "series": "gaussian", "order": 2, "date": "2026-09-17", "title": "Pair-Generated Completion of Gaussian Physical States", "subtitle": "Closed quadratic generators, faithful two-particle seeds, and nontruncatable current physicality in a machine-checked gauge-field model.", "href": "research-pair-generated-completion-gaussian-physical-states.html", "pdf": "research-pair-generated-completion-gaussian-physical-states.pdf", "doi": "10.5281/zenodo.22818924", "summary": "A symmetric pair kernel and canonical quadratic creator reconstruct every even sector; the normalized two-particle seed faithfully recovers the Gaussian modulus.", "primary_theme": "representation-reconstruction", "themes": [ "representation-reconstruction", "invariance-identity", "formalization-proof" ], "domains": [ "Mathematical physics", "Formal methods" ] }, { "id": "gps3", "collection": "publications", "subtype": "preprint", "series": "gaussian", "order": 3, "date": "2026-09-17", "title": "From Pair-Generated Fock Structure to Physical Particle Semantics", "subtitle": "Completed Bose/Fock representations, analytic carrier realization, and the boundary of asymptotic particle identity in a machine-checked gauge-field model.", "href": "research-from-pair-generated-fock-structure-to-physical-particle-semantics.html", "pdf": "research-from-pair-generated-fock-structure-to-physical-particle-semantics.pdf", "doi": "10.5281/zenodo.22820148", "summary": "The Gaussian pair receives an exact completed Bose/Fock realization with intertwined Poincaré symmetry while asymptotic-particle identification remains a separate boundary.", "primary_theme": "representation-reconstruction", "themes": [ "representation-reconstruction", "invariance-identity" ], "domains": [ "Mathematical physics", "Formal methods" ] }, { "id": "gps4", "collection": "publications", "subtype": "preprint", "series": "gaussian", "order": 4, "date": "2026-09-26", "title": "Gaussian Pair Geometry and Physical Radiative Response", "subtitle": "Quadratic-sector variational stress, physical-helicity response, and exact information compression in a machine-checked gauge-field model.", "href": "research-gaussian-pair-geometry-physical-radiative-response.html", "pdf": "research-gaussian-pair-geometry-physical-radiative-response.pdf", "doi": "10.5281/zenodo.23001929", "summary": "A faithful three-parameter covariance passes through response maps that retain less information: zero variational stress, one-parameter radiative response, and finally a scale-independent normalized Bose pair.", "primary_theme": "representation-reconstruction", "themes": [ "representation-reconstruction", "invariance-identity", "boundary-measurement" ], "domains": [ "Mathematical physics", "Formal methods" ] }, { "id": "gps5", "collection": "publications", "subtype": "preprint", "series": "gaussian", "order": 5, "date": "2026-09-29", "title": "Source-Aware Weyl-Reduced Celestial Representation", "subtitle": "Joint source-output symmetry and positive-measure obstruction to fixed-source isometry for radiative two-particle Clebsch–Gordan kernels.", "href": "research-source-aware-weyl-reduced-celestial-representation.html", "pdf": "research-source-aware-weyl-reduced-celestial-representation.pdf", "doi": "10.5281/zenodo.23029056", "summary": "Source-aware Weyl reflection admits an exact joint Hilbert reduction, while a positive-measure Gram defect rules out almost-everywhere fixed-source isometric realization of the normalized physical kernel.", "primary_theme": "representation-reconstruction", "themes": [ "representation-reconstruction", "invariance-identity", "relational-organization", "formalization-proof" ], "domains": [ "Mathematical physics", "Celestial holography", "Formal methods" ] }, { "id": "gps6", "collection": "publications", "subtype": "preprint", "series": "gaussian", "order": 6, "date": "2026-10-02", "title": "The Physical Celestial Clebsch–Gordan Transform of a Radiative Bose Pair", "subtitle": "Direct-integral completion, source-Weyl geometry, and all-label uniqueness on the intrinsic physical source range.", "href": "research-physical-celestial-clebsch-gordan-transform-radiative-bose-pair.html", "pdf": "research-physical-celestial-clebsch-gordan-transform-radiative-bose-pair.pdf", "doi": "10.5281/zenodo.23108946", "summary": "On the intrinsic physical source range, the cross-ratio and full signed principal-series transforms are injective for every physical external-label pair, while the retained bounded completion remains conditional on one explicit uniform core estimate.", "primary_theme": "representation-reconstruction", "themes": [ "representation-reconstruction", "invariance-identity", "formalization-proof" ], "domains": [ "Mathematical physics", "Celestial holography", "Formal methods" ] }, { "id": "bio1", "collection": "publications", "subtype": "preprint", "series": "relational-biology", "order": 1, "date": "2026-09-28", "title": "Relational Anatomy of Cell Fate Across Lineage-Resolved Perturbation Experiments", "subtitle": "A finite relational calculus for state, identity, history, and fate across biological systems.", "href": "research-relational-anatomy-cell-fate.html", "pdf": "research-relational-anatomy-cell-fate.pdf", "doi": "10.5281/zenodo.23004119", "summary": "Across lineage-resolved perturbation experiments, exact state–fate recovery concentrates near lineage identity while future-selective alignment remains measurable below exactness.", "primary_theme": "relational-organization", "themes": [ "relational-organization", "invariance-identity", "evidence-validation" ], "domains": [ "Systems biology", "Single-cell biology" ] }, { "id": "bio2", "collection": "publications", "subtype": "preprint", "series": "relational-biology", "order": 2, "date": "2026-10-01", "title": "Relational Organization and Directional Stability Across Mouse Organogenesis", "subtitle": "Relational comparability, developmental direction, and representation stability across the Mouse Organogenesis Spatiotemporal Transcriptomic Atlas.", "href": "research-relational-organization-directional-stability-mouse-organogenesis.html", "pdf": "research-relational-organization-directional-stability-mouse-organogenesis.pdf", "doi": "10.5281/zenodo.23090479", "summary": "A stage-blind spatial-relational carrier reveals recurrence and many-to-many organization; local directional resolution depends on comparison context while the aggregate directional sign persists across the tested representation family.", "primary_theme": "relational-organization", "themes": [ "relational-organization", "invariance-identity", "evidence-validation", "continuation-stability" ], "domains": [ "Systems biology", "Developmental biology", "Spatial transcriptomics" ] } ], "relations": [ { "from": "ns1", "to": "ns2", "type": "continues" }, { "from": "ns2", "to": "ns3", "type": 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"shared_question" }, { "from": "gps5", "to": "gps6", "type": "continues" } ] }