Complementarity-First

道生一，一生二，二生三，三生萬物。
The Tao gives rise to One; One gives rise to Two; Two gives rise to Three; Three gives rise to the myriad things.

More than two thousand years ago, the Tao Te Ching posed a question that still reaches into the foundations of science: how can a world of innumerable distinct things arise from something more unified than the things themselves?

The Taichi Diagram gives the question a visual form. Dark and light are different, yet neither appears as a self-sufficient object. Each is defined within one whole, curves around the other, and carries a trace of its complement. DNA gives the image a living counterpart. Its two strands are distinct and oppositely oriented, but their precise relation allows either one—when the right cellular machinery is supplied—to guide reconstruction of the other.

These are inspirations, not equations. Complementarity-First does not claim that Laozi, the Taichi Diagram, or DNA already contains quantum theory, gravity, or electromagnetism. They motivate a sharper scientific question:

What if relation comes before object?

What if particles, fields, space, and time are not the most primitive entries in nature’s inventory, but later structures through which a deeper relational whole becomes organized and observable?

Foundational Releases I and II develop that question across eighteen public records. Release I contains nine technical papers and an overview, ranging from the primitive relation to quantum foundations, relational time, finite/local gravity, and a bounded Unified Dynamics synthesis. Release II adds three papers on time, three on electromagnetism, a reproducibility dataset, and an overview.

The program is ambitious, but it follows a strict rule:

Nothing may be declared to “emerge” merely because the language makes it sound natural.

A poetic resemblance is not a derivation. A mathematical possibility is not a law of nature. A finite computation is not automatically a continuum theorem. Every step must say what was present, what was added, what followed, what failed, and what remains open.

Relation before object

Complementarity-First represents its proposed primitive schematically as

$$\mathcal C=[a\dashv b].$$

The symbols $a$ and $b$ are distinguishable roles inside the completed relation $\mathcal C$. They are not assumed to be two fully formed objects that existed first and were connected later. The proposal is therefore one of difference without separability: distinction is real, but the roles receive their meaning within a larger completion.

This “priority” is explanatory, not temporal. The claim is not that a relation waited and then manufactured objects. The question is whether object-like carriers, composition rules, geometries, dynamics, and measurements can be reconstructed after relational completion is taken as the starting point.

The bare relation does not provide a vector space, real or complex numbers, dimension, probability, continuity, a metric, a causal cone, a differential equation, an action, a state space, or a measuring apparatus. Release I’s foundational paper makes this underdetermination explicit through independence models: the same relational slogan can coexist with different mathematical carriers and physical rules.

That is why the program uses the word selector. A selector is additional structure that narrows the possibilities: a carrier, a positivity rule, a real form, an orientation, a differential, a boundary condition, a composition law, a state, or an experimental interface.

A compact summary is

$$\text{observed result} = \text{carrier and state} + \text{relation} + \text{selector} + \text{dynamics} + \text{readout}.$$

A selector does not create everything that appears afterward. A door does not manufacture the person who walks through it; it only makes passage possible. The discipline of naming each door is the common method of both releases.

Part I — Release I: building the grammar

Release I at a glance

Release I is the broad foundation of the program. Its nine technical papers ask different questions and use different kinds of evidence:

Strand	Central question	Main contribution
Relational foundation	What does the primitive relation mean, and what does it not determine?	A precise primitive, selector discipline, and independence models showing that probability, geometry, dynamics, and complex quantum theory are not already hidden in the notation.
Quantum reconstruction	Which operational assumptions are needed before complex quantum theory can be recovered?	A conditional reconstruction audit with exact countermodels separating the roles of local equivalence, purification, composition, and probability assumptions.
Two-rebit readout	Can globally real information be invisible to separated local measurements?	An exact hidden-coordinate theorem and concrete joint-gate readout procedures.
Operational objectivity	Can observers agree on a complete public record without determining the full state?	A finite countermodel separating reproducible public objectivity from tomographic completeness.
Relational time	Does a readable clock automatically give time an arrow?	A resource account of records, maintenance, fuel, waste, recurrence, and entropy export.
Finite/local gravity	Can Lorentzian and Regge-like structure arise from paired incidence and transport?	A conditional route from incidence to Lorentzian geometry, transport, Palatini–Regge structure, and two null polarizations on a finite periodic lattice.
Local Regge transfer	Why did a broad transfer rule fail, and what information was missing?	Descriptor-local source sufficiency, prospective blind tests, and a conditional curved-Regge identity.
Six-sector cancellation	When must a local response vanish exactly?	A Reynolds-averaging theorem for an intrinsic six-sector zero mechanism.
Unified Dynamics	Can quantum and gravity descendants share one finite relational architecture?	A common dual-pair/BF-type kernel, exact bridge integration, and a clearly identified variation-space obstruction.

The important point is not that all nine papers have the same status. They do not. Release I deliberately keeps conceptual proposals, conditional theorems, exact countermodels, finite calculations, prospective tests, negative results, and open selectors separate.

How the two releases grow out of classic TCG

Before the Complementarity-First releases, the project had already developed a substantial body of work under Twistor Configuration Geometry (TCG). This earlier, “classic TCG” phase began from twistor and configuration spaces—especially $\mathbb{CP}^3$—and organized candidate gauge, representation, geometric, and numerical structures through explicit postulates, named residuals, and obstruction–construction arcs. Its June 2026 structural review mapped that corpus; it did not claim that TCG was experimentally confirmed or complete.

Releases I and II do not erase or quietly rewrite that earlier work. They ask a more foundational question: which parts of the TCG architecture can be reconstructed from a completed complementary relation, and which must still be supplied?

Release I is the main bridge. Complementarity-First TCG: Paired Incidence, Transport, and the Finite/Local Gravity Architecture was created as a non-duplicative successor to the classic review. It recasts the geometric core in terms of paired chiral incidence, faithful exchange of the two null rulings, and distinct transport classes. With declared choices of rank, real form, orientation, coframe, connection, simplicity data, and action, the construction reaches a Lorentzian null cone and a finite/local Palatini–Regge gravity architecture. On the supplied periodic lattice, eliminating the independent Lorentz connection reproduces the Regge Hessian, and the physical null quotient contains two gravitational-wave polarizations.

The central bridge remains open:

Paired-incidence twistor kinematics does not yet force Palatini–Regge dynamics without additional selectors.

The project has tested both ends of that bridge, but it has not proved that incidence uniquely selects the coframe, connection, simplicity constraints, action, arbitrary triangulation, or continuum theory. Nor do the two releases retroactively validate classic TCG’s earlier chamber-level numerical claims.

Release II extends selected lessons rather than the whole classic TCG apparatus. It carries paired roles, typed carriers, complement operations, and selector discipline into new conditional studies of one-time geometry, quantum clocks, Hodge structure, Maxwell theory, radiation, and quantization. In this chronology, classic TCG is the geometric ancestor; Release I is the audited bridge and finite/local consolidation; Release II is a controlled extension into time and electromagnetism.

The missing step from “Two” to “the myriad things”

The foundational paper does more than introduce the notation $\mathcal C=[a\dashv b]$. It asks what would make such a primitive scientifically useful. Four tests are proposed for a candidate completed relation: its roles must be distinguishable; the relation must constrain them; neither role should exhaust the target description by itself; and the completion must add something nontrivial beyond simply listing two labels.

Passing those tests still does not make the theory generative. To move from a completed pair to networks, histories, fields, or many-body structure, an enriched theory must provide controlled composition, iteration, transformation, or network formation. Symbolically one might hope for a rule that combines completed relations, but writing a composition sign does not supply the composition law.

This is a crucial boundary in the opening paper. The Tao-inspired sequence “One gives rise to Two; Two gives rise to Three; Three gives rise to the myriad things” motivates the research program, but the formalism begins after distinction is already present. It does not prove a transition from undifferentiated One to Two, nor a theorem from Three to the many. “Genesis” names the explanatory target, not a completed cosmogenesis.

That honesty shapes the rest of Release I. Rather than pretending that one primitive symbol contains every later structure, the release treats quantum theory and gravity as parallel reconstruction tests. Each branch asks how much can be built once the missing composition, carrier, geometry, dynamics, and empirical interface are supplied explicitly.

Why quantum theory does not fall out of a pair

The quantum-reconstruction paper begins by asking what the word quantum requires before it has precise content. A bare complementary relation does not yet supply preparations, effects, probabilities, reversible transformations, composites, purification, local tomography, or a rule for combining systems. It does not decide whether amplitudes are real, complex, or quaternionic.

One conditional route starts with a causal operational framework and then adds two stronger principles: a form of local equivalence and an equivalent-system purification condition. Together with an external reconstruction theorem, those inputs can close a route to finite-dimensional complex quantum theory.

The countermodels are as important as the positive route. Finite classical probability theory can satisfy part of the package while failing purification. Real quantum theory can satisfy another part while failing the selector needed for complex closure. Neither extra principle does all the work by itself.

The same audit applies to probability. Binary complementarity and normalization do not uniquely force the Born rule. Additional structure—such as affine behavior under mixing, continuity, or independent-product assumptions—must be supplied before a unique trace-type probability rule follows at the stated scope.

Release I therefore does not say “quantum theory emerges from complementarity.” It says something more useful: the route can be decomposed into independent assumptions, and exact countermodels reveal which assumptions are doing real work.

The same caution applies to purification and entanglement. A theory in which every mixed state has a suitable pure completion already contains substantial structure: a notion of composite system, a state cone, reversible dynamics, and a rule for what counts as an equivalent purifying environment. Complementarity may motivate the search for such a completion, but it does not supply the operational machinery by itself. Likewise, nonseparable states do not follow merely from having two complementary roles. Their existence depends on how composites are built and which states and effects are admitted.

Complex numbers are treated similarly. Real quantum theory provides an exact counterexample to the idea that every quantum-looking operational feature automatically selects the complex field. A route to standard complex quantum theory may close under stronger assumptions, but the scalar field is part of what must be explained, not something that can be inserted unnoticed.

This also sharpens an early Complementarity-First conjecture about probability. Perhaps the state visible to an observer is a restricted image of a more complete relational state:

$$\text{complete relational state} \longrightarrow \text{accessible state} \longrightarrow \text{observed probability}.$$

The first arrow represents restricted access, marginalization, or a quotient-like passage. The second is the evaluation of the accessible state by a measurement. This “projection of a projection” picture is suggestive, but Release I does not promote it into a derivation of objective chance or the Born rule. It remains a research direction.

A quantum coordinate that waits for reunion

The most vivid exact result in Release I concerns rebits, the real-number counterparts of qubits.

A two-rebit state has ten independent real symmetric coordinates, while the span of separated real product measurements reaches only nine. One global direction is silent to that interface. It can be represented by

$$s(\rho)=\operatorname{tr}\!\left[(J\otimes J)\rho\right].$$

The coordinate is part of the full state, yet separated laboratories using only the stated real-local, one-copy resources cannot read it directly for arbitrary mixed states.

Reunite the systems, however, and the situation changes. The paper gives two exact transducers. One uses a connected real joint pulse. The other uses a CNOT gate followed by ordinary local measurements and a parity calculation. Under that gate, the hidden operator is rotated into a product-measurable one:

$$C(J\otimes J)C^{T}=X\otimes Z.$$

The joint operation does not create the coordinate. It turns an existing global feature into a readable population or parity signal.

Copy depth and reference structure add another layer. Two separated copies can reveal $|s|$, while the sign remains tied to an oriented reference under the stated restrictions. The lesson is broader than rebits:

Observability belongs to a state-plus-interface, not to a state in isolation.

Control topology, number of copies, shared orientation, and the allowed final measurement can determine whether a real physical coordinate is invisible, partially visible, or exactly readable.

Objective facts without complete knowledge

A companion paper asks whether public agreement implies a complete description of reality.

It constructs a detailed public certificate: observers declare their access, calibrate interventions, preserve evidence pedigree, reproduce the procedure, and agree on every implemented statistic. Two distinct states pass the same complete certificate. Every public product outcome has the same probability for both states.

The agreement is real. The observers have not made an error. Their interface is simply noninjective: more than one underlying state produces the same public record.

A separately admitted global measurement then distinguishes the two states strongly: in the paper’s finite example, the public product outcomes are identical while the global query separates the states with total-variation distance $3/5$, giving an equal-prior discrimination success probability of $4/5$. The example therefore separates two achievements:

• Operational objectivity: qualified observers can establish a stable, reproducible fact relative to a declared interface.
• Tomographic exhaustiveness: that interface uniquely determines the full underlying state.

The first does not imply the second. A map can be reliable without being one-to-one with the territory.

This is one of Release I’s most important conceptual results because it reframes “hidden information.” Missing information need not be mystical or unknowable in principle. It may be perfectly well defined yet inaccessible to a particular public architecture.

A clock is not an arrow

Relational time can describe one subsystem changing with respect to another without assuming an external universal clock. But a variable that orders events does not explain why time appears directed.

A film running backward still has an ordered sequence. What looks wrong is the behavior of records: smoke returns to a candle, fragments assemble into a glass, and memories disappear toward what we normally call the future.

Release I separates a readable clock from the physical machinery that sustains a record arrow. Stable records require writable memory, unused capacity, error detection, repair, organized free energy, and somewhere for entropy and discarded information to go. A reversible interaction can write a record and erase it when reversed. A finite closed controller can preserve information for a long time and still confront recurrence, exhausted capacity, or accumulated waste.

The result is not a universal lifetime formula for every memory. It is a structural boundary:

The thermodynamic arrow depends on the economy of creating, protecting, and exporting records; it is not supplied for free by a clock variable.

The past is not merely what comes earlier in an ordering. It is what has left stable evidence.

Records as a bridge from time to geometry

Release I also asks what stable, calibrated records can reveal about geometry. Suppose a finite network preserves enough information about which signals or displacements are null-related, how local frames are aligned, and how comparisons change around loops. Under the admitted reconstruction conditions, those records can recover a finite Lorentzian geometry.

That does not mean a memory device creates spacetime. The records are evidence carried by an already specified operational architecture. Nor do they exhaust every underlying degree of freedom. A finite set of metric and incidence data may reconstruct the Lorentzian geometry relevant to the measurements while leaving spinorial, orientation, or hidden-carrier information undetermined.

This is the geometric counterpart of the objectivity result. A public record can be sufficient for one target—such as a finite metric reconstruction—without being a complete description of the total carrier. Release I repeatedly replaces the question “Is the description complete?” with the more precise question “Complete for which operational target, under which interface?”

From incidence to finite/local gravity

The gravity branch asks whether geometry can be reconstructed from incidence—which elements meet, overlap, or satisfy a null relation—rather than assumed from the start.

Complementarity alone does not produce four-dimensional Lorentzian spacetime. The construction first selects a rank-two paired-chiral carrier, a suitable real structure, spatial and temporal orientation, displacement data, transport laws, simplicity conditions, gluing rules, and an action architecture.

The transport analysis itself has layers. The two chiral sectors may be transported independently; they may be constrained to respect a complement relation; or they may be locked into a still narrower helix-like subclass. Treating the locked case as though it were the only possible transport law would hide a selector. The paper therefore classifies the possibilities before choosing one.

Once those ingredients are explicit, a striking conditional chain becomes possible. On a selected Hermitian real slice, incidence becomes a determinant-null condition. Polarizing that determinant yields a Lorentzian conformal metric. Additional nondegeneracy and simplicity conditions permit common-coframe data. Transport around loops separates curvature from coframe nonclosure, and the branch reaches a discrete first-order Palatini–Regge architecture related to general relativity.

On one frozen periodic lattice, the physical metric quotient has six components away from the characteristic cone. On the nonzero null cone, the rank drops by two, leaving exactly two physical null polarizations—the familiar count for classical gravitational radiation. Eliminating the independent connection also produces a response matching the corresponding Regge Hessian coefficient by coefficient on the tested momentum fibers.

These are exact finite/local achievements. They are not quantum gravitons, an arbitrary-mesh theorem, a continuum limit, or a full derivation of nonlinear Einstein gravity. Their value lies in showing how far an incidence-and-transport architecture can be carried while every selector remains visible.

When failure becomes part of the result

Release I records failed routes instead of rewriting them as successes.

A scalar “helix phase” was tested as a possible universal transport variable. In the local family examined, it did not select a unique physical global phase. Broader matrix-valued or nonlocal mechanisms remain open, but the simple shortcut failed.

A broad gravity-response transfer failed more dramatically. The failure revealed that the changed geometry carried local incidence and normalization data that the proposed transfer rule had ignored. The research then moved to richer local descriptors. In later tests, the geometry, descriptor, and predictions were frozen before the target responses were examined.

Across three authenticated fixtures, nearly half a million components were checked prospectively within the admitted finite family. The result is strong evidence for descriptor-local source sufficiency and a conditional curved-Regge identity in that family. It is not an arbitrary-triangulation law or external independent replication.

A separate gravity paper studies the opposite phenomenon: when symmetry forces a response to be exactly zero. For a complete six-sector orbit with exact $S_3$ equivariance, Reynolds averaging isolates the invariant part. If that part is absent, the six contributions cancel exactly.

The two results answer different questions. One asks what information is sufficient for a nonzero response. The other identifies a symmetry that forces zero. Their coexistence is a model of the release’s “anti-flattening” rule: success, failure, and exact cancellation must not be summarized as one vague statement that “the gravity calculations worked.”

A common grammar for quantum theory and gravity

The Unified Dynamics paper asks whether the quantum and gravity branches can live inside one finite relational architecture.

Its starting point is a real doubled carrier $W=E\oplus E^*$ with a cross-pairing, a grading, a positive exchange, and paired transport. That one carrier supports distinct descendants: positive-cone structures useful for operational quantum theory and symplectic structures useful for dynamics. The broad doubled carrier is still too permissive to select gravity, so the paper enriches it with a rank-two Jordan/spin-factor structure before the Lorentzian branch becomes available.

On the quantum side, the synthesis incorporates a “Quantum Bridge” program. At finite scope it distinguishes process orientation from state orientation, identifies nonlocally silent global directions, studies which generators preserve the relevant positive cones, and separates positivity from complete positivity and trace preservation. In ordinary language, it asks not only whether a map sends allowed states to allowed states, but whether it remains physically valid when an untouched ancillary system is present. Encoded carriers can close some minimal quantum gaps even when the larger hidden-carrier and elementary-type questions remain open.

These results do not turn the primitive relation into a finished quantum channel theory. They show that once the operational carrier and order structure are supplied, the relation-first architecture can host exact questions about positive semidefinite order, CP/CPTP semantics, nonlocal generators, and encoded propagation.

The paper then identifies a common BF-type kernel, a first-order pairing between field-like and curvature-like variables. The same kernel can host two descendants.

In the gravity branch, the field-like variable is constrained into a tetradic form built from coframe data, and varying that coframe allows a curved sector. In the compact relational branch, the analogous variable is treated as an independent multiplier-like degree of freedom, and its variation imposes a different condition.

The common action grammar therefore does not choose the physical branch. The branches differ in their admissible configuration and variation spaces. Release I calls this the variation-space selector obstruction.

A second coherence problem also remains open: the primitive role exchange, the orthocomplement used in quantum-style structures, and the parity operation used in gravity have not been proved to descend from one universal complement operation. Similar notation is not enough.

The Unified Dynamics synthesis is consequently substantial but bounded. It provides a common carrier, common kernel, exact finite bridges, and a maturity ledger. Its gravity side also consolidates the descriptor-local and zero-germ branches and records a conditional local curved-Regge identity with 1,818 authenticated historical admissions on three fixtures. That count certifies the admitted finite history of the test family; it is not a proof for every triangulation.

The synthesis does not derive Newton’s constant, the cosmological constant, particle masses, an absolute length or duration, a continuum unification, or a parameter-free prediction.

What Release I handed forward

Release I’s deepest achievement is architectural. It converts broad foundational questions into typed, testable problems:

• Can controlled composition and “Three-to-the-many” be derived from the primitive relation rather than merely inspired by it?
• What selects the Born rule, purification, and nonseparable composition?
• What chooses the physically relevant carrier, real structure, dimension, orientation, and absolute scale?
• Can local transport and Regge results be extended to global gluing, arbitrary meshes, and a continuum limit?
• What selects the variation space that separates gravity from other descendants?
• Can the program produce a quantitative, parameter-free experimental prediction?

Release II does not retroactively close these questions. It takes a selected subset—especially the rank-two carrier, complement operations, clock structure, and field-form architecture—and follows them into time and electromagnetism.

Part II — Release II: from one-time structure to electromagnetism

One time direction, not two role labels

Release II begins with a common misunderstanding: if the primitive relation contains two roles, does that imply two dimensions of time?

No. At the primitive level, no metric or time count exists. Two role labels are not two timelike coordinates.

After a finite Euclidean Jordan framework and a causal-carrier bridge are supplied, the Time branch asks what happens when a primitive role and its full algebraic complement are both required to remain primitive. Under that stronger condition, the carrier has rank two. Its nonclassical simple descendants are spin factors with one distinguished completion direction and an $m$-dimensional distinction sector. Twisting a positive pairing by the canonical complement gives signature $(1,m)$.

Within that declared framework, there is one timelike direction and $m$ spacelike directions. The value of $m$ and the absolute duration of one second are not yet fixed.

The same complement can perform another job on another carrier. Applied to one leg of a suitable identity-pairing tensor, it produces a singlet-like state; on the selected complex-qubit carrier, this is the Bell singlet. That result is not electromagnetism, and the exchange dynamics is not gauge symmetry. It illustrates a principle that becomes central in Release II: the meaning of an operation depends on the carrier on which it acts.

From a causal carrier to a readable clock

A one-time carrier is not automatically a clock. Release II distinguishes a raw relational magnitude, a normalized interval, a supplied proper interval, a shared comparison parameter, quantum phase, a readable transition, and the thermodynamic arrow.

A quantum system becomes minimally phase-readable only when the chosen state and observable contain at least one nonzero oscillating frequency component. Writing down a Hamiltonian is not enough.

For clock comparisons, the observed endpoint signal separates into propagation and local calibration. In a supplied weak-field setting, complete mass-energy coupling is sufficient for common internal spectral scaling at the retained order. But the framework does not force universal matter coupling: a complement-compatible species-dependent clock model provides a counterexample.

A two-level clock can also hide certain perturbations behind a simple rescaling, while a connected three-level system can expose a change in spectral shape. This motivates a possible multiclock experiment, but Release II does not claim that such an experiment has been performed or that a numerical redshift anomaly has been predicted.

Why three spatial dimensions appear—conditionally

The first Electromagnetism paper imports the one-time carrier with $m$ spatial directions and then supplies a decisive extra choice: field-like objects are represented by two-forms.

The two-form space splits into

• $m$ planes containing the time direction, and
• $m(m-1)/2$ purely spatial planes.

If an invertible map is required to exchange those complementary sectors, their dimensions must match:

$$m=\frac{m(m-1)}{2},$$

whose nontrivial positive solution is

$$m=3.$$

The result is a conditional one-time-plus-three-space balance. Time alone did not select three space dimensions; the argument also used the two-form degree and the invertible sector exchange. Nor does equal dimension choose a unique metric, orientation, constitutive law, or Hodge operator.

From a Hodge arena to Maxwell theory

A Hodge operator relates complementary two-forms. In a suitable four-dimensional Lorentzian setting, applying it twice gives a minus sign, so the two-form space behaves in one limited sense like a complex vector space.

Release II does not infer that structure from resemblance alone. Reciprocity, closure, reality, orientation, and Lorentz-admissibility conditions are added to a constitutive map before a conformal Lorentzian Hodge arena follows.

Even then, Maxwell theory is not complete. A pointwise algebraic operator does not supply the exterior derivative, a potential $A$, the relation $F=dA$, locality, gauge redundancy, sources, or an action.

The second Electromagnetism paper adds those layers explicitly. Under a supplied differential complex, one-form potential, locality, quadraticity, first derivatives, constant background, and variational principle, the most general real local quadratic first-derivative action is the Maxwell kinetic term plus a constant theta term, up to boundaries.

The paper keeps three operations separate:

• Hodge action on field strengths;
• electric–magnetic duality, which rotates nonzero fields;
• gauge transformation, which changes the potential while leaving the field strength fixed.

A principal-bundle connection can be described as a horizontal/vertical complement, and curvature measures its nonintegrability. But complementarity does not choose a preferred connection. Compact $U(1)$, integral flux, charge units, monopoles, and the observed matter spectrum all require further global or material input.

The paper also constructs an exact finite Abelian descendant after supplying a periodic cochain complex, a constitutive matrix, a central phase, and a Maxwell branch. It has finite gauge invariance, Bianchi closure, current conservation, flat holonomies, and topological sectors. It is a controlled descendant, not a derivation of continuum electromagnetism from the primitive relation alone.

Light, helicity, and the boundary before QED

For a nonzero source-free null plane wave, the real electric and magnetic fields are transverse, orthogonal, equal in magnitude, and jointly determine the energy-flow direction. This is a genuine modewise complementary relation.

It is not a universal pointwise law. Because Maxwell theory is linear, superposed waves can produce events where the electric field is nonzero and the magnetic field vanishes.

Release II also separates Hodge chirality $\sigma$, frequency sign $\operatorname{sgn}(\omega)$, and helicity $h$. With fixed conventions,

$$h=\sigma\,\operatorname{sgn}(\omega),$$

but the three labels are not identical. Complex conjugation reverses chirality and frequency together while preserving helicity; parity reverses helicity; electromagnetic duality phases the Hodge sectors.

The arrow of time therefore does not select photon helicity.

Quantization introduces another boundary. The reduced Maxwell phase space has a symplectic pairing, but canonical commutation relations require a supplied $\hbar$ and a quantization rule. A Fock space also requires a positive-frequency complex structure. That structure acts on reduced phase space, whereas the Hodge operator acts on spacetime two-forms. They are not the same object, and classical electromagnetic geometry does not uniquely choose a vacuum.

Once matter representations are supplied, gauge covariance can build scalar and spinor QED classes. Power counting and anomaly cancellation constrain them but do not choose the electron, masses, or charge values. Infrared physics adds soft-photon dressing, so a local perturbative action alone does not supply the complete physical charged sector.

Release II therefore reaches a carefully marked QED boundary. It develops conditional radiation, helicity typing, free quantization structures, and certain topological quantum relations. It does not derive numerical $\hbar$, a preferred vacuum, matter content, renormalization, infrared completion, or full QED.

Its companion dataset, CEM-D1, links the Electromagnetism papers to exact finite certificates, fixtures, scripts, and claim-to-evidence maps. Those checks strengthen traceability; they do not replace manuscript proofs, prior literature, external peer review, or independent replication.

What the two releases show together

Similar-looking operations are not automatically the same

Across the two releases, many operations look alike: role complement, time reversal, tensor-leg complement, quantum orthocomplement, Lorentz parity, Hodge duality, electric–magnetic duality, gauge transformation, positive-frequency complex structure, and a clock generator.

A loose story could merge them into one grand “duality.” The program refuses.

Each operation has a carrier and an algebra. An involution on a rank-two causal carrier is not the Hodge star on two-forms. Hodge duality is not gauge redundancy. A singlet-producing tensor twist is not an electromagnetic field. A clock Hamiltonian is not a photon-helicity operator.

This carrier-and-algebra firewall is one of the program’s most useful conceptual tools. It prevents analogy from silently becoming identity.

Failures belong in the map

The releases also argue for an unusual standard of scientific maturity: the boundary of a result is part of the result.

A conceptual inspiration is labeled as inspiration. A theorem keeps its assumptions. A finite certificate is not promoted to a continuum law. A balanced dimension count is not called a unique metric. A failed transfer is not rewritten as a success. An internal AI-assisted audit is not called external human peer review.

This “anti-flattening” discipline matters especially in a large foundations program, where a chain of conditional results can easily be retold as a single unconditional derivation.

One program, two distinct releases

Release I builds the grammar: primitive relation, selector discipline, quantum assumption audits, interface-relative observability, record-based time asymmetry, finite/local gravity, explicit failed transfers, exact cancellation mechanisms, and a common but branch-incomplete dynamics kernel.

Release II follows selected threads into a one-time carrier, quantum clocks, conditional three-space balance, Hodge structure, Maxwell reconstruction, radiation, helicity, quantization, and the QED boundary.

The connection is real, but Release II does not revise Release I retroactively. A later result may illuminate an earlier open problem without changing what the earlier paper proved.

The combined reconstruction ladder is roughly

$$\text{completed relation} \longrightarrow \text{selected carrier} \longrightarrow \text{composition and geometry} \longrightarrow \text{differential dynamics} \longrightarrow \text{modes} \longrightarrow \text{quantization} \longrightarrow \text{matter and measurement}.$$

Nearly every arrow contains an explicit selector. That is not a weakness to hide; it is the diagnostic output of the program.

The frontier

The two releases turn several broad mysteries into sharper questions:

• Can controlled composition be derived from the primitive completed relation?
• Can the “projection of a projection” idea become a genuine account of objective probability and the Born rule?
• What selects purification, complex amplitudes, and nonseparable composition?
• Why should the physical field degree be two, and what selects the sector exchange that yields three spatial dimensions?
• Can a unique constitutive or Hodge structure be selected rather than supplied?
• Can finite/local gravity survive arbitrary meshes, global gluing, refinement, and a continuum limit?
• What selects a positive-frequency structure and vacuum on general backgrounds?
• What chooses the variation space, matter content, charge pattern, and absolute physical scales?
• Can the program produce a parameter-free prediction or a realizable multiclock test?

These are not decorative questions left after a completed theory. They are the frontier exposed by making the dependencies explicit.

A different kind of foundational ambition

Complementarity-First does not presently offer a completed theory of everything. Its ambition is methodological as well as physical: reconstruct as much as possible from a relation-first starting point, while refusing to hide the assumptions that make each step work.

Across Releases I and II, the program identifies information that is real but interface-hidden; separates public objectivity from complete state determination; distinguishes clock order from thermodynamic irreversibility; builds conditional finite Lorentzian and Regge structures; supports a one-time carrier under a declared rank-two bridge; derives a conditional one-time-plus-three-space balance for two-form sectors; reconstructs a Maxwell host layer by layer; separates chirality, frequency, and helicity; and marks the point where classical electromagnetism stops short of selecting quantum state, matter, and full QED.

Just as important, it records what those constructions do not yet explain.

Physics advances when an equation succeeds. It also advances when a hidden assumption is dragged into the light and turned into a question that can be derived, tested, rejected, or shown to be indispensable.

That is the wager connecting the two releases:

Begin with relation. Add nothing silently. Distinguish every carrier. Name every selector. Preserve the failures. Then ask how much of the physical world can genuinely be rebuilt.

Scientific-status note: This article is a popular-science synthesis, not a technical paper in either release. Foundational Releases I and II are author-controlled preprint and data corpora. Their internal AI-assisted reviews, exact certificates, and separated audit lanes are not external human peer review or external independent replication. The program does not claim that primitive complementarity has already derived probability, spacetime, electromagnetism, matter, or quantum electrodynamics without additional assumptions.