Can distinct subjects belong to one experiencing whole? Within Recognition Science’s shared physical architecture, we derive an exact criterion: every finite collection of felt occurrences belongs jointly to a subject if and only if the all-occurrences profile lies in the closure of existing subjects’ profiles. For a nonempty felt domain, closedness yields an existing whole; nested membership preserves distinct participants. The physical derivations establish matter–photon correlation under the complete atomic source, a fixed observable with an absolute correlation margin, and all-time record retention under a specified holding interaction. Signed operators give exact coherent code capture. A complete finite receiving Hamiltonian captures coherent input with error at most C_v/√N for N bank cells and any normalized initial stock, while retaining the native stock clock and every finite passive reference. A normalized product partner evolving under its independent native clock preserves the same bound. With injectively matched contacts covering the bank, the full receiving and contact Hamiltonian also gives a bank-size-independent constant, including coherent inputs and every finite passive reference. These results assume supplied stock and contacts. The remaining connections are physical realization and completeness, recognition’s experiential identity, actual finite subject composition, and realization of the whole-subject limit. These conditions distinguish the positive account from its unfinished universal derivation. AI-use disclosure: OpenAI Codex assisted with source analysis, Lean formalization, manuscript drafting, and independent critique within the author’s Recognition Science research.
Can distinct subjects belong to one experiencing whole? Within Recognition Science’s shared physical architecture, we derive an exact criterion: every finite collection of felt occurrences belongs jointly to a subject if and only if the all-occurrences profile lies in the closure of existing subjects’ profiles. For a nonempty felt domain, closedness yields an existing whole; nested membership preserves distinct participants. The physical derivations establish matter–photon correlation under the complete atomic source, a fixed observable with an absolute correlation margin, and all-time record retention under a specified holding interaction. Signed operators give exact coherent code capture. A complete finite receiving Hamiltonian captures coherent input with error at most C_v/√N for N bank cells and any normalized initial stock, while retaining the native stock clock and every finite passive reference. A normalized product partner evolving under its independent native clock preserves the same bound. With injectively matched contacts covering the bank, the full receiving and contact Hamiltonian also gives a bank-size-independent constant, including coherent inputs and every finite passive reference. These results assume supplied stock and contacts. The remaining connections are physical realization and completeness, recognition’s experiential identity, actual finite subject composition, and realization of the whole-subject limit. These conditions distinguish the positive account from its unfinished universal derivation. AI-use disclosure: OpenAI Codex assisted with source analysis, Lean formalization, manuscript drafting, and independent critique within the author’s Recognition Science research.
What physical structure makes an acting, remembering system a person, and what makes its later experience belong to the same subject? Recognition Science connects this question to retained comparisons and the relationships an action changes. We derive exact constraints on that connection. A fixed reversible update stores and rereads a finite history; its main-state trajectory through one tape cycle determines the entire encoded initial state. Linearity excludes exact readout of every encoded pure state when the apparatus must also leave it unchanged and uncorrelated with the record. Exact universal duplication of a native signal is incompatible with linear evolution, while reversible transfer is possible. Participant consent survives grouping of subjects precisely when authorship is constant within each group. A unique fixed-total ledger extension retains native account updates and the external bond’s participant effects. At a common native operand product, endpoint pulse-energy changes equal the corresponding scaled cost and signed-harm changes. These results constrain physical history, transfer and authority. Identifying that history with an experiencing subject still requires an occurrence-level experiential identification and a sound and complete law of subject composition. We state those obligations on the same physical objects.
Recognition Science describes one ledger of recognition events, yet experience arrives from inside separate perspectives. We ask what in the ledger's own dynamics makes a perspective, for one explicit operation: the native recognition step, in which two eight-state clock channels exchange occupation, post a three-component current and move an integer loop flux. Boundaries. For the algebra of native events, every closed invariant subspace of histories is a join of atoms, the atoms are exact superselection sectors with no environment involved, and the atoms an actual history occupies are fixed at its beginning. Neither a symmetric rule nor an element of that algebra selects among them, although a larger read algebra crosses these walls. Participants. Inside a boundary the postings select. Exactly a four-dimensional subspace of the 64-dimensional cell never acquires neutral weight under any record: two persistent loop currents and an occupation oscillation. Three postings expose every other state, and the selected states are exactly those that pass the eight-tick window on the loop edge with certainty. On every network of contacts in its round order the kept states obey a parity law, the kept projection commutes with every round word, so composition creates no kept weight, and participation on a connected network is joint. Other timings act through one token mechanism, which decides births, fair and gated participation, random timing and what a participant's own record reads of its world. Records. A participant's own record decides its status; the conditional present purifies; its long-run motion is a classical chain that is reversible exactly on the participant classes and carries a stationary circulation elsewhere. Every record reads each site only within the same twelve directions, and composites of participants add only crossed products of their members' reads. What is supplied. The book locates every stated premise and identification: the step and its loop-edge routing, the window's account and tick, the genesis state, contact locality, orientation and posting order, the gate and the independence of attempts, the relay's extra terms, least-cost booking of postings, the capture apparatus, the photon dictionary, the present and the experiential reading of a sure subject. On the ledger's torus, locality, symmetry and the existence of a contact place the contacts on nearest-neighbour pairs, and the native posting is the product of eighth-turns of the relay's photon-free terms. It gives the case for the experiential reading and states every open problem exactly. Full manuscript, 402 pages. Preliminary manuscript shared for discussion. It has not been peer reviewed.
A physical identification requires a domain of experiments, a realization, and an observation that distinguishes competing mechanisms. We construct these for the δ framework. Within finite causal quantum experiments, computable Choi data are equivalent to finite arithmetic programs producing valid instrument approximations at every requested accuracy. A separate pointer reader preserves the quantum posterior and supports adaptive composition. For the native two-atom census, the actual join update and common-mode retention select golden scaling and a signed contraction. Coherent return selects its minimal conserving completion; an independently calibrated spectral band then selects its constant interaction. A bright-mode construction and a stable short-time calibration procedure supply an explicit realization and uncertainty budget; measured duration and frequency supply the dimensional units. We derive a general endpoint identity between stored record energy and comparison imbalance, and distinguish the monotone fresh-record trajectory from coherent recurrence. The logical-to-physical bridge also has a sharp boundary: an explicit instance of the proposed completion generator has no effective value-reflecting physical reader or numerical comparison receipt. Sequence completion requires precisely the corresponding halting-oracle resource, not an unexplained scalar cost. This obstructs operational completion while leaving purely proof-language transport distinct. Native implementations of identical logical strength nevertheless carry different physical receipts. Joint covariance and the exact endpoint law state the valid relationship between those quantities. Finally, calibrated return and three-outcome tests distinguish the relevant phase and recording alternatives, with quantitative error bounds. First public preprint release, version 1.0. The files include the PDF and the main TeX file. AI-use disclosure: AI assistance was used for source analysis, mathematical exploration, manuscript drafting and revision, diagram preparation, and computational verification support. GPT-6 Astra reviews assessed arguments, scope, readability, and schematics. These were internal model reviews, not external peer review. Jonathan Washburn is the sole listed author and is responsible for the released manuscript.
A physical description must preserve distinguishable occurrences, the information needed to compare them, and records available to later interactions. We examine what these requirements force within Recognition Science, keeping the premises of each implication explicit. Finite record constructions give arithmetic with a ledger of logical commitments. A specified comparison apparatus, continuous reporting and reference calibration fix the reciprocal cost, while a positive additive reading and a first costly join force golden scaling. A linking requirement selects three dimensions within the stated spherical spatial class; a complete one-bit cyclic pass through three binary coordinates then has minimum length eight. Factorization, order and calibration determine the corresponding recognition weight. In a finite quantum carrier, preservation of calibrated sharp-decision optima forces exact state recovery, including correlations with a retained reference. We also identify what these mathematical results require of a physical realization: acquisition of the supplier state, complete resource accounting, attachment of controller and record dynamics, turnoff, and record retention. Ethical and economic effects act on the same physical bond ledger. The experiential interpretation requires a further admissibility law and a distinct subject-composition condition. The result is a connected account of forced structure and its physical premises, with explicit boundaries between a uniqueness theorem, a constructed representation and an enacted process.
When the conditions under which a record is formed remain fixed, a physical theory may represent that record completely by a unary law of the state observed. This paper asks what structure is forced when the same independently certified physical identity gives different complete records under different formation conditions. The initial datum distinguishes two typed empirical roles, while the state identity of the formation side is derived from its complete behavior. Failure of factorization through the first projection proves that the formation-side role cannot be deleted. The complete row and column behaviors of the primitive law then determine two kernel pairs and their coequalizers. Unique descent retains every observable distinction while removing every redundant label, and the resulting realization is terminal among all exact role-preserving realizations. The product pairs the reduced roles; a pullback extracts the combinations on which records can actually be formed. Only after these steps does exponential transposition identify each surviving formation class with one complete response map. The resulting bijection supplies the state criterion and establishes the observation-state object. Compatibility with the antecedent theory preserves the independently given physical state space and yields the physical–observation law in which a fact is generated jointly by the state observed and the state of observation. The same construction gives exact criteria for conditional, label-free, and joint identifiability and selects the same-source pullback on which transport may subsequently be defined. A nonzero coherent response on that pullback yields the phase-transport fundamental equation, the first fundamental equation written directly on observation space. Quantum theory subsequently enriches this canonical interface. Coherent response and full circular phase select the complex field; reversible binary mixing yields CP1 ∼= S2 ; independent composition creates the four-dimensional event domain; response-event identity glues probabilities across complete contexts; and Gleason representation with marginal consistency gives the Born trace pairing. The two-qubit correlation tensor then yields the singlet cosine law, the CHSH inequality, the Tsirelson bound, and the Horodecki spectral criterion. Bell violation is thereby identified with the absence of a positive global answer section across incompatible observation states. The quantum formalism is thereby closed into one architecture: complex state geometry describes coherent physical possibility, complete observation states specify the ways in which facts may form, the Born interface joins them, and quantum instruments carry a realized fact into subsequent dynamics. Fixed observation sections recover classical unary laws, while smooth equivariant enrichment lifts relativistic frame geometry and internal gauge geometry to the same joint domain. The central result is ontological. Physobser Theory admits observation into objective physical reality not as a mind, an external readout, or a perturbation, but as an irreducible state-bearing axis; a fact is generated at its lawful interface with physical state. Category theory is the proof instrument. The discovered physical content is the dual-axis constitution of facts, which supplies a common foundation for quantum, classical, relativistic, and gauge physics.
A durable quantum record, the location of its coherence, and a uniquely actual outcome are different physical questions. We study their separation in a supplied finite-dimensional quantum theory. An explicit, time-independent apparatus couples a system–detector encoding to a controller, a distinct archive, and a finite returning source. A conditional energy penalty suppresses release of the original record without deleting its return coupling. An invariant reduction and a one-sided spectral-gap estimate yield a certified interval with archive occupation above 0.98438, controller-latched occupation above 0.99161, and filled-but-unlatched weight below 2.402 × 10^-7 in one stated design. The same record statistics admit different source-label overlaps and hence different coherence on a specified retained boundary. A conserved product of complementary exchanges accesses that coherence when the finite source is included. Given a calibrated multiregister reader, its finite-duration response separates the coherent apparatus from an independently added archive-gated reduction law, with the added process left active during readout. A conservative example retains a response gap above 0.01717 after separately stipulated one-percent error allowances. The contribution is the finite construction and its quantitative retention, access, and readout interfaces. Quantum carriers, Hamiltonian couplings, trace readout, source preparation, and the reader are supplied; local reader synthesis, empirical calibration, absolute rate selection, and unique-event actualization are not established. Paper code: CFQR-P1 (Complementarity-First Quantum Records — Paper 1). The associated bundle contains the technical supplement, editable LaTeX, numerical checking programs and rational certificates, and selected Lean sources with returned build and axiom-audit evidence. The 39 supporting declarations are partially formalized; eleven recorded type excerpts contain printing elisions. This is not end-to-end formalization, external human peer review, an experimental detection of fundamental collapse, or a derivation of unique-event actualization. Author-owned manuscripts, documentation and mathematical data are CC BY 4.0; author-owned software is MIT, subject to the bundle’s licence map and third-party notices.