The exterior identifiability theory (papers 1-3 of this program) is turned interior: in the collision-model architecture of quantum Darwinism, the causal structure itself hands out operation credentials, and the question becomes whether the world can certify its own factorization from the records it keeps. Generator level: one-sided sufficiency with a closed-form sine law; the parity-twist theorem (redundancy is structurally powerless against exactly one global ghost); four restoration laws with derived constants (tilted writes (4/3)/sin^2 eta; second readout basis 8/5 exactly; one odd-dimensional cell free, with the interior/exterior quantifier reversal; dissipation (4/15)(5+p)/p: objectivity needs an open world). Statistics level: the chain law (relational timing with gentleness dampers), the complementarity floor with interior optimal write strength, and the dividend: weak records at the interior optimum extract MORE frame information than projective records, superlinearly (~K^1.85, sustained through K = 10, factor 5.1 at K = 10), with mechanism (shared-fragment covariance conditioning), the readout gap split in half (product bases recover half the quantum-Fisher gap at every K), and re-collision potency with an intra-fragment two-time accumulation mechanism confirmed two ways. Pre-registered; deaths ledgered.
The exterior identifiability theory (papers 1-3 of this program) is turned interior: in the collision-model architecture of quantum Darwinism, the causal structure itself hands out operation credentials, and the question becomes whether the world can certify its own factorization from the records it keeps. Generator level: one-sided sufficiency with a closed-form sine law; the parity-twist theorem (redundancy is structurally powerless against exactly one global ghost); four restoration laws with derived constants (tilted writes (4/3)/sin^2 eta; second readout basis 8/5 exactly; one odd-dimensional cell free, with the interior/exterior quantifier reversal; dissipation (4/15)(5+p)/p: objectivity needs an open world). Statistics level: the chain law (relational timing with gentleness dampers), the complementarity floor with interior optimal write strength, and the dividend: weak records at the interior optimum extract MORE frame information than projective records, superlinearly (~K^1.85, sustained through K = 10, factor 5.1 at K = 10), with mechanism (shared-fragment covariance conditioning), the readout gap split in half (product bases recover half the quantum-Fisher gap at every K), and re-collision potency with an intra-fragment two-time accumulation mechanism confirmed two ways. Pre-registered; deaths ledgered.
An interior observer cannot step outside its world to test the quantum probability rule; everything it knows arrives through records written into its own memory. This paper asks what such an observer can certify about the rule from those records alone, within a minimal two-record collision register. Results: the register's complete memory-side statistics (census) in closed form, making it a self-calibrating interior tomograph; an interior Gleason theorem at first order (the audit's response matrix has full rank with kernel exactly the Born-model tangent; the threshold is two records); the global forgery geography (a bounded shell and a lattice stratum pass every identity) with an identity-futility theorem proving this necessary and an exact repair (one PSD condition on a back-action-corrected moment matrix, complete at two records with gauge classified); the completed arena (det M_c = sin^2 phi (1 - |b|^2): one complex PSD condition is physicality plus tomography, its imaginary part the register's measurable complexness); the real-amplitude strike (complexness is credential-relative: cell dimension and readout sharpness; with both enforced, real registers are convicted by the census's zero channels at a dial rate of 0.40 census gap per unit certified sharpness); and a hardware campaign on ibm_kingston in which the audit detected, localized, mechanism-confirmed, and time-tracked a device systematic. Pre-registered throughout; failed predictions ledgered in an appendix.
Version 1 (first deposit, 2026-08). 19 pages. Every quantitative claim traces to a pre-registered evidence block with an archived log in the companion zip; the ledger of failed predictions is an appendix of the paper. A long-running dispute asks whether a quantum world selects its own decomposition into subsystems from the Hamiltonian and the state alone. Stoica (Adv. Theor. Math. Phys. 26, 3895 (2022)) proves that a structure so constructed cannot be both essentially unique and physically relevant, the non-uniqueness being modulo the unitaries commuting with H; Soulas, Franzmann and Di Biagio (arXiv:2512.07468) object that producing a second structure that way modifies the input pair, and prove a positive uniqueness theorem under two hypotheses. Both are correct, about different groups, and this paper makes the difference arithmetic. Working inside the collision architecture of the companion flagship (doi:10.5281/zenodo.22014601, all versions), where an interior memory writes records of a system and audits itself from them, the two invariance groups an interior audit actually has are measured. FIRST, the audit's Hamiltonian-side content is exactly constant on the orbits of the commutant of H, the fibres of the transport map are exactly those orbits, and the resulting gauge has the closed form sum_i m_i^2 - 1 in the eigenvalue multiplicities: the degeneracy has a computable size, three dimensions inside sixteen for a generic four-level Hamiltonian, five at (2,3), and larger exactly when the symmetry group is NON-ABELIAN (Heisenberg gives nine; abelian symmetry forces no spectral degeneracy). SECOND, the audit's total content is invariant not under that commutant but under the stabiliser of the PAIR (H, psi), which is trivial precisely under the Soulas hypotheses: the orbit holds the Hamiltonian side fixed to 2.7e-15 and pays for the second structure entirely on the state side, 1.14. The stabiliser formula quantifies exactly when their free-action condition holds and by how many dimensions it fails otherwise. THIRD, the record statistics carry their own blindness: the directions invisible to the census, whatever the state and the time, form a group, and for a register read in one basis per cell it is exactly span{I, T} at every fragment count, proved by a symplectic argument over F_2 requiring no induction -- in this deposit, by two algorithmically independent F_2 implementations plus a dense-matrix verification. That scope is the result rather than a caveat: the one-bit blindness is the price of a one-basis readout, and it is the only thing that price buys; reading a second basis on every cell collapses the group to the identity and credentials the full matrix algebra. The twist is the product of the observer's own precession with all of its own readouts, T = P R_1 ... R_k exactly, so the blindness group is the CENTRE of the credentialed algebra: an interior observer cannot see the centre its own operations generate. The credentialed algebra is everything commuting with that one bit, of dimension d^2/2. Blindness under this reading is an identity and not a similarity: for T in the blindness group the census under rho and under T rho T-dagger agrees exactly at trace distance 0.740, so no additional sampling can separate them. The paper prints the response functional every margin and census count is computed from, together with its grid and state. Around the group sit its measured collapse conditions: the price list of restorations (menus that eject the twist restore visibility at costs that double register by register, 10/20/40 contexts on the z-menu and 4/8/16 on the y/z-menu at k = 2, 3, 4, stated as observed at three points, not derived); the sorting condition for which twist configurations a restoration menu revives, named as reach membership of the displacement in the Krylov closure of the menu (63/63 exact at k = 2 in three independent engines, 255/255 at k = 3 in exact rational arithmetic; an all-time reach lemma proves the decision grid decision-faithful and shows it deliberately not span-complete); the genericity of visibility (the blindness locus is a union of alignment strata computed in part: a QND family at the minimal codimension 2 and twist families indexed by subsets of cells at codimension 2k, with a bounded search that surfaced a mixed partial-twist family the hand count had missed); and both branches of the open-world dichotomy reproduced from the group definition alone. The transport side is independently rebuilt: the W-alone computation the framework's kill switch depends on was reconstructed from the printed setting alone and the switch does not fire. A closing section isolates the mechanism shared with an earlier half-space result and shows, against the natural reading, that the two halves are distinct subspaces meeting in a quarter: one lemma, distinct instances. All quantitative claims were pre-registered before their runs. The ledger of failed predictions is an appendix and is kept in full, including a posted mechanism that died, a symmetry law corrected to Schur's criterion, a numerics trap caught only because a posted claim came back wrong, engine deaths from the exact-census campaign convicted by their own gates, and errors printed in earlier drafts and caught in review. The delineation of what is inherited from the literature is stated throughout; the paper asserts no priority claims.
Quantum Darwinism explains why the world agrees about a system: redundant classical records make its pointer observable objective. We ask the complementary question, what it would take for a region of the world to be the continuation of a system rather than a description of it, and organize the answer around one quantity, the coherent information of the history channel from an origin to a region, I(R > X)=S(X)-S(RX) on the Choi state of the dynamics. For a pure global state this is log d minus what the rest of the world knows about the origin, so inheriting is that everybody else be ignorant, and objectivity and individuality are complementary. From this one quantity, three standard facts (strong subadditivity, global purity, data processing) and four ways of cutting the world (space, time, body versus records, and large scale) we obtain the following. Uniqueness of the heir and its causal-clique shape in spacetime; the size of the minimal heir in terms of Darwinian redundancy, with the constant kappa(0.1)=0.026, its form in the currency of recording strength for unequal witnesses, where the bound needs no exchangeability hypothesis, and a shared-secret environment that separates objectivity from heritability; a classification of interactions by degradability, under which pointer interactions never produce an heir. A realization theorem for what two disjoint regions can jointly inherit: their maximal correctable algebras commute, every commuting pair with a multiplicity matrix is realized as the maximal pair of an explicit channel, and what the two regions hold in common is always abelian, of dimension the number of connected components of a bipartite graph that the channel fixes -- so that the shareable part of an ancestry is exactly its classical part. An exact Zeno law for bodies whose dynamics does not commute with what is recorded, whose extended-body form is a classical Markov chain with unistochastic transition matrix and whose criterion is quantum non-demolition, and, for imperfect records, the fact that a perfect record is NOT the fastest way to take a body's identity: the loss is fastest at an interior record strength, where its rate exceeds the perfect-record rate by a factor 2/theta in the rotation angle; a budget inequality under which a lineage that acts on the world spends itself, with a closed frontier for qubits by convexity and a non-convexity for qudits. An existence criterion via information-preserving structures; a de-ordering lemma for biographies in indefinite causal order; and a security formulation in which exclusivity is the privacy of the root's classical record. Most of the physics is other people's and every theorem is attributed in place; Section 1.3 lists one by one what is not, with the realization theorem at the head of that list, and two companion notes carry the two longest proofs. We report, with equal weight, what was tried and fell: a proposed dynamical law of non-inheritance, a dynamical selection of subsystems, and a localization diagnostic, all retracted after adversarial review, and we propose a measurement of the minimal heir on an existing superconducting quantum-Darwinism platform.
Objective facts in quantum Darwinism are values recorded redundantly in many independently accessible fragments of the environment. Redundancy does not create additional logical information, so its thermodynamic meaning has remained unclear. We show that it creates an exact work asymmetry between controllers with different access architectures. For a record cloud F and a partition P into blocks that cannot be jointly controlled, the reversible isothermal erasure penalty relative to a global controller is kBT times the partition total correlation. If the source event X is supplied as catalytic classical side information, subtracting the corresponding penalty gives the source-loss law FPT=kBT[∑B∈PI(X:FB)−I(X:F)]. We call this the thermodynamic factuality charge. It ranges from −kBTH(X) for perfect secret sharing to (∣P∣−1)kBTH(X) for perfect broadcast objectivity. Its normalized form defines a thermodynamic record number between 0 and ∣P∣. We derive Landauer--Darwin bounds, endpoint-rigidity certificates, exact growth and partition-refinement laws, spectrum-broadcast saturation, and closed formulas for noisy classical and quantum collision models. The theory does not modify quantum mechanics or posit objective collapse; it identifies the thermodynamic resource generated by redundant records under restricted control.
A quantum memory that accumulates k successive records of a single system can audit itself: its memory-side statistics obey polynomial identities, and its physical realizability is a positivity question. The companion paper (Gleason from Inside, doi:10.5281/zenodo.22014602) proved the two-record certificate (identity ideal + one back-action-corrected moment inequality M*) and left the k >= 3 ladder open. This note closes it for the single-collision comb architecture at every k. The entire identity structure is generated by the transverse Bloch block of the per-record collision channel, read in its two operator orders: a route-damping chain law (every skip-pair correlation as a sum over sine-pair routes, each damped by the visibility of every record strictly between its sine vertices) and a response transfer law carrying odd higher-sine routes; both are census-exact at machine precision through five records at every span and start. The identity variety's free chart has dimension exactly 2k+1, one transport identity per added record. The completeness theorem: a chart point is realizable if and only if its outcome probabilities are valid and the FIRST pair's M* is positive semidefinite; every later adjacent certificate is a consequence (the transported effective state inherits the Bloch ball). The proof is a constructive, optimization-free rung inversion; machine confirmations include 200/200 exact round trips, a 1703-point redundancy test with zero violations, and exact inversion of all 1094 points of a persisted certification sample. The comb moment hierarchy collapses at level one: identities do all equality work (linear in k) and a single two-record inequality does all positivity work forever. The frontier is named: multi-collision cells, reused cells, and non-commuting rotation axes are outside the theorem. The ledger of failed predictions, including two wrong transfer compositions killed by census gates, is an appendix.
Quantum Darwinism explains effective classical objectivity through the selective proliferation of information about preferred quantum states into multiple environmental fragments. Its mature formulations operate within quantum theory, using a system-environment decomposition, decoherence or einselection, and information-theoretic or broadcast-structure criteria for redundant accessibility.This paper asks an upstream question from Registration Theory (RT): what makes a physical distinction a record before that record is described as information available to an observer? Canonical RT answers that retained registration is persistent organization constraining later evolution, that a distinction becomes a physical record only when it remains consequential, and that persistent physical organization is prior to information extracted from it.The paper assembles a theorem-backed finite-model chain now available in the RT corpus. Canonical ACRF dynamics supplies write-retain-read consequential history. The exact finite-amplitude ACRF-4 quotient identifies a nine-dimensional host-host-boundary state. The certified consequence-minimality theorem (DOI 10.6084/m9.figshare.34063464) shows that the retained relational boundary contributes irreducible future-consequence directions. The spectrum-preserving ACRF-8 redundant-record theorem (DOI 10.6084/m9.figshare.34063500) then proves an explicit local witness in which one quotient-valid source distinction is written into two disjoint retained fragments that are locally recoverable, counterfactually separable, and independently readable, giving RRT(q)≥2 under the stated criteria.The resulting distinction from Quantum Darwinism is precise but bounded. RT recordhood is consequence-based, while Darwinian objectivity is an accessibility-and-redundancy criterion formulated within quantum theory. The ACRF witness demonstrates redundant retained record formation without assuming Hilbert space, density operators, mutual information, decoherence, einselection, Born probabilities, or an observer-defined environment. Therefore, multiple persistent records of one distinction are not definitionally identical to Quantum-Darwinian redundancy.The paper does not claim that Quantum Darwinism is false or that RT has derived quantum mechanics, decoherence, Born probabilities, a mutual-information redundancy plateau, or macroscopic objectivity. Instead, it proposes a disciplined hierarchy: consequential distinction → retention → persistent record → branching → redundant retained records → redundant accessibility → environmental objectivity. The final two steps remain open in RT. A future bridge must dynamically select and scale multi-host redundancy and map consequence-bearing RT records into quantum environmental fragments that satisfy decoherence and strong objectivity conditions.