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.
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.
Hardware companion to "Gleason from Inside". Three sessions on ibm_kingston (554 of 600 free-tier seconds): the interior Born audit ran end to end, self-calibrated, certified positivity live at the lattice boundary, and kept its readout thermometer clean (claim A); the quantitative Born bound was not issued, exactly as pre-committed, because its noise-model condition failed; and that failure is the finding: schedule-accumulated coherent crosstalk on one coupler, detected by the cross-context identity, localized by zero-write baselines, converted into a gauge by schedule harmonization (five-fold collapse of the violation), and tracked in time (the phase flips sign within a single calibration epoch; coherence time 3 to 60 minutes; our own recalibration attribution falsified and corrected). Detect, localize, discriminate, track, on 9.2 minutes of free-tier time. The discipline (hash-frozen analysis, pre-committed outcome tables, credential lint extended from topology into time) is documented as a result in itself.
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.
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.
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.
Note: description expanded on 2026-10-14 for readability. It adds no new predictions or criteria. The frozen pre-registration is the attached PDF, unchanged since publication. Status: the experiment was run on 2026-10-14, after this record was published. Results, including every pre-registered test, will be reported in a separate record linked here. In plain language Theory says a quantum system never completely forgets where it started, even when its dynamics are chaotic. This leftover memory is called a quantum birthmark (Graf et al., Phys. Rev. X, 2026). Theory also says the birthmark should be larger when the system's rules run the same forwards and backwards in time (time-reversal symmetry) than when that symmetry is broken. This record pre-registers a test of that prediction on IBM's ibm_kingston quantum processor. We built two nearly identical sets of 4-qubit circuits. One set has time-reversal symmetry and the other does not. Both use exactly the same gates, so they experience the same hardware noise. We measure how often each circuit returns to its starting state, compared with the 1-in-16 chance level, and predict that the symmetric set shows about 1.67× more memory than the broken set. All predictions, pass/fail criteria, circuits and analysis code were deposited here before any quantum hardware was used. What is tested, and what is not Tested: whether the return probability stays above the ergodic baseline 1/16 at depths 8–23, and whether that excess is larger for the time-reversal-symmetric class by the ratio exact numerics predict for these fixed instances. Not tested: the withdrawn temporal-memory claims of 10.5281/zenodo.20470129. The birthmark is closed-system coherent memory, which measurement and reset erase, so no outcome here bears on those claims. Not tested: the universal random-matrix value 1.889. At this size (N = 16) the circuit family itself gives about 1.66, so a finite-size difference is expected. Not a quantum-advantage claim: a 16-dimensional system is exactly simulable. This is a hardware-validation experiment. Design Hardware: ibm_kingston, physical qubits 108–109–118–129 as an open chain, selected by a no-QPU calibration audit (included as v6_backend_audit.zip). Circuits: a kicked-Ising Floquet period Kx(a/2) → D(h1) → Kx(b) → D(h2) → Kx(a/2), with D(h) = exp(−iΣhiZi)·exp(−iπ/4 ΣZiZj), at exactly 6 CZ per period. COE (symmetric): h1 = h2. TRSB (broken): h1 = h + d, h2 = h − d. The classes differ only in virtual-Z angles. Instances: 16 seeded COE/TRSB pairs (seed 20261013), run at every depth from 8 to 23 (48–138 CZ). Observable: P(t) = |⟨0000|Ft|0000⟩|². The primary statistic is the readout-mitigated excess ratio R = ECOE / ETRSB, where E is the mean of P(t) − 1/16. A noise fidelity common to both classes cancels in R. Controls: 32 deep circuits (depths 60–63) as a decoherence-floor check. 8 state-preparation monitors. 16 readout-calibration circuits. Run: one SamplerV2 job of 568 circuits at 256 shots each, with dynamical decoupling and twirling off and the execution order shuffled. Predictions Quantity COE TRSB R Excess over 1/16, depths 8–23 (noiseless, primary) 0.0896 0.0537 1.667 Same instances, infinite-time limit 0.0952 0.0634 1.502 Circuit family, 10,000 random draws — — 1.661 Random-matrix reference, N = 16 — — 1.889 Under four simulated noise models (nominal, pessimistic, and each with coherent errors), the mitigated R stays between 1.64 and 1.77. The shot-noise standard deviation of R at 256 shots is 0.070–0.125. Pre-registered decision criteria Test Pass condition H1 (primary): symmetry dependence 99% CI lower bound of R > 1.0 H2 (primary): quantitative agreement 99% CI of R intersects 1.54–1.87 and is at most 1.0 wide S1: birthmark above decohered floor Window excess minus depth 60–63 excess, 99% CI lower bound > 0, for both classes S2: matched fidelity between classes 0.85 ≤ FCOE/FTRSB ≤ 1.15 S3: instance-level agreement Pearson r ≥ 0.80 against exact predictions S4 (flag only): state prep and drift Monitors ≥ 0.95, drift ≤ 0.045 Overall verdict: CONFIRMED if H1, H2 and S2 all pass; PARTIAL if H1 passes but H2 or S2 fails; NOT CONFIRMED if H1 fails. Every test is reported whatever the outcome. Uncertainty comes from a 10,000-sample parametric multinomial bootstrap over every circuit's counts, with instances held fixed. Amendment 1 (v1.1.0, made before any data) Amendment 1 changed two things relative to v1.0.0 (10.5281/zenodo.23355804): Shots: reduced from 1024 to 256 per circuit for QPU budget, cutting estimated execution from about 152 s to about 38 s. H2: changed from "point estimate in 1.54–1.87" to the CI rule above, because at 256 shots the point rule would falsely fail 20–25% of the time under the pessimistic models. A CI-width cap of 1.0 keeps H2 informative. Circuits, instances and predictions are unchanged. The trade-off is that H2 is now a weaker test. Provenance Every reported number is derived by script from raw counts: Source and transpiled circuits are saved as QPY. Before submission, every transpiled circuit is mapped back to 4 qubits and its unitary checked against the exact model to < 10−8. The analysis reads its decision bands only from predictions.json and its data only from the raw results file. Submission is gated on the DOI of this record. Files: The PDF is the authoritative pre-registration. predictions.json holds every predicted number and decision band. birthmark_prereg_v1.1.0.zip contains the circuit builder, verification, submission and frozen analysis scripts, plus simulated-data self-tests. v6_backend_audit.zip is the pre-submission calibration audit. Known limitations Small system size (N = 16), so the random-matrix value is not expected. The prediction is specific to depths 8–23 and to these 16 fixed instances. The noise models exclude leakage, TLS fluctuations and crosstalk from outside the chain. T1 relaxation biases P(0000) upward, which pulls R toward 1 (conservative). One backend, one path, one job: no replication. Data: CC BY 4.0. Code: MIT. Principal investigator: Amit Brahmbhatt, Quantum-Clarity LLC.
The cryptography arc of the observation-theory campaigns, eleven registered runs in exact finite toy models, arranged as three movements. What such an audit certifies, an engineered secret-sharing plateau that is a step where an interaction-borne one is not, a conditional information certificate that proves non-garbling without a threshold, unanimous scalar leakage orderings that carry no task guarantee outside certified comparability, and two entropy accountings whose difference turns over while their ratio does not. Where it stops, a constant carries zero entropy, so an audit built from informations is blind to a trapdoor by that bound while it sees a declared one-bit leak immediately, and only a procedure's declared freedom is auditable because the artifact carries no record of the search behind it. Where it does not stop, reading an ensemble that is not orthogonal costs two bits of information for each unit of induced error while an orthogonal ensemble is read perfectly and leaves no trace, and one classical record is held in full by both consumers while one shared correlation is held by one. Three of the eleven runs failed their declared bars and are reported with their design errors named alongside the corrected registrations. Every number is bound by assertion to a committed evidence record. The models are toy models chosen for exact enumeration, nothing is claimed about computational hardness or asymptotic security, no real cipher, protocol, curve, device, or deployed system is modeled or evaluated, and no attack is developed.