The Cosmochrony Research Programme — Roadmap and Paper Inventory

This repository contains the source of the programme synthesis paper The Cosmochrony Research Programme: A Structural Roadmap and Paper Inventory.

It is the central registry of the whole Cosmochrony corpus: it inventories every paper, documents the dependency graph between them, and tracks their status. It is the reference to consult first to understand how the pieces fit together.

Version 2.46 records the I-4 correction in Q6a 2.6 and its consumers GS-Note 2.3, Q12 1.8 and GGS-Note 2.3. A gauge charge in Q6a, a function constant on the projection fibres, is a function of the observable state; its identification with a conserved physical charge is open. Q6a's two continuum hypotheses do not determine a connection: the structure group, its representation and the connection are supplied, curvature measures the path dependence of transport, flatness is only local, and the uniqueness of the Yang–Mills action holds under an explicit truncation. Q12 takes the connection of the admissible principal bundle as supplied, not as the unique one compatible with the Foundation constraints. Registry entries, table rows, graph nodes and the Q6a bibliography note record these statements. Programme 2.46 was deposited as Zenodo record 23713025 (concept DOI 10.5281/zenodo.19759956).

Version 2.45 records the I-3 correction in Foundation 2.6 and its consumers NIF-Note 1.6, Q6a 2.5, FM-Note 3.3, Q5a 3.3, Q5b 2.3, Q14 3.3, E2 2.3, Gravity 3.6, SG-Note 2.4 and QS-Note 2.3. Irreducibility of the admissible fibre follows from A1 and A3 and a representation-theoretic dictionary only under an additional sector reading of A3, not derived, on which a generator-stable decomposition counts as premature selection. The discreteness of quantum transitions is postulated by A4, not derived: on the supplied Heisenberg shell realisation a realised saturation depth is an integer (O22), and the existence of such a depth is not established. The Projective Observability Principle is an adopted principle, and the physical reality of the proto-state is an interpretive reading. The white paper proposes the substrate $\chi$ and the relaxation mechanism; Foundation derives neither from A1--A4. In Gravity and SG-Note the coherence extensivity hypothesis [H-ext] stays explicit and distinct from the sector reading. These corrections close the attributions to Foundation; the existence of a locking depth and the status of O22's own integrality argument remain open. Registry entries, table rows and graph nodes record these statements. Programme 2.45 was deposited as Zenodo record 23678698 (concept DOI 10.5281/zenodo.19759956).

Version 2.44 records the I-2 correction in TempProj 1.5, LCII 1.5, LC-O1 1.2 and LC-Synthesis 2.3. In TempProj the quadratic Born-Infeld law and the Weil filling law alone fix the scalar temporal residual at the attained values of the total residual (depths $n \le (q-1)/2$), and only there; the temporal splitting of the supplied co-metric is not necessary for that uniqueness and identifies the value as the temporal component of the capacity flow without selecting it, using neither the coefficient values nor the signature. The Lorentzian kinematic reading uses the signature and the hypothesis [H-cone]; the light cone $B = 1$ is reached by the exact torus load of LC-O3. In LCII the factor $\sqrt{f(2-f)}$ is a normalised capacity factor, not a Lorentzian structure. Registry entries, table row and graph nodes record these statements. Programme 2.44 was deposited as Zenodo record 23675486 (concept DOI 10.5281/zenodo.19759956).

Version 2.43 records the I-1 correction in Q7 2.1, SpinRotationNote 1.6, H2 1.1, U1 2.1, Q5a-O2 2.1 and EG-Note 2.3. No source supplies a value of $A_z$, $A_H$ or $A_\tau$ on established inputs: Q8 leaves the common value of an invariant form free, Q10 bounds the ratio $A_H/A_Z$ under [U], [W], [R] and [T] and gives an absolute value only under its scale input [S], U1 leaves [U] open, and the O-series exponent data do not support [U]. H2 proves the statement formulated as [H2] in Q5a version 2.0 (Hypothesis 4.3 there), the last deposited version of that framework, and discharges no hypothesis of the current Q5a; [H-w] is open. Entries, table rows, bibliography notes and graph nodes carry these statements. Programme 2.43 was deposited as Zenodo record 23672098 (concept DOI 10.5281/zenodo.19759956).

Version 2.42 records the joint F/G correction in Q14 3.2, FM-Note 3.2 and GGS-Note 2.2. The supplied Heisenberg dictionary, associated Weil action and spinor doublet are distinct. Connection-dependent admissible readings retain both unproved continuum hypotheses of Q6a: a smooth effective fibre bundle and a differentiable spatial continuum, the latter open in Q5a. No map selecting the doublet is constructed. Entries, table row, bibliography and graph carry these conditions. The retired standalone obstruction note audits the earlier selection claim; its present-tense wording does not describe Foundation 2.5.1, which states non-selection. Its integrated successor is the cited source. Programme 2.42 was deposited as Zenodo record 23667596 (concept DOI 10.5281/zenodo.19759956).

Version 2.41 records ENT-E2 2.2, ENT-Note 1.3.1 and Foundation 2.5.1. These versions state that the matched-block result $S_{\mathrm{ent}}(n)=\log r_{\mathrm{pair}}(n)$ of ENT-E1 holds under a supplied purity of the joint state, which ENT-E1 does not derive; ENT-E2 2.2 no longer calls it unconditional. In the registry, the ENT-Note entry, table row and graph node state the formula under ENT-Note's closure hypothesis (supplied purity with diagonal pairing) and, for independently sampled blocks, ENT-E2's further conditions; the general-block conditions of the ENT-E2 entry, table row and graph node, and the ENT-Note, ENT-E1 and ENT-E2 bibliography notes, now carry that purity, and the ENT-Note and ENT-E2 notes also the general-block conditions, including the O17 transfer gap; the ENT-E1 table row's status separates $w_j=1$ from the flat spectrum given a supplied purity. Programme 2.41 was deposited as Zenodo record 23666558 (concept DOI 10.5281/zenodo.19759956).

Version 2.40 is a narration pass on the registry. In the passages it corrects, listed here, entries, table rows, graph nodes and the abstract state current results and limits directly instead of recounting earlier versions; this is not an exhaustive removal of version history from the registry, and O31 remains a withdrawal notice. The Foundation entry, table row and graph node, the abstract, the Level 2 overview and the HeisenbergStructure entry state that the carrier contract extracted from A1–A3 and Born–Infeld parity does not select $\mathrm{Heis}3(\mathbb Z/q\mathbb Z)$ (Foundation Theorem 5.7), so the carrier is supplied. The admissible pair entropy $\log 2$ is attributed to ENT-E2, with its singlet input from Q3, and is conditional on the independent hypotheses (H-carrier) and [H-inv], which A1–A4 do not establish; the ENT-Note entry carries the same conditions. Between them, the ENT-Note, ENT-E1 and ENT-E2 entries, the ENT-E1 and ENT-E2 table rows and graph nodes state that ENT-E1 proves the admission-orthogonality identity and, for matched blocks, the diagonal Schmidt pairing and the flat spectrum under a supplied purity of the joint state, deriving neither that purity nor the pair closure. The Q7 entry reserves $A_z$ for the coefficient of $k_Z^2$ of a full-rank spatial block, which Q7 does not evaluate. The O4 graph node carries O4's bibliographic title, and the Q13 table row version 1.6. Version narration is also removed from the PTO, Cosmology, TrajBr, LowLCapacity, HeisenbergStructure, SRN and LCII passages. Figure 1 shows the side annotations of O30–O33 under their nodes, draws dashed every arrow whose edge the interactive graph types as conditional, postulated or interpretive, and its caption gives each typing; the graph types O29→O30 as interpretive and adds O30→Q14 and Q14→AOG-Note (postulated) and AOG-Note→CHO (conditional). In Foundation 2.5's wording, A3 preserves the open directions but does not by itself forbid an erasure of their relative phases; the 2.36 paragraph below keeps the wording of that release. The identifications $F_n \simeq V\rho$ in the FM-Note entry, in HeisenbergCarrierObstruction and on the fermionic-matter and Q14 web pages are not resolved in this version. Programme 2.40 was deposited as Zenodo record 23662275 (concept DOI 10.5281/zenodo.19759956).

Version 2.39 records Foundation 2.5. Foundation cites ENI Corollary 6 with its own premises on each projection (surjectivity, observables defined by the projection, a level not isomorphic to the one below), which A1–A4 do not supply and which are open for the programme's strata. The ENI entry, table row and graph node state ENI's theorem as a one-way implication under these premises (Theorem 3), with the redundancy equivalence of Corollary 5 and colour confinement under the same premises at the colour stratum; ENI motivates A2 without deriving it. The Foundation entry states that the proto-state is defined and its structural indeterminacy derived from A1 and A3, that irreducibility and non-commutation require a representation-theoretic dictionary, and that the axioms do not select the Heisenberg group (Foundation Theorem 5.7); the Level 1 overview states the same conditions. The effective metric read from the principal symbol is conditional on [H-L] and the open lifting hypothesis [H-lift] of Q5b; the signature result gives $(-,+,+)$ on the rank-three block only. Foundation writes $\mathcal W$ for the finite Weil modules of the supplied Heisenberg–Schrödinger carrier, one per central character $c$, the member at $c$ being the Weil block $V_c$ of O27, whose Weil action is not the Heisenberg action; $V_\rho$ denotes only the spinor carrier $\mathbb C^2$ supplied conditionally by O23. The identifications $F_n \simeq V_\rho$ in the FM-Note entry, in HeisenbergCarrierObstruction and on the fermionic-matter and Q14 web pages are not resolved in this version. Programme 2.39 was deposited as Zenodo record 23645389 (concept DOI 10.5281/zenodo.19759956).

Version 2.38 records PTO 1.5, ENT-Note 1.3 and LC-Synthesis 2.2. PTO separates cumulative span retention (immediate), exact stepwise monotonicity (conjectural), the numerical bound, which holds within a relative tolerance of $10^{-6}$ after burn-in (exactly for $q \le 101$, only within tolerance for $q = 151$ and $211$), and an order on states, which requires [H-acyc]; its stability table is recomputed from archived pipeline outputs, with the q = 211 row now taken from the archived run (194 steps). ENT-Note 1.3 states capacity-level one-way activation as a conjecture supported within tolerance; LC-Synthesis 2.2 reads PTO as a candidate trajectory proxy and takes the clock factor from TempProj. Programme 2.38 was deposited as Zenodo record 23643977 (concept DOI 10.5281/zenodo.19759956).

Version 2.37 records Q6a 2.4. Q6a attributes to the Foundation paper the derivation of the structural indeterminacy of the proto-state from A1 and A3, and states that the retention of phase coherence is not derived from A3 alone; its results are unchanged. The Q6a entry, table row, bibliography note and graph node carry the new version. Programme 2.37 was deposited as Zenodo record 23628375 (concept DOI 10.5281/zenodo.19759956).

Version 2.36 records the Foundation 2.4 cycle (Foundation 2.4, QS-Note 2.2). Foundation states the homogeneous dimension $D_{\mathrm{hom}} = 4$ as a property of the supplied Heisenberg carrier, local on $G_q$ for $n \ll \sqrt{q}$ and not identified with $3+1$ spacetime; it writes complex amplitudes on the supplied carriers, coherence excluding a classical probability mixture but not real amplitudes; phase coherence is not derived from A3 alone, which preserves the open directions but not, by itself, their relative phases; the Born weight is an additional rule; projective incompleteness does not guarantee the initial transition; and its results table gives the Einstein, Yang–Mills and Einstein–Yang–Mills results of Gravity, Q12 and Q13 with their hypotheses (the Einstein condition being sufficient), deriving no coupling hierarchy. QS-Note states that, under an explicit representation-theoretic reading of the fibre, the axioms restrict its algebraic structure but do not select it, and that, for the explicitly studied generic blocks at $q = 53$ and $q = 101$, O23 finds exactly two faithful $\mathrm{SU}(2)$-valued constituents of the restricted Weil module without a derived rule selecting the spinor carrier. Foundation's axiomatic level attributes discreteness to A3 and A4, and states that the complex carriers are supplied. The Foundation and QS-Note entries, table rows and graph nodes are aligned, and the white-paper sentence on the spectral entropy functional states the Gravity conditions. Programme 2.36 was deposited as Zenodo record 23627504 (concept DOI 10.5281/zenodo.19759956).

Version 2.35 records the LC/2η cycle (TempProj 1.4, LorentzCapacity 1.4, LC-O1 1.1, LC-O2-O1 2.1, LC-O3 1.1, LC-Synthesis 2.1, LCII 1.4; Cosmology 2.4 only corrects its import of TempProj). LCII states the fibrewise residual R(x)/γ as a capacity increment per ordering step, read as gravitational time dilation under [H-cone] and the occupancy–lapse postulate. The Lorentz-capacity papers take a supplied co-metric of the conditional form of Q11 Corollary 6.1, diag(−A_τ, 2λ, 2λ, 2λ), whose two coefficients are independent and fixed by no source; after a rescaling of τ it is proportional to η, and the normalisation g = 2η is a choice of units. The identification of the light-cone speed of that co-metric with the Born–Infeld bound per ordering step, which Q11 names as the missing coupling datum, is the named hypothesis [H-cone] of the LC kinematic chain. The no-go of LC-O2-O1 holds for any postulated flat-space value, the boost mathematics of LC-O1 is proved for η, and the temporal projector of TempProj uses only the signature and the decoupled temporal block. The LC entries, table rows, graph nodes and edges are aligned accordingly; the graph edge Q6b → LCIIo1 is replaced by Q5b → LCIIo1, and conditional edges Q11 → TempProj and Q11 → LCo1 are added. Edges follow the LC citations: PTO → LorCap is removed, and LCII → LCo3 and BI → LCo3 are replaced by LorCap, TempProj and LCIIo1 → LCo3. Programme 2.35 was deposited as Zenodo record 23620172 (concept DOI 10.5281/zenodo.19759956).

Version 2.34 records the Q6a 2.3 cycle (Q6a 2.3, Foundation 2.3, GS-Note 2.2; Q12 1.7 and Q6b 2.1 only align their description of Q6a). Q6a reads SU(2) off the spinor carrier supplied by O23, under the neutral-sector hypothesis of O27: the group acting faithfully on that carrier is SU(2), a consistency statement and not a selection, and no uniqueness or minimality of SU(2) is established. The Foundation axioms do not select the carrier; Foundation lists the SU(2) gauge structure as conditional and the Standard Model gauge group as open, O31 version 2.0 being a withdrawal notice, states the large-q continuum limit as open requirements, and establishes no co-metric coefficient value (Q10 and Q11 do not derive diag(-2,2,2,2)). GS-Note states O28, O29, O30 and Q7 as they currently are. Q6a's connection is conditional on two continuum hypotheses, one of them the spatial continuum that Q5a leaves open, and the Yang–Mills action is a structural motivation. In the dependency graph the edge Q5b → Q6a is replaced by a conditional edge Q5a → Q6a and an edge Q5b → Q6b, since Q6a cites Q5a and not Q5b, while Q6b cites Q5b. Entries for O31, O32, Q5a, U1, W1 and H2 state their current content without narrating earlier versions. Programme 2.34 was deposited as Zenodo record 23617230 (concept DOI 10.5281/zenodo.19759956).

Version 2.33 records GS-Note 2.1. GS-Note identifies no gauge group: U(1) is structural on premises carried as input, SU(2) is conditional on a supplied carrier, and O31 withdraws every derivation of SU(3) and of the composite. Q12 and Q13 take the gauge group as a supplied compact group, and GS-Note takes no metric coefficient from Note 2: Q5b gives a rank-three co-metric and Q11 a rank-four form only for a supplied extension, so $g = 2\eta$ is not established. The Q6a entry, table row and graph node are aligned with the Q6a source: gauge charges are fibre invariants, U(1) is the residual phase symmetry, SU(2) is read as the minimal non-abelian admissible group under a supplied carrier, SU(3) is a structural hypothesis, Q6a does not use O31, and its connection is conditional on two continuum hypotheses. The GS-Note entry, table row and graph node are updated accordingly. Programme 2.33 was deposited as Zenodo record 23605095 (concept DOI 10.5281/zenodo.19759956).

Version 2.32 records Gravity 3.5 and its consumer cascade (Q12 1.6, Q13 1.6, EG-Note 2.2, SG-Note 2.3, LC-O2 1.3). Gravity works on a supplied Riemannian metric: its identification with an operator built from the admissibility data is not established, [H-lift] is open, Q5b gives a rank-three co-metric, and no metric coefficient value is established. The infrared dominance of the Einstein term is structural and conditional (a non-zero matched coefficient and $R L_4^2 \ll 1$, by power counting). Among linear two-derivative carriers the Born–Infeld classification leaves a trace parameter $\alpha$ of the spectral carrier free, second-order data determining at most $|1-\alpha d|$; the saturation condition applied to the Ricci endomorphism selects $\alpha = 0$, and the non-uniqueness lies in the sector function. LC-O2 uses a supplied Lorentzian co-metric with a postulated flat temporal reference and the Q11 Corollary 6.1 form under its hypotheses. The edges Q11 → Gravity and Gravity → LCII are removed as result dependencies; conditional edges Q11 → LCII and Q5b → LCII are added. Programme 2.32 was deposited as Zenodo record 23576541 (concept DOI 10.5281/zenodo.19759956).

Version 2.31 records SG-Note 2.2 and GGS-Note 2.1. Both notes work on a supplied Riemannian metric; its reading as the emergent metric of the emergent geometry sub-programme is conditional on the unestablished spatial-limit hypothesis [H-L], the open lifting hypothesis [H-lift], a supplied rank-four extension and a continuation from Riemannian signature that is not performed, and no metric coefficient value is established. SG-Note states the conditions under which the Einstein tensor dominates the renormalized metric variation (a non-zero matched Einstein coefficient and $R L_4^2 \ll 1$) and the conditional stationarity at leading local infrared order. GGS-Note states the Lorentzian continuation as open in the geometric and gauge sectors and types the spectral stratification as an organising reading. Their registry entries, table rows, bibliography entries and graph nodes are updated; the emergent-geometry edges to Q12 and Q13 carry the full list of conditions, and two conditional edges from EG-Note to SG-Note and GGS-Note record that only the emergent reading of the metric depends on the geometric branch. Programme 2.31 was deposited as Zenodo record 23473240 (concept DOI 10.5281/zenodo.19759956).

Version 2.30 records Q6b version 2.0. On a supplied Heisenberg carrier, under the unestablished spatial-limit hypothesis [H-L] and the open lifting hypothesis [H-lift], Q6b assembles a rank-three co-metric whose non-degenerate block has signature $(-,+,+)$ under [H-hyp$_{\mathrm{red}}$]; $(-,+,+,+)$ needs a supplied rank-four extension (Q5b-O2), and no coefficient value is established. Flux conservation gives a leading Newtonian exterior only for a supplied spherically symmetric, asymptotically flat extension with an asymptotically homogeneous exterior; the Schwarzschild form needs external dynamical input, with no uniqueness claim; the horizon reading is interpretive; the relation to the Einstein equations is conditional on matching data, an assumed matter functional and a Lorentzian formulation that is not available. The Q6b entry, its results row, its bibliography entry and its graph node are rewritten accordingly. The registry also records EG-Note 2.1, which aligns the statements it takes from Q6b; Q12 1.5, whose base space is supplied and whose citation of Q5b is corrected; and Q13 1.5, in which the Lorentzian continuation is open in the geometric sector as well as in the gauge sector.

Version 2.28 synchronises the PRS 3.0 / A4-Note 3.0 source contract and its consumers: Q14 3.1, EBJ 2.1, PYO 2.1, PYL 3.0.1, AAR 1.3, Q11OF 1.1, CHO 1.1, AOG-Note 1.8, KUD 1.5, TPC 1.2 and FM-Note 3.1, deposited in the same cycle as NPI 1.0.1 and SRN 1.5 (registry entries unchanged). Statuses are typed per result. PRS: under a contraction hypothesis the compression remainder of the projected Dirac square is the Schur complement $-N^\dagger N \preceq 0$ (zero-order only under a symbol condition), equal to the projective endomorphism of Q14 only when $\Pi_S D^2 \Pi_S^* = \mathrm{Lich}$; under the generation-reading hypothesis [H-Gen] a $J_\Pi$-commuting locking operator gives $u = 0$; the Schur-null and Schur-transverse loci form a dichotomy proved under explicit hypotheses, which locus holds being open (the exact $\mathfrak{sl}2$ opening, produced by $[E,F]=H$, reaches the locking operator only under the transport hypothesis [H-Tr]); no mechanism for a non-zero split is derived. A4-Note: the radicand quartic coefficient is chart-dependent and selects no lock, the first contact is chart-independent when it exists, the Lorentzian genus is not determined, and the Front D factorisation is formal. EBJ: its finite witness has $J^2 = +1$ and lies outside H-Gen. Q14 3.1 states $E\Pi \preceq 0$ as an explicit hypothesis. The commutation $[\gamma_5, R_b] = 0$ is the hypothesis [H-WS] of Q11OF, part (i) (a scalar on the chiral carrier; the value $-1$, part (ii), is used only by AOG-Note), carried by CHO and AOG-Note; the $J_3$ signal comes from the $\mathfrak{sl}_2$ commutator $[E,F]=H$, not from the Heisenberg bracket (AAR 1.3). The registry entries, table rows, dependency figure, bibliography entries and interactive-graph nodes carry these statements; PRS and the A4-Note are typed conditional, the edges PRS to A4-Note and A4-Note to EBJ are typed conditional, and the node suffix "Written against Q14 2.0" is removed from PRS and the A4-Note and the corresponding clause is removed for CHO, AOG-Note and Q11OF. The versions listed above, together with NPI 1.0.1 and SRN 1.5, were deposited on Zenodo on 2026-10-07: PRS 3.0 Zenodo record 23222634 (concept DOI 10.5281/zenodo.20601040), A4-Note 3.0 Zenodo record 23222712 (concept DOI 10.5281/zenodo.20633931), Q14 3.1 Zenodo record 23222683 (concept DOI 10.5281/zenodo.20218409), EBJ 2.1 Zenodo record 23222741 (concept DOI 10.5281/zenodo.20763532), PYO 2.1 Zenodo record 23222779 (concept DOI 10.5281/zenodo.20767498), PYL 3.0.1 Zenodo record 23222840 (concept DOI 10.5281/zenodo.20767265), AAR 1.3 Zenodo record 23222518 (concept DOI 10.5281/zenodo.20601228), Q11OF 1.1 Zenodo record 23222547 (concept DOI 10.5281/zenodo.20601245), CHO 1.1 Zenodo record 23222590 (concept DOI 10.5281/zenodo.20735907), AOG-Note 1.8 Zenodo record 23222608 (concept DOI 10.5281/zenodo.20693084), KUD 1.5 Zenodo record 23222888 (concept DOI 10.5281/zenodo.21109812), TPC 1.2 Zenodo record 23222927 (concept DOI 10.5281/zenodo.21115977), NPI 1.0.1 Zenodo record 23222955 (concept DOI 10.5281/zenodo.21207750), SRN 1.5 Zenodo record 23222984 (concept DOI 10.5281/zenodo.21380026) and FM-Note 3.1 Zenodo record 23223000 (concept DOI 10.5281/zenodo.20562665). Programme 2.30 was deposited as Zenodo record 23469866 (concept DOI 10.5281/zenodo.19759956).

Version 2.27 synchronises FM-Note 3.0, PYL 3.0 and PYO 2.0, which type the fermionic and mass sectors on the Q14 3.0 hypotheses. [H-Spin] (a spin solder) and [H-Weak] (a distinct $U(2)$ weak factor $E_{\mathrm{weak}}$) are separate hypotheses supplied by no source; the $\mathfrak{sl}2(\mathbb{C})$ tensor algebra is proved on supplied model data only; the hypercharge line $L_Y = \wedge^2(E{\mathrm{weak}})$ rests on [H-Weak], the exterior square of the soldered spinor doublet being trivial under [H-Spin]; Lorentz chirality (left-admissibility, an input branch) is distinct from weak $V{-}A$; and $R_b = W(-I)$ commutes with $\gamma_5$ only under the hypothesis [H-WS] of Q11OF, no group-level Weil-to-spin map being available at the primes of the corpus (superseded in 2.28). PYL records a conditional weak determinant line and the ordering of the three levels of the model operator $\mathrm{diag}(1, \tfrac12 + u, \tfrac12 - u)$, read as $E_\Pi^2|{\mathbb{C}^3{\mathrm{gen}}}$ only under the named hypothesis [H-Res]; the level-to-generation map is not established and no mass value is claimed. PYO states that $E_\Pi^2$ fixes the squared Yukawa levels, not the morphism, under [H-Res], [H-Sq], [H-Fac] and [H-Grad]; the projection of the $\mathfrak{sl}2$ lift onto its $J\Pi$-odd anti-Hermitian part vanishes, by representation theory, for the projection as defined and is not the polar generator, so the physical polar class is open and the choice of the $J_\Pi$-odd part is a modelling choice that no source justifies. The registry entries, table rows, dependency figure, bibliography entries and interactive-graph nodes carry these statements; the edges into PYL and PYO are typed conditional and the PYO-to-NPI edge interpretive, NPI's reference to a trivial polar class being an open consumer correction. FM-Note 3.0 is Zenodo record 23111382 (concept DOI 10.5281/zenodo.20562665), PYL 3.0 Zenodo record 23111395 (concept DOI 10.5281/zenodo.20767265) and PYO 2.0 Zenodo record 23102550 (concept DOI 10.5281/zenodo.20767498). Programme 2.27 was deposited as Zenodo record 23118577.

Version 2.26 synchronises Q14 3.0. Q14 now states what the fermionic sector rests on: the finite carrier acts through $\mathrm{SL}(2,\mathbb{Z}/q\mathbb{Z})$, so a real metaplectic model and a doublet carrying $\mathfrak{sl}_2(\mathbb{C})$ are supplied model data, on which the tensor algebra is proved; the Lorentz reading rests on a spin solder [H-Spin] and the electroweak reading on a distinct $U(2)$ weak factor [H-Weak], neither supplied. The Q14 entry, table row, figure node, bibliography entry and interactive-graph node carry these results. The Q11-to-Q14 edge is typed conditional: Q11 Corollary 6.1 supplies a Lorentzian signature under its stated hypotheses, which is all Q14 uses; spin soldering remains an input. PRS, the A4-Note, CHO, AOG-Note and Q11OF were written against Q14 2.0 and are flagged as open consumer corrections in the registry text and the graph. Q14 3.0 was deposited as Zenodo record 23071163 (concept DOI 10.5281/zenodo.20218409). Programme 2.26 was deposited as Zenodo record 23071204.

Version 2.25 synchronises Q11 2.0 and Q5b 2.2.1. Q11 proves that invariance under a spatial $\mathrm{SU}(2)$ action leaves the temporal coefficient free: with the action trivial on the ordering line and spin one on the spatial sector, every invariant form is $\alpha,k_\tau^2 + \beta,Q_{\mathrm{sp}}$ with independent scalars and no mixed term, and no linear $\mathrm{SU}(2)$ action on four real dimensions fixes a Lorentzian form up to an overall factor. The identification of $\tau$ with BFS depth is a modelling input with a free step, and fixing $A_\tau/A_H$ needs a datum coupling the temporal and spatial normalisations that no source supplies. Q11 closes a derivation route, not the possibility $A_\tau = 2$. Q5b 2.2.1 describes Q11 2.0 and Q10 2.0.1 as they stand. The Q11 entry, table row, figure, bibliography and dependency graph carry these results; the W1-to-Q11 and U1-to-Q11 edges are removed, a Q7-to-Q11 edge in the interactive graph records the supplied spatial action, and the edges from Q11 to the consumers of the former values are marked pending revision. Q11 2.0 was deposited as Zenodo record 23024499 (concept DOI 10.5281/zenodo.20098387) and Q5b 2.2.1 as Zenodo record 23024508. Programme 2.25 was deposited as Zenodo record 23024512.

Version 2.24 synchronises Q8 2.0 and Q10 2.0, deposited as Zenodo record 23002451 (concept DOI 10.5281/zenodo.19879909) and Zenodo record 23002454 (concept DOI 10.5281/zenodo.19880900), together with Q5b 2.2 (Zenodo record 23023118, concept DOI 10.5281/zenodo.19686700) and Q10 2.0.1 (Zenodo record 23023127), which aligns Q10's description of Q5b with Q5b 2.2. Q8 proves that the Heisenberg commutator supplies no central coefficient, that a positive constant central coefficient needs a term of homogeneous degree four and a length scale, and that for a supplied fully invariant rank-three target $A_H = A_Z = 2\lambda$ with $\lambda$ free. Q10 proves a sharp ratio lemma and a conditional isotropy theorem under named inputs, with the absolute value only from an independent scale; no coefficient value is derived. Q5b records [H-lift], the full-rank extension Q5b-O2 and the coefficient values Q5b-O3 as open. The synthesis, inventory, figure, bibliography and dependency graph carry these results; the circular Q8-to-Q10 edge is removed. Q6b, Q11, the emergent-geometry note and the other consumers of the former values remain marked pending revision. Programme 2.24 was deposited as Zenodo record 23023148.

Version 2.23 synchronises W1 2.0.1, deposited as Zenodo record 22926106 under concept DOI 10.5281/zenodo.19886319. W1 withdraws its claimed proof of [H-w]. Its exact summation inequality concerns a separately defined finite-window proxy under a relative profile estimate that U1 never proved. Under the specified five-block calibration, the proxy's target is a sum through depth 22, not the infinite series formerly claimed. The bridge to Q5a's response-average weights, their separate directional limits [H-w′], and a common positive limit [H-w] remain open. The synthesis, inventory, bibliography and dependency graph now carry that distinction. Q10 and the other downstream papers remain pending their own audits. Programme 2.23 was deposited as Zenodo record 22945485.

Version 2.22 synchronises U1 2.0. U1 proves an unconditional equidistance obstruction for finite Heisenberg multiplication generators; a separate adjacent-character example excludes the claimed uniform modulus for their sum. Its former proof of [U], its $O(q^{-1/2})$ rate and the claimed Q10/Q7 closure are withdrawn, while [U] remains open. The inventory, bibliography and both graph surfaces now record that result. W1's quantitative step imports the withdrawn U1 rate and awaits its own audit; Q10 and the other downstream papers remain pending. U1 2.0 is deposited as Zenodo record 22905732, under concept DOI 10.5281/zenodo.19881146. Programme 2.22 was deposited as Zenodo record 22913308.

Version 2.21 synchronises Q9 2.0. The Q9 entry now records a kinetic Mosco limit conditional on [K] and [R], with the energy scale retained in its modulation bound. Its free kinetic form selects no nonzero central character, and the relative moment estimate applies to individual vectors in a cone rather than defining a closed coercive form. Q9 no longer discharges [H-lift] or establishes bridge non-obstruction or a geometric coefficient $A_H$. The programme synthesis, Q5b/Q6b rows, Q9 inventory entry, bibliography and both graph surfaces carry that distinction; the Q9-to-Q10 edge remains a citation edge, without theorem supply. The downstream paper audit continues in the agreed Q9–U1–W1–Q10–Q8–Q11–Q5b order.

Version 2.20 retypes the Q7 entry for Q7 version 2.0, whose central result changes. Q7 now states the requirements an equivariant bridge would have to meet and proves those that follow from representation theory on the supplied carrier. Q7 distinguishes the measured-space identification [ID], target action [ACT], real rotation compatibility [INV] and adapted unitary transport [ADAPT]. Abstract intertwiners exist once the isomorphic modules are supplied. The rank-two spatial principal symbol of Q5b cannot equal a positive rank-three Casimir form. A new positive spatial target remains to be constructed. The Casimir reading of the central coefficient, the isotropy fit, the transfer of a discrete compression to the continuum symbol, and the values imported from Q8, Q10, U1 and Q11 are withdrawn. Status changes: the Q7 row becomes proved for the requirements on the supplied carrier with the identification recorded as open, and the Q7 node is redrawn accordingly in both figures, with the interactive graph's status letter moving from structural to proved and its description naming the open geometric hypotheses; the arrow leaving Q7 loses the proved colour and the Q7-to-Q9 edge is no longer drawn on the spine; the terminal edge into the co-metric result box is likewise demoted and the box marked pending revision; the physical-path prose no longer lists O29 among the suppliers of the dimensional bridge, the dependency edge being kept since Q7 cites O29 for the audit of the measured rank; and the Q5a-to-Q5b-O3 chain is no longer recorded as closed, with a second gap at the Q7 step and a circular junction beyond it. The three edges this release is about -- O29 to Q7, Q7 to Q8 and Q7 to Q9 -- now carry the graph's own edge typing, which states what each does and does not supply. The Q8, Q10, U1, W1 and Q11 entries are marked pending revision on the surfaces that assert their results, each pending its own step in this cascade. The Q5b and Q6b entries are marked too: each asserts the co-metric on the strength of those values, Q6b's own remarks calling it fully explicit and fully determined. The Lorentz-capacity entries, which consume the values rather than deriving them, carry the marker on the value, and on their own conclusions only where those conclusions restate it.

This registry version describes Q7 version 2.0, deposited on 19 September 2026 as version record 10.5281/zenodo.22838313 of concept 10.5281/zenodo.19802123; the bibliography cites the concept DOI.

Version 2.19 synchronises O26 2.1 in the synthesis, inventory row, bibliography and interactive graph. Under O26 Hypothesis 4.4(a), the embedded products lie in the symmetric square, with rank at most three for dimension two: the rank-four target is excluded under that contract alone. Tests 1–2 are implementation checks. The O28–O29 ranks measured in End(H_eff) do not measure End(V_rho), and occupy no row of the embedded-covariance decision table. The admissible embedding remains open. No primary status or dependency edge is changed.

Version 2.18 synchronises the NIF-Note 1.5 release in the Branch I synthesis, inventory row, bibliography note and interactive graph. It separates ENI's one-way implication from the conditional representation route, records temporal order under [H-acyc] and irreducibility under the representation dictionary, carries the dimension and generating-pair premises for non-commutation, and attributes the finite obstruction to HeisenbergStructure 2.1. The Heisenberg group, non-trivial central character and associated Weil action remain supplied. The Born rule and Q5b spatial limit [H-L] remain open. No new result or status reclassification is introduced.

Version 2.17 types the status of every paper on one vocabulary of seven labels (proved, structural, numerical, conditional, heuristic, open, synthesis), with a primary label per paper carried identically by the inventory row, the synthesis paragraphs where they state a status, the dependency figures and the interactive graph. Numerical and conditional are defined in the conventions; synthesis becomes a graph status. Primary labels re-audited against the papers' own status statements: EBJ proved with open items; O25, O28 and O32 numerical; HeisenbergStructure, O18, O27, Q5a, AOG and SRN proved with open items; O21, O23 and Q9 conditional; Q6a open; the presentation notes and the Lorentz-capacity synthesis typed synthesis; figure styles corrected for the white paper, Born-Infeld, Q1, Q3, O18, O22, O24, O27, O29, O30, O31, Gravity and E2, and the dependency-figure styles are brought into line with the rows throughout.

The re-audit of every primary against the papers' own status statements also retypes O10, O11, O13, PTO and LowLCapacity numerical; O16, O20, O24, Q5b, Q10, Q13, U1, W1, LCII, LorCap, TempProj, SpectralRelaxation, FibreErasure, Thermodynamics, Q3, ENT-E2 and Gravity conditional on the hypothesis each names; O4, O19 and TPC open; Q12, KUD and Lorentz (a proved negative result about a posited truncation) proved; Cosmology heuristic; O22 structural; O6 keeps its proved primary with the confinement corollary now recorded conditional, O8 structural on an empirical premise, CHO conditional on the inherited central-phase lift, TopInv and O31 with their secondary labels; the O4 and O6 rows and paragraphs state the current negative results.

The pass also removes the last bare-word status cells (O29 numerical, O30 conditional), defines heuristic and the principal-contribution rule in the conventions, reorders the graph legend on that vocabulary, and restates the contribution cells of H2, TopInv and ENT-E1 and the short titles of Q9, U1 and W1, so that each names the hypothesis or the open extension its result carries. The graph node descriptions are swept against the rows over the whole surface, correcting those that stated a retracted derivation (O4), an unestablished observable (O19) or an identification the paper does not prove (Q7), and Q6b is retyped conditional on the Q5a Mosco hypotheses and [H-L] on all four surfaces.

The status conventions state the secondary-label rule as mandatory for an open or conditional item of the paper's own principal result, and it is applied by predicate over all rows. Two claims the registry itself refutes are withdrawn: the free-fraction identification of the capacity radius with the metric radius (LCII), and the gravitomagnetic reading of the Lorentz vector sector, which its paper lists as open.

Version 2.16 synchronises HeisenbergStructure 2.1 (15 August) and the 28--31 August release wave: O25 1.5, O27 2.0, Q5a 3.2, Q5b 2.1, Q12 1.4, Q13 1.4, Q14 2.0, and the Gauge Structure, Gauge--Gravity Stratification, and Fermionic Matter presentation notes. It consolidates the retired standalone HCO record into HeisenbergStructure 2.1, preserves the separation between supplied-data theorems and emergent-base readings, and records the exact [H-F] $\Rightarrow$ [H-lift] scope of Q9. O29's finite-precision diagnostics are numerical rather than exact carrier-identification theorems, and O30 is a conditional $3\times3$ model distinct from O28's measured covariance. It also distinguishes the Heisenberg/Schrödinger representation identified by Stone--von Neumann from the separate associated Weil action. The registry and website graph remain a single 116-node artefact. It also synchronises the September releases: O29 2.0, O30 2.0, O26 2.0, O28 2.0, the Spectral Admissibility presentation note 2.0, PYL 2.0, EBJ 2.0, PRS 2.1, A4-Note 2.1, FM-Note 2.1 and PYO 1.10.1, and aligns the bibliography titles of thirteen entries with their deposited records. Version labels of Foundation, Q9, NIF-Note, ENT-Note, the white paper and SpectralAdmissibility are aligned with the deposits, the Branch III description is restated on the open bridges, and the dependency graph gains numerical and conditional statuses and the edges O25 to O26/O27, O28/O29 to O30, O31 to O32 and SGN/CC-Note to the Spectral Admissibility note; it records the Q11OF central Weil lift resolution, the AOG proved status and the O14, O31, O32 and SGN row corrections, reverses the AAR/PRS edge, removes the unsupported AAR to Q11OF, Gravity to A4-Note, SRN to Q14 and O31 to TPC edges, types the O28 to O30 edge as interpretive, retypes O26 Level II as a conjecture, corrects the O32 bibliography note, and reduces the CHO node to CHO's own results.

Version 2.2 records the finite (S_3) countermodel to the published Heisenberg carrier-selection argument. The algebraic properties extracted from A1--A3 do not force a central commutator, class-two nilpotence, a finite Heisenberg group, or a Weil carrier. Found and HeisStr are therefore reclassified, while results internal to a supplied Heisenberg/Weil carrier retain their status.

Version 2.7 updates the SRN inventory row for spin-rotation-note v1.4: an independent downstream representation audit shows the Dirac-conjugated fermionic bilinear carries exact Higgs-typed electroweak quantum numbers in every tree-level Yukawa sector, permitting but not deriving a composite Higgs condensate; the pre-existing soldering audit is untouched. No new paper, node, or edge is registered; the corpus count remains 116.

What This Paper Is

The Cosmochrony programme develops a pre-geometric framework in which physical structure — spacetime, quantum mechanics, gauge symmetry, and Standard Model observables — arises from a single primitive: the local structure of admissible non-injective transitions between observable states. The corpus comprises 116 papers across three theory branches:

• Branch I — Foundation track: four axioms organise the admissibility framework. Their published carrier-selection argument is refuted by a finite (S_3) countermodel; the Heisenberg/Weil carrier remains a supplied realisation.
• Branch II — O-series (spectral admissibility): derives the canonical pair-capacity observable and its fibre/representation structure. The proposed $\delta_{\mathrm{pair}}\to\beta^*$ continuation is now recorded as a refuted native Heisenberg transfer and retained only as a cross-substrate phenomenological prescription.
• Branch III — Q-series and companion papers: develops conditional mathematical models toward quantum mechanics, spacetime geometry, gauge structure, and further observables. It contains proved internal results, but the physical chains retain supplied carriers and open bridges such as the Born rule, [H-L], and the colour factor.

Role in the Repository

• Paper inventory: the authoritative list of all papers and their status.
• Dependency graph: covers all 116 inventory entries, is maintained here, and is exported as an interactive HTML visualisation copied to the website for publication at https://cosmochrony.org.
• Coherence: updated whenever a new result is obtained or a new paper is created, so the programme stays traceable.
• Video workflow: VIDEO-WORKFLOW.md is the source of truth for scientific video production and publication; videos.json is the canonical video inventory.

Compilation

pdflatex -output-directory=out tex/program.tex
cd out && bibtex program && cd ..
pdflatex -output-directory=out tex/program.tex
pdflatex -output-directory=out tex/program.tex

Links

• 🔗 DOI: 10.5281/zenodo.19759956
• 🌐 Interactive dependency graph: https://cosmochrony.org/science/cosmochrony_graph

Citation

J. Beau, The Cosmochrony Research Programme: A Structural Roadmap and Paper Inventory, Zenodo, 2026. DOI: 10.5281/zenodo.19759956.

Acknowledgements

Portions of the editorial refinement benefited from iterative interactions with large language models, used as analytical assistants. All claims and final formulations remain the sole responsibility of the author.