Zero Paradox Version Registry
Update this file first on any version bump. README.md Framework table and GUIDE.md Reading Paths are verified against this register.
| Document | Formal Version | Filename | Companion Version | Comp AR | Notes |
|---|---|---|---|---|---|
| ZP-A Lattice Algebra | v1.19 | ZP-A_Lattice_Algebra.pdf | v1.11 | Y/Y | v1.19: rendered Lean citations synced to post-reorg files/namespaces (SSOT-driven).C8 dual-date templating (Initial/Current meta line; hardcoded month removed).v1.17: C8 dual-date — subtitle templated via version_line (First released / This version); hardcoded month removed. v1.16: FMC uniformity (Step 4b) — residual AFA-necessity assertions softened to “argued” (metatheoretic declaration, R-AFA cross-framework note, CC-2 validation-table cell); comp v1.10 same. v1.15: FMC precision (sweep Step 4, against fmc.md) — CC-2 box “structurally required”/”ruled out”/”incompatible” softened to “argued”; named falsifier added; status line marked argued, not a derivation. v1.14: CC-2 label → Forced Metatheoretic Commitment — formal:a6b182ee comp:7f40ab94 |
| ZP-B p-Adic Topology | v1.11 | ZP-B_pAdic_Topology.pdf | v1.11 | STALE | C8 dual-date templating (Initial/Current meta line; hardcoded month removed).v1.10: rendered self-version tags removed from C2/C3 corollary titles + “null state” → ⊥ in AX-B1 note (C1 sweep) — formal:68da2ed3 comp:4f7498ea |
| ZP-F The Counterexamples | v1.5 | ZP-F_The_Counterexamples.pdf | v1.13 | STALE | C8 dual-date templating (Initial/Current meta line; hardcoded month removed).v1.4: vocab fix — “null state” → “⊥” in preamble; palette rebuild — formal:cd25d8fc comp:e5701ed2 |
| ZP-C Information Theory | v1.20 | ZP-C_Information_Theory.pdf | v2.7 | STALE | v1.20: rendered Lean citations synced to post-reorg files/namespaces (SSOT-driven).C8 dual-date templating (Initial/Current meta line; hardcoded month removed).v1.18: rendered self-version refs removed — P₀ note (“Version 1.4 updates this”) + Open Items row (C1 sweep) — formal:9759be79 comp:fb2cd7c4 |
| ZP-D State Layer | v1.15 | ZP-D_State_Layer.pdf | v1.13 | STALE | v1.15 / comp v1.13: rendered Lean citations synced to post-reorg files/namespaces (SSOT-driven).v1.14: R-PA prior-art note — T is the standard p-adic ball-indicator ONB (van der Put basis) / Kozyrev p-adic wavelet basis (Kozyrev 2002), with p-adic-QM context; paired with the CLAIMS Convergence row. C8 dual-date templating (Initial/Current meta line; hardcoded month removed).v1.12: rendered self-version refs removed — DP-1 title tag + T2 “R3 (v1.6)” (C1 sweep) — formal:f644e376 comp:db8ed80e |
| ZP-E Bridge Document | v3.23 | ZP-E_Bridge_Document.pdf | v1.11 | STALE | v3.23: rendered Lean citations synced to post-reorg files/namespaces (SSOT-driven).C8 dual-date templating (Initial/Current meta line; hardcoded month removed).v3.21: FMC precision (sweep Step 4, against fmc.md) — R-AFA “the metatheoretic necessity of AFA is derived” → “argued, not proved (a metatheoretic squeeze, not a derivation)” + named falsifier added; CC-2 status lines split the proved structural fixed point (T-EXEC, axiom-free) from the argued set-membership reading; “establish that Foundation is incompatible” → “make the case that” — formal:ecd54df3 comp:1b4c17b0 |
| ZP-G Category Theory | v1.15 | ZP-G_Category_Theory.pdf | v1.9 | STALE | v1.15: rendered Lean citations synced to post-reorg files/namespaces (SSOT-driven).v1.14: R-AX named AX-G2 as the standard strict-initial-object property (Carboni-Lack-Walters 1993) + the AX-G1+AX-G2 = non-trivial-strict-initial note; prior-art positioning paired with the CLAIMS Convergence section. C8 dual-date templating (Initial/Current meta line; hardcoded month removed).v1.12: rendered self-version refs removed — 24 status/provenance tags + “Version 1.0…1.1” narratives + Supersedes (C1 sweep; cross-doc ZP-H v1.0 citations kept) — formal:2af3526b comp:e9014e47 |
| ZP-H Categorical Bridge | v1.17 | ZP-H_Categorical_Bridge.pdf | v1.14 | STALE | C8 dual-date templating (Initial/Current meta line; hardcoded month removed).v1.16: rendered self-version removed — endnote + R-FORCING tag (C1 sweep; 21 cross-doc citations kept per scope) — formal:b2cd69f7 comp:b81238d3 |
| ZP-H Native Categories Addendum | v1.2 | ZP-H_Native_Categories_Addendum.pdf | N/A | STALE | C8 dual-date templating (Initial/Current meta line; hardcoded month removed).v1.2: rendered Lean-file citations synced to post-reorg basenames (ZPH_* -> *, ZPH_MC1 -> MC1Bridge).v1.0: Initial release — snap floor realized in native Mathlib categories: fB_functor → TopCat (⊥ = inverse limit ⋂ B(0,2⁻ⁿ) = {0}), fD_functor → ModuleCat ℂ (⊥ = StateSpace 0 initial; isometric embeddings), fC_functor → KleisliCat PMF (⊥ = Fin 0 initial; fC_no_return = AX-G2 as theorem); mc1_correspondence capstone. Correspondence half of MC-1 formal; identity half a commitment. Lean: ZPH_TopFunctor/ZPH_HilbFunctor/ZPH_InfoFunctor/ZPH_MC1.lean; [propext, Classical.choice, Quot.sound] — formal:00d1d40a |
| ZP-I Inside Zero | v1.13 | ZP-I_Inside_Zero.pdf | v1.23 | STALE | v1.13 / comp v1.23: rendered Lean citations synced to post-reorg files/namespaces (SSOT-driven).C8 dual-date templating (Initial/Current meta line; hardcoded month removed).v1.11: rendered self-version removed — register section headers + T-IZ status cells + endnote (C1 sweep) — formal:2ef0bc04 comp:8f71f95f |
| ZP-J Self-Reference | v2.5 | ZP-J_Self_Reference.pdf | v1.29 | STALE | comp v1.29: rendered Lean citations synced to post-reorg files/namespaces (SSOT-driven).C8 dual-date templating (Initial/Current meta line; hardcoded month removed).v2.5: rendered Lean citations synced to post-reorg files/namespaces the v2.4 pass missed (ZPJ.lean -> SetTheoryAFA.lean; ZeroParadox.ZPJ.* -> ZeroParadox.* namespace flattened; ZPE.da2_bottom_characterization -> bare, now in Snap.lean).v2.4: rendered Lean-file citations synced to post-reorg basenames (ZPJ_AczelConn.lean -> AczelConn.lean, etc.).v2.2: rendered self-version refs removed (C1 sweep); null glyphs fixed. comp v1.26: FMC precision (sweep Step 4) — Key Results box + T-EXEC body line split the proved structural fixed point (axiom-free) from the argued set-membership reading. comp v1.25: ScaleBridge wired into maintained build → §6 “future work” bridge retired (2-adic argument now formalized), §7 common-ancestor (ValBridge) framing added, §8 adds ℤ₂ as 3rd concrete model (flagged Classical.choice-carrying vs axiom-free T-EXEC). comp v1.24: APG directed-graph diagram (self-loop), arithmetic analogy scoped, depth rephrased to intrinsic descent, self-loop redrawn as dashed curve (Dan 2026-06-15) — formal:146e11b1 comp:578c9d76 |
| ZP-J AFA Addendum | v1.6 | ZP-J_AFA_Addendum.pdf | N/A | STALE | v1.6: rendered Lean citations synced to post-reorg files/namespaces (SSOT-driven).C8 dual-date templating (Initial/Current meta line; hardcoded month removed).v1.5: rendered Lean-file citations synced to post-reorg basenames (ZPJ_* -> *).v1.3: rendered self-version ref removed from endnote (C1 sweep); fixed scaleᵏ null glyph — formal:8d7346ee |
| ZP-J Wheel Addendum | v1.3 | ZP-J_Wheel_Addendum.pdf | v1.3 | STALE | C8 dual-date templating (Initial/Current meta line; hardcoded month removed).v1.3: rendered Lean-file citations synced to post-reorg basenames (ZPJ_Wheel/WheelFrac -> Wheel/WheelFrac).v1.1: WheelFrac.* citations → ZPJ_WheelFrac.* (Lean namespace standardization); comp v1.1 same. v1.0: Initial release — wheel of fractions ⊙_S A = (A×A)/≡_S is a Wheel (Carlström Def 1.1, 14 fields), choice-free [propext, Quot.sound]; inf_ne_bot porthole (∞≠⊥ given 0∉S). Lean: ZPJ_WheelFrac.lean; fix() guard added (PDF build standards). comp v1.0: ZP-J_Wheel_Illustrated_Companion.pdf — plain-language (division-by-zero made total; ∞=/0, ⊥=0·/0; wheel-vs-meadow diagram; instWheel + inf_ne_bot; porthole connection) — formal:ed028de2 comp:0ba1f949 |
| ZP-J Keystone Addendum | v1.2 | ZP-J_Keystone_Addendum.pdf | N/A | N/A | v1.2: rendered Lean-file citations synced to post-reorg basenames (ZPJ_* -> *).v1.1: honest-scope precision — the single-carrier “snap is one crossing” carries no NEW commitment; it rests on the framework’s existing ⊥/ε₀ identification (MC-1 / OQ-E2), endpoints proved (floor non-wf via real ⊥, axiom-free). v1.0: Initial release — thin addendum recording two machine-checked keystone probes. (1) Lawvere face-split (ZPJ_Lawvere.lean): in Set no face is a Lawvere instance (Cantor — nontrivial_lattice_no_witness, q2_no_witness), the computability face genuine (computability_face_fixedPoint, wraps Mathlib recursion theorem); fixedPoint_of_witness / no_witness_of_fixedPointFree axiom-free. (2) Well-foundedness boundary (ZPJ_Boundary.lean, ZPJ_BoundaryBridge.lean): the snap as a ν→μ crossing — relation level (floor_not_wellFounded axiom-free; snap_crossing) + QPF bridge (snap_boundary_two_registers), best-effort; full Taylor coalgebraic (next-operator / Pataraia / General Recursion Theorem) open, cited to Taylor/AMM. Honest fences throughout (probe; no-new-commitment; open Rung-C) — formal:857ec9ae |
| ZP-K Computational Grounding | v1.9 | ZP-K_Computational_Grounding.pdf | v1.12 | STALE | v1.9 / comp v1.12: rendered Lean citations synced to post-reorg files/namespaces (SSOT-driven).C8 dual-date templating (Initial/Current meta line; hardcoded month removed).v1.7: version changelog removed from preamble; palette rebuild. comp v1.10: four_way_diagram — removed the redundant internal caption String that overlapped the “Computation (Kleene)” box (Diagram Rule 4). comp v1.9: FMC precision (sweep Step 4) — DA-1 Path 1 splits the axiom-free structural fixed point from the literal ⊥={⊥} (ZF+AFA setting) — formal:1fa45e72 comp:a205918c |
| ZP-L Incomputability Convergence | v1.3 | ZP-L_Incomputability_Convergence.pdf | v1.6 | STALE | v1.3 / comp v1.6: rendered Lean citations synced to post-reorg files/namespaces (SSOT-driven).C8 dual-date templating (Initial/Current meta line; hardcoded month removed).v1.1: rendered version changelog removed + 3 null glyphs fixed (subscript-letter entities ₙ/ₒ → markup) (C1 sweep); comp v1.4: strip footer version — formal:d975fa9f comp:1b075124 |
| ZP-M Kleene-Ordinal Bridge | v1.3 | ZP-M_Kleene_Ordinal_Bridge.pdf | v1.5 | N/— | v1.3 / comp v1.5: rendered Lean citations synced to post-reorg files/namespaces (SSOT-driven).C8 dual-date templating (Initial/Current meta line; hardcoded month removed).v1.1: rendered version changelog removed from title note + endnote (C1 sweep); v1.0: snapEmbed type bridge, hfp gap closed, zpm_triangle, R-M.1; comp v1.3: rendered self-version removed from Key Results header (C1) — formal:b510ab50 comp:0af8ce63 |
| ZP-N The Constructive Snap | v1.0 | ZP-N_The_Constructive_Snap.pdf | N/A | N/— | v1.0: Initial release. The choice-free constructive companion to ZP-L — the ε₀ snap from below, rebuilt syntactically on ordinal notations (ONote), never touching Mathlib’s choice-saturated Ordinal. Three snap results choice-free ([propext] only, free even of Quot.sound): exp_lt_term, omegaPow_no_fixedpoint (no notation is a fixed point of x↦ω^x), tower_strictMono (the ω-tower climbs without bound below ε₀). Finding: ZP-L’s Classical.choice at ε₀ is representational, not intrinsic (inherited from Mathlib’s Ordinal). Side finding: tower_NF carries Classical.choice (the syntax→semantics bridge). Minimality (ε₀ the LEAST fixed point) open. Editorial PASS 2026-07-12. Lean: ConstructiveOrdinals.lean — formal:6819800f |
| ZP-P The Fixed-Point Fork | v1.5 | ZP-P_The_Fixed_Point_Fork.pdf | N/A | N/— | v1.5: rendered Lean citations synced to post-reorg files/namespaces (SSOT-driven).v1.4: rendered Lean-file citations synced to post-reorg basenames (ZPP_* -> *).v1.3: re-aimed the categorical-instance choice note per Veltri (FSCD 2021) literature review — the ν-side Classical.choice is a Mathlib M-type artifact, not a necessity (polynomial-functor final coalgebras are choice-free); choice genuinely enters only for the non-polynomial finite-powerset functor (full AC for the set-quotient; countable choice + LLPO for Worrell’s limit); added “where choice genuinely enters” remark + Veltri/Ahrens citations (R1). C8 dual-date templating (Initial/Current meta line; hardcoded month removed).v1.1: Added categorical-parent instance as Lean witness (ZPP_Coalgebra.lean: fix_isEmpty μ-empty choice-free, cofix_nonempty ν-inhabited Classical.choice, categorical_fork_strict); set theory/computation referenced (ZP-J/ZP-K) not re-framed. v1.0: synthesis layer — abstract fork schema (lfp/gfp collapses iff unique fixed point) choice-free in Lean: fork_le, collapse_of_unique, unique_of_collapse, fork_collapse_iff [propext, Quot.sound]; number-system instance via Ostrowski: completions_exhaustive, real_not_equiv_padic [propext, Classical.choice, Quot.sound]. Generalizes ZFC+Foundation/AFA orthogonal-contact-point claim; three tiers (schema/instances/unification), hard fence (cross-instance identity = type boundary) + soft fence (not every fork is μ/ν). Lean: ZPP.lean, ZPP_Ostrowski.lean, ZPP_Coalgebra.lean — formal:cbb4be58 |
| ZP-R Cross-Category Fixed Point | v1.0 | ZP-R_Cross_Category_Fixed_Point.pdf | N/A | N/— | v1.0: Initial release. Synthesis / placement layer — locates and realizes the framework’s self-application fixed point ⊥ as a Lawvere fixed point across three faces: refuted in Set (Cantor; reflexive_object_refuted, not_monotone_not), obstruction-free but not a reflexive object in the monotone/domain regime (monotone_regime_derives_pinned; Scott D∞ unbuilt), realized in the computability face (eval_point_surjective, computable_no_fixedpointfree, selfref_fixedpoint_exists_computable — the crossing). R1 fork (fork_collapse_iff via instance_pinnable_iff_fork_collapse); R2a/b existence-as-selfApp + uniqueness-extra (lawvere_fixedpoint_selfApp, selfApp_pinnable, existence_without_uniqueness); R4 μ/ν = Lawvere regimes (mu_nu_branch_exclusion). Scope: existence-as-Lawvere (computability face) vs uniqueness + location (fork/AFA face: t_exec/t_exec_iff, quine_atom_unique, unique_fp) each proved but face-local and non-composable (F1/F2) — the computability face is non-unique (infinite_quine_family). Global identification held as a fenced conjecture. Choice-free spine, choice-carrying computability realization. Lean: RequirementsGap/MetaFork/LawvereBridge/SetTheoryAFA/SelfApp/ComputableCrossing/Kleene — formal:3bcf9350 |
| ZP-R Diagonal Family Addendum | v1.0 | ZP-R_Diagonal_Family_Addendum.pdf | N/A | N/— | v1.0: Initial release. Addendum to ZP-R — the complete diagonal-family roster tied to ⊥, organized by the μ/ν fork. Supersedes the private ZP-W “Zero as a Wall” draft. Engine: negation_no_fixedpoint, lawvere_fixedpoint (Wall.lean; choice-free). Wall faces μ (self-reference cannot close): Cantor (cantor_via_engine), Russell (russell_via_engine), Turing (no_self_decider), the wall wf_no_selfloop — all Wall.lean choice-free; Tarski (tarski_no_internal_truth, Tarski.lean), Curry (curry_paradox/curry_no_bottom, Curry.lean). Floor faces ν (self-reference closes): Quine atom (t_exec/t_exec_iff, SetTheoryAFA.lean), Kleene quine (computability_face_fixedPoint, Lawvere.lean; choice-carrying), Löb + Gödel 2nd (loeb, godel_two, Loeb.lean; choice-free), Rice exists-but-undecidable (rice_face_has_bottom, quine_exists_yet_rice, Rice.lean; choice-carrying). Gödel 1st between the columns (via lawvere_fixedpoint). Unification = Lawvere 1969 / Yanofsky 2003 (cited); contribution = axiom-free core formalization (computability faces choice-carrying) + tie to ⊥ (placement, not new theorem); cross-face identity a type boundary (ZP-P hard fence / ZP-R F2) — formal:19000586 |
| ZP-Q The Frame-Change | v1.0 | ZP-Q_The_Frame_Change.pdf | N/A | N/— | v1.0: Initial release. Synthesis layer, ZP-P sequel — ⊥→ε₀ as a change of point of view. §I frame-flip schema (fork_is_frameflip, ForkFrameChange.lean; choice-free [propext, Quot.sound]); §II per-domain instances (valuation/Riemann sphere: snap_is_frameflip / RiemannSphere.lean; category: catseam_is_frameflip; set-theory/computability/Hilbert/information referenced; reals NO-GO); §III universal + walls (order-theoretic universal holds; the categorical Lawvere universal meets a proven wall, Cantor/Lawvere.lean; cross-domain identity a type boundary). Three tiers; “the fence is the bridge”; the bottom never positively represented; static Riemann-sphere figure. Editorial PASS 2026-07-12 — formal:f1a726ea |
| Zero Paradox Foreword | v2.11 | Zero_Paradox_Foreword.pdf | N/A | N/A | v2.10: §IV cited Yanofsky (2003) + Lawvere (1969) for the diagonal-fixed-point unification (prior-art positioning; paired with the new CLAIMS “Convergence with established work” section). C8 dual-date templating (Initial/Current meta line; hardcoded month removed).v2.8: FMC uniformity — CC-2 metatheoretic row “Foundation is ruled out” → “argued to be ruled out”. v2.7: §IV names Lawvere’s fixed-point theorem as the recognized unification of the diagonal family (Cantor/Russell/Gödel fixed-point lemma/Kleene); fence firmed — ZP “locates” the diagonal fixed point, not “is”. v2.6 added the keystone — formal:2cca89c9 |
| ZP Philosophical Question | v1.13 | ZP_Philosophical_Question.pdf | N/A | N/A | C8 dual-date templating (Initial/Current meta line; hardcoded month removed).v1.11: fix() guard via Paragraph override; “bridge” → “connecting argument”; “in ZP’s reading” de-duplicated — formal:bfdde106 |
| ZP Choice-Free Core Addendum | v1.3 | ZP_Choice_Free_Core_Addendum.pdf | N/A | N/A | C8 dual-date templating (Initial/Current meta line; hardcoded month removed).v1.3: rendered Lean-file citations synced to post-reorg basenames (ZPx_* -> ).v1.1: WheelFrac. citation → ZPJ_WheelFrac.* (Lean namespace standardization). v1.0: Initial release — the conceptual core is choice-free; T-SNAP axiom-free; Classical.choice confined to the analytic realizations (inherited from Mathlib); dependence ≠ necessity (open). Anchored on AxiomProfile.lean — formal:18acc791 |
Comp AR column key: Y/Y = current comp hash adversary-reviewed + remediated (or confirmed clean). Y/N = reviewed, fixes identified but not yet applied. N/— = not yet reviewed.
Last updated: May 2026
Script Hash Verification + AR Tracking
The formal:XXXXXXXX comp:XXXXXXXX tokens in the Notes column above are SHA-256 (first 8 chars) fingerprints of the corresponding build scripts in .claude-local/. The Comp AR column tracks adversary-review status for each companion, backed by .claude-local/ar_status.json.
Session start — run once before touching any build script:
python .claude-local/check_hashes.py
A hash MISMATCH means a script was modified without a version bump and PDF rebuild. An AR status of STALE means the companion script changed since its last adversary review — re-review required before merge.
Post-fix workflow — after applying adversary-review fixes, rebuilding the PDF, and updating the hash in register.md, run one command to close the loop:
python .claude-local/check_hashes.py --mark-remediated ZP-X
This computes the current comp hash, writes it to ar_status.json as remediated, and updates the Comp AR column in this file automatically. For fixes identified but not yet applied, use --mark-reviewed ZP-X instead (sets Y/N).