Toledo — Equation Library of the Human–AI Readout Programme (v1.6.0): Information Discrete Mathematics as root extension R2, resistance ladder with reproduction evidence, 1,267 coded entries, MCP server, static API, website, catalogue

Abstract

v1.8.0 (2026-09-08). Version DOI: recorded once minted (concept 10.5281/zenodo.22537318). Commits `d786116`/`8954bcf` (Religious Attribution Non-Collapse), `8be7433`/`ef3adc7`/`270c2af` (executable-equations registrar review), `cb03ab6` (Internal-Consistency ladder + mechanical clearing fixes), `fd57ffd` (consistency-grader per-cell evidence fix), `ca9f9df` (causal-sweep merge), `d0d4709` (URCF turbulence merge), `325c477` (spectral-ceiling family merge, 4 objects), `9a41c95` (URCF_RD_All tower family merge, 17 objects), `4d381e1` (consistency-sidecar recompute + site/API rebuild for the two merges above), plus this release-prep redo. - **Internal-Consistency ladder (IC-0…IC-3)** (`cb03ab6`, `docs/CONSISTENCY_SPEC_v0_1.md`, founder instruction 2026-09-08: "at minimum [Toledo] must be systematically self-consistent"): `scripts/compute_consistency.py` grades every canonical entry and root row across seven equation-clearing audit dimensions (schema, structure, tier, symbols, coq, duplicates, lineage), reading the confirmed findings already produced by `ops/clearing/audit_*.py`, and writes read-only sidecars under `registry/consistency/ .json` plus `INDEX.json` — never a truth score, orthogonal to and never merged with the resistance ladder R0–R6. `needs_reader` is an honest state, not a pass. `scripts/v18_clearing_fixes.py` applied the subset of confirmed findings that are mechanical and need no outstanding founder ruling (15 `tier.cell_table` status moves, 125 wrapper header-comment tier corrections). - **Evidence fix** (`fd57ffd`, `ops/clearing/CHECKER_2026-09-08.md` Block 1): the grader initially left `evidence.cells` empty for every clean dimension pass, so "never examined" and "checked and clean" were indistinguishable from the sidecar alone — the exact three-state confusion the spec's own sec.0 forbids. `grade_entry` now copies each dimension's own `cells_run` disclosure (from its `findings_ .json` header) into `evidence.cells` as `{cell: "pass"}` for every examined cell with no finding against that code, `"fail"`/ `"needs_reader"` for a cell a finding id (` . # `) names, and leaves a genuinely unexamined cell absent — never defaulting to `"pass"`. Verified corpus-wide (no sidecar left with empty real-cell evidence) and idempotent; a regression test was added. - **Corpus reading, this checkout**: **1,912** sidecars (**1,302** readings + **610** roots). Readings: IC-0 **1,148** · IC-1 **27** · IC-2 **127** · IC-3 **0**; **1,274** carry at least one open finding (`flag: "IC-F"`). Roots: IC-0 **466** · IC-1 **51** · IC-2 **93** · IC-3 **0**; **610** carry at least one open finding. No entry holds IC-3 yet — that rung needs clearance rows (`ops/clearing/clearances.jsonl`), which do not exist in this checkout. See README's new "Internal-Consistency ladder" section. - **Religious Attribution Non-Collapse (RANC)** (`d786116`/`8954bcf`): one new reading, `weld/H.51.v1`, from "Plural Interfaces, Singular Commitments" v1.0 sec.8.1 (Yaoharee Lahtee) — a five-level non-collapse chain (model output, product policy, institutional norm, actor belief, person-specific religious classification). `phi_check` found no existing match; parented on `weld/H.33.v1` (Core Epistemic Structure non-collapse) as the closest prior discipline, tier `Definition` per the source's own framing, `coq_status: open_prop`. `origin.doi` patched to the minted Zenodo record `10.5281/zenodo.22660591` once available. - **Executable-equations registrar review** (`8be7433`/`ef3adc7`/`270c2af`, founder ruling `BBL-2026-09-08-243` item 2): acting under chair delegation, `EQ-001/P.45.v1` (Lorentz boost pair) set `reviewed_ineligible` — `sympy`'s parse shattered the bare identifier `Gamma_R` into single-letter symbols and dropped the statement's second clause, so its IR does not represent the source statement; `EQ-001/P.63.v1` built and cross-checked instead. Evidence citations (`registry/reproduction_card_index.json`, `registry/executable/INDEX.json`) repointed at the glosa commit that actually holds the reproduction cards (an earlier citation pointed at a commit filed before the card existed there). - **Causal-memory root extension** (`ca9f9df`, `registry/proposals/causal_sweep.json`): **27** new readings from a 2026-09-08 sweep of causal-memory-programme records (41 raw new-branch objects deduped to 27 across three judged parts). `scripts/v18_causal_merge.py` re-verified every parent code and alias against the live registry, assigned real `.v1` running numbers per (root, domain) replacing the proposal's `??` placeholders, and appended one LINEAGE `assigned` event per entry. New readings land under `EQ-015/H` (2), `weld/B` (1), `weld/M` (3), `CMC/P` (1), `Face.10.IdentifiabilityGate/M` (1), `weld/S` (1), `weld/P` (4), `EQ-001/P` (9), `EQ-015/P` (3), `CMC/M` (1), `MQ08-stepper/M` (1) (2+1+3+1+1+1+4+9+3+1+1 = 27). All 27 are `coq_status: open_prop` (tier as proposed, never raised); each got its own `coq/canonical/.v` open-proposition stub, individually `coqc`-verified to compile (27/27 clean, no proof attempted). See README's new "Causal-memory root extension" section. - **URCF turbulence instance** (`d0d4709`, `registry/proposals/urcf_turbulence.json`): one new reading, `weld/P.05.v1`, the Retained-Information Relaxation-Inertia turbulence prediction equation (τ_R dI_R/dt + L_R I_R = S_R + η_R) from a standalone research pack never deposited on Zenodo (`origin.doi: null`). `instance_of` `weld/S.01.v1` (the Finite-Memory Laplacian/Telegraph Generator this equation instantiates in a new domain) and `instance_of` `EQ-008` (a structural, not author-cited, match to IDM/Genesis root `EQ-008`'s `L_R := D_W − W`) — the proposal file's own `"root/EQ-008"` prefix did not match the registry's bare-root citation convention and was corrected. Its own `does_not_resolve` caveat is preserved verbatim in `drift_note`: this reading does **not** close Genesis root gap T2 (the harder, still-open state-dependent `L_R[I_R]` case) — it is the easier linear/time-invariant sub-case only. `coq_status: open_prop`, `coqc`-verified to compile. See README's new "URCF turbulence instance" section. Related: `docs/TURBULENCE_KNOWLEDGE_LEDGER_2026-09-08.md` (`d42ad50`) — 13 turbulence/Navier-Stokes sources read in full at intake, 4 Coq files independently compiled and tier-checked; strongest verified fact recorded: `ker(L_R) = constants`, axiom-free. - **Spectral-ceiling family** (`325c477`, `registry/proposals/spectral_ceiling_family.json`, after independent adversarial re-verification `ops/urcf_tower/REVERIFICATION_2026-09-08.md`): **4** new readings, `weld/M.40.v1`–`weld/M.43.v1`. `weld/M.40.v1` (Anderson-Morley sharp curvature ceiling, witness form over `Q`) and `weld/M.43.v1` (`ker(L_R) = constants` under connectivity) are `partial_overlap`: each is trimmed to only the half of its source claim not already covered by an existing reading (`q_formal/M.05.v1` and `L_R/M.22.v1` respectively), with `relations[]` cross-referencing the pre-existing code for the overlapping half rather than re-registering it. `weld/M.41.v1` (Dirichlet energy PSD/gauge/stencil/second-difference) and `weld/M.42.v1` (Rayleigh-quotient ceiling `lam <= 2*dmax`, division-free) are `genuinely_new`, registered in full. All four Coq files (`InfoSpectralCeilingSharp.v`, `RDL_GammaSpectral.v`, `RDL_SpectralCeiling.v`, `URCF_RD_All.v` module Graph / `RDL_Graph.v`) recompiled and Print-Assumptions-verified in this repo — axiom-free. - **URCF_RD_All tower family** (`9a41c95`, `registry/proposals/urcf_rd_all_family.json`, same reverification pass, `scripts/v18_tower_merge.py`): **17** new readings, `weld/M.44.v1`– `weld/M.60.v1`, capturing a private tower file (`URCF_RD_All.v`, Module RD, never previously deposited or registered) covering a Peano/PA model-theory tower across Genesis roots `D`, `RD3`, `RD4`, `Z`, `Q` and `R`: successor non-collapse and injectivity, `D`'s commutative-semiring package, order/well-foundedness, the `toNat : D -> N` isomorphism, term-language homomorphisms, elementary equivalence, a Hilbert-style proof system, `D` as a model of PA, the constructive consistency of PA (`weld/M.52.v1`, `Con_PA`, axiom-free), a **classically-dependent** sibling consistency proof (`weld/M.53.v1`, `Con_PA_classical` — `Print Assumptions` names exactly one axiom, `Classical_Prop.classic`; kept as a distinct entry, never presented as axiom-free and never folded into `weld/M.52.v1`), PA-truth transport, Dedekind categoricity, a metric/Tarski betweenness layer, the discrete Leibniz product rule, `Q` as a field, and `R` as a Bishop-regular Cauchy-sequence ordered field with Cauchy-completeness. **14** of the 17 are `genuinely_new` (verified by corpus-wide keyword search against `CANONICAL.json`, zero matches, per entry); **3** are `partial_overlap`: `weld/M.44.v1` (only `RD4` successor-injectivity is new; the `succ<>zero` half duplicates `RD3/M.01.v1`, dropped rather than re-registered), `weld/M.58.v1` (only the pointwise Leibniz rule is new; the bundled discrete-FTC half duplicates `A2/M.03.v1`/ `Z/M.06.v1`, physically omitted from the Coq file, not just the registry entry), and `weld/M.60.v1` (kept whole rather than trimmed — the overlapping piece, a near-trivial pointwise-add-commutativity fact against a structurally different prior `R` representation (`R/M.33`–`M.37.v1`), is a small fraction of the object; the overwhelming majority — full order, multiplicative inverse, completeness, metric, convergence, continuity — has no prior reading). All 17 Coq files `coqc`-recompiled and `Print Assumptions`-verified in this repo: 16 axiom-free, 1 (`weld/M.53.v1`) correctly disclosing its one classical axiom. - **Consistency sidecars recomputed, site and both static APIs rebuilt** (`4d381e1`): re-ran `scripts/compute_consistency.py` over the 21 new entries (all land on IC-2, no open finding) and `make build`, `python3 site/build_site.py --out site/dist --strict`, `python3 -m toledo_m