[{"type":"thinking","thinking":"So E-011's validated formula:\n\nλ_n = 1 − Σ_{j=1}^n C(n,j) η_{j−1} − Σ_{j=2}^n (−1)^{j−1} C(n,j)(1−2^{−j})ζ(j)\n\nwhere η_k are the Laurent coefficients of −ζ′/ζ at s=1 (the \"eta\" Stieltjes-like constants, η_0 = −0.577... wait η_0 here = −γ? Let me check: E-011 printed η_0... In E-021's P2, eta_0 = −0.576975292 — but γ = 0.577215. Hmm η_0 = −0.57697529... That's NOT −γ (−0.5772157). Difference ~2.4e-4? Actually STATE.md said \"η₀=−0.576975 (= −γ within σ₁-tail 1.2e-3 ✓)\" — hmm, but that was for the zero-side computation where σ₁ tail affects η_0. η_0 (true) = −γ = −0.57721566. E-021 computed −0.57697529, off by 2.4e-4 — consistent with σ₁ tail 1.2e-3? Off by 2.4e-4, fine.\n\nBut the REAL issue: in E-011's convention, λ_n = 1 − Σ C(n,j)η_{j−1} − Σ (−1)^{j−1}C(n,j)(1−2^{−j})ζ(j). So:\n\nS_f(n) [E-021's λ = S_∞ − S_f + 1] should correspond to S_f = Σ C(n,j)η_{j−1}... and S_∞ = 1 − Σ(−1)^{j−1}C(n,j)(1−2^{−j})ζ(j) − 1? Let's match:\n\nE-011: λ_n = 1 − Σ_j C(n,j)η_{j−1} − Σ_{j≥2} (−1)^{j−1} C(n,j)(1−2^{−j})ζ(j).\n\nE-021: λ_n = S_∞ − S_f + 1 where S_∞ = Σ_{j=1}^n (−1)^j C(n,j)(1−2^{−j})ζ*(j), ζ*(1) = log(4π)+γ.\n\nCompare: E-011's second sum −Σ_{j≥2}(−1)^{j−1}C(n,j)(1−2^{−j})ζ(j) = Σ_{j≥2}(−1)^j C(n,j)(1−2^{−j})ζ(j). E-021's S_∞ adds the j=1 term: (−1)^1 C(n,1)(1−1/2)ζ*(1) = −n·(1/2)(log 4π+γ). So S_∞(E-021) = [E-011 second sum] − (n/2)(log4π+γ).\n\nLagarias's actual decomposition (Thm 5.1 / (4.11)): S_∞(n) = (1/2)n log n + c₁n + O(1) — the measured residual → −0.25, so E-021's S_∞ matches Lagarias's definition and is asymptotically correct.\n\nAnd E-011: λ_n = 1 − Σ C(n,j)η_{j−1} + [S_∞ − (n/2)(log4π+γ)]·... wait let me redo. E-011: λ_n = 1 − Σ_j C(n,j)η_{j−1} − Σ_{j≥2}(−1)^{j−1}C(n,j)(1−2^{−j})ζ(j).\n\nSet Σ_{j≥2}(−1)^{j−1}(...) = −S_∞ + j1-term where j1 term of S_∞ = −n/2 (log4π+γ). So −Σ_{j≥2}(−1)^{j−1} = S_∞ − (−n/2)(log4π+γ)?? Let me be careful:\n\nS_∞ = Σ_{j=1}^n (−1)^j C(n,j)(1−2^{−j})ζ*(j) = −(n/2)(log4π+γ) + Σ_{j=2}^n (−1)^j C(n,j)(1−2^{−j})ζ(j).\n\nE-011 sum: Σ_{j=2}^n (−1)^{j−1} C(n,j)(1−2^{−j})ζ(j) = −Σ_{j=2}(−1)^j(...) = −[S_∞ + (n/2)(log4π+γ)].\n\nSo E-011: λ_n = 1 − Σ_j C(n,j)η_{j−1} + S_∞ + (n/2)(log 4π+γ).\n\nE-021 claims λ_n = S_∞ − S_f + 1 with S_f = Σ_j C(n,j)η_{j−1}. These differ by (n/2)(log4π+γ)! E-021's S_f is MISSING the (n/2)(log4π+γ) term... no wait, it differs by that additive term. Hmm, but that term is only O(n) ~ 1e4, not 1e170.\n\nSo that discrepancy doesn't explain the explosion. The explosion must be in the η_j values themselves. E-021 computes η_j via zero-side: η_j = τ_j + (−1)^{j+1}σ_{j+1} + (−1)^j. But D-033 §3 says η_j ≈ (−i)^{j−1}σ'_j... Hmm no wait, that's about a different η.\n\nHold on. There are TWO different η's! In Lagarias's paper:\n- The arithmetic η_k: Laurent coefficients of −ζ′/ζ(1+u) — these DECAY/GROW? η_k ~ (−1)^k... The η_k grow like... η_k for ζ: related to Stieltjes, η_k ~ (−1)^{k+1}(...). Actually η_0 = −γ, η_1, ... these are O(1) growing slowly.\n- The zero-side η_m in Lagarias (4.10): η_m = Σ_ρ (1−(1−1/ρ)^{m+1})... no.\n\nWait, in Lagarias (2.x)/(4.x): η_m := Σ_ρ [1 − (1 − 1/ρ)^{m+1}]/(m+1)? Hmm no.\n\nActually in Lagarias's paper he defines (4.10):\nη_m = τ_m + (−1)^{m+1} σ_{m+1} + (−1)^m? That matches E-021's P2 formula. But what IS this η_m? In Lagarias, η_m := Σ_ρ ρ^{−m} ... no. Let me think about magnitudes. If η_m = τ_m + (−1)^{m+1}σ_{m+1} + (−1)^m with τ_m = (−1/2)^{m+1}ζ(m+1, 1/2): Hurwitz zeta ζ(m+1,1/2) = (2^{m+1}−1)ζ(m+1) ≈ 2^{m+1}. So τ_m ≈ (−1/2)^{m+1}·2^{m+1}ζ(m+1) = (−1)^{m+1}ζ(m+1) ≈ (−1)^{m+1}. So η_m = O(1) alternating — good, these are the arithmetic η (Laurent coefficients of −ζ′/ζ at 1), consistent: η_0 = −γ... wait η_0 = τ_0 + (−1)σ_1 + 1. τ_0 = −(1/2)(log4π+γ) ≈ −(1/2)(2.5310) = −1.2655. Hmm, −1.2655 − σ_1 + 1. σ_1 = Σ_ρ 1/ρ... paired: Σ 1/(ρ(1−ρ)) over upper zeros ≈ 0.046191/2? No — σ₂ = Σ|ρ|⁻² = 0.046191 and Σ_upper 1/(ρ(1−ρ)) = Σ_upper 1/|ρ|² ≈ 0.0230955 = −B. So η_0 = −1.2655 − 0.0230955 + 1 = −0.2886?? That's not −0.57697. Hmm wait: 1 − 1.2655 − 0.0231 = −0.2886. But the script printed η_0 = −0.576975292 = −2×0.288487. Interesting — exactly 2× −0.2884876. So maybe σ_1 as computed = sum over upper of 1/(ρ(1−ρ)) but the TRUE σ_1 = Σ_all 1/ρ = 2× that? Let's check: η_0 should be τ_0 − σ_1 + 1 with σ_1 = Σ_ρ ρ^{−1} = −0.0230955·... hmm.\n\nActually classical: Σ_ρ 1/ρ = 1 + γ/2 − (1/2)log4π = B-ish. The constant B in ξ′/ξ = B + Σ(1/(s−ρ)+1/ρ) with B = −Σ_ρ 1/ρ = −0.0230955·... wait D-036 says B = −1 + log2 + (1/2)logπ − γ/2 ≈ −0.0230955. And Σ_ρ 1/ρ = −B? No: B = −Σ_ρ (1/ρ + 1/(1−ρ))/2 ... For symmetric zeros, Σ_ρ 1/ρ = Σ_ρ 1/(1−ρ), and B = −Σ_ρ 1/ρ. Known: Σ_ρ 1/ρ = 1 + γ/2 − (1/2)ln(4π) ≈ 0.0230957 (positive). Hmm: 1 + 0.2886 − 1.2655 = 0.0231. Yes! Σ_ρ 1/ρ = +0.0230957.\n\nSo in η_0 = τ_0 + (−1)^1 σ_1 + (−1)^0 = τ_0 − σ_1 + 1 = −1.2655 − 0.0230957 + 1 = −0.2886. But true η_0 = −γ = −0.5772. Hmm, −0.5772 = 2×(−0.2886)! Interesting. And the script printed −0.576975 ≈ −0.5772 ✓ — because the script's σ_1 computed 2×0.0231? Script: s = sum(1/(r(1−r)) for r in rho_upper); 1/(ρ(1−ρ)) for ρ=1/2+iγ is 1/(1/4+γ²) ≈ 1/γ² — real, ~2×Re(1/ρ)? Re(1/ρ) = (1/2)/(1/4+γ²). So 1/(ρ(1−ρ)) = 1/(1/4+γ²) = 2Re(1/ρ). Sum over upper γ of 1/(ρ(1−ρ)) = Σ_upper 2Re(1/ρ) = Σ_all Re(1/ρ) = Σ_all 1/ρ (real) = 0.0230957. OK so script's σ_1 = 0.0230957 correctly. Then η_0 = −1.2655 − 0.0231 + 1 = −0.2886?? But the script printed −0.576975!\n\nHmm wait, let me recompute τ_0 = −(1/2)(log(4π)+γ) = −(1/2)(2.53102+0.57722) = −(1/2)(3.10824)?? log(4π) = 2.531024. +γ = 3.10824. Half = 1.55412. τ_0 = −1.55412. Then η_0 = −1.55412 − 0.0230957 + 1 = −0.57722 ✓ = −γ. \n\nSo η_0 correct. Now: does the η_j sequence stay O(1)? τ_j = (−1/2)^{j+1}ζ(j+1,1/2). ζ(m,1/2) = (2^m − 1)ζ(m). τ_j = (−1/2)^{j+1}(2^{j+1}−1)ζ(j+1) ≈ (−1)^{j+1}(1 − 2^{−(j+1)})ζ(j+1) → (−1)^{j+1}. So η_j = τ_j + (−1)^{j+1}σ_{j+1} + (−1)^j ≈ (−1)^{j+1}[ζ(j+1) − 2^{−(j+1)}ζ(j+1) + σ_{j+1} − 1] → (−1)^{j+1}[ζ(j+1)−1] → 0 alternating. Fine — η_j O(1), and the true η_j from E-011 are also O(1)-ish? E-011 η_k = Laurent coefficients of −ζ′/ζ(1+u) = 1/u + Σ η_k u^k. η_0 = −γ ≈ −0.577 ✓ matches.\n\nSo both definitions agree and η is O(1). Then why does S_f = Σ C(n,j)η_{j−1} explode as 8.8e170?!\n\nWait — precision! η_str[j] = mp.nstr(..., full_digits) — computed at mp.mp.dps = full_digits+50, fine. But σ_{j+1} for j+1 ≤ 16 from zero sums; for j+1 > 16, set to 0 (tail < 1e-13). Fine.\n\nHmm, but the SIGNS: is the E-021 formula η_j = τ_j + (−1)^{j+1}σ_{j+1} + (−1)^j correct vs E-011's η? η_0 ✓. Check η_1: E-011 prints η_1. True η_1 = ... η_1 = −(γ²/2 + ...)? Actually η_1 = γ_1 + γ²/2 − π²/16... hmm not sure. Numerically η_1 ≈ −0.0728? Let me just compute from script formula: τ_1 = (−1/2)²ζ(2,1/2) = (1/4)(2²−1)ζ(2) = (3/4)(π²/6) = π²/8 = 1.2337. η_1 = τ_1 + σ_2 + (−1) = 1.2337 + σ_2 − 1. σ_2 computed as 2Re Σ_upper ρ^{−2}. Σ_ρ ρ^{−2} = σ₂-ish. Note Σ_ρ ρ^{−2} = (Σ... ) known: Σ_ρ ρ^{−2} = 1 − π²/8 + ... hmm. Actually Σ_ρ ρ^{−2} = λ-related: = 0.04619? D-036 says σ₂ := Σ_ρ |ρ|⁻² = 0.046191 — that's |ρ|⁻², not ρ^{−2}. Script computes Σ ρ^{−2} = 2Re Σ_upper ρ^{−2}. Known: Σ_ρ ρ^{−2} = (π²/8 − ...) Let me recall: λ_2-related... Σ_ρ ρ^{−2} = 1 − π²/8 + 4γ_... I don't remember. The script printed σ_2 in the log — let me check the log earlier lines.\n\nActually, let me step back and compare directly with E-011's η values. Fastest: write a small comparison script computing η_j both ways (E-011's Stieltjes division vs E-021's zero-side formula) for j up to ~50, and also compute S_f(n) with E-011's η for n up to 5000 to see whether plain Σ C(n,j)η_{j−1} explodes.\n\nActually WAIT. Look at E-011's formula again: λ_n = 1 − Σ C(n,j)η_{j−1} − Σ(−1)^{j−1}C(n,j)(1−2^{−j})ζ(j). And D-033 §3 said: \"bounding Σ_j C(n,j)η_{j−1} termwise gives ~σ₂·14·(15/14)ⁿ — exponential. The true sum has a THREE-WAY cancellation (η-sum, ζ(j)-sum, Stieltjes-sum)... Σ C(n,j)η_j ~ c(1−i/14)ⁿ, modulus ~ e^{n/392} — the measured λ_n ~ (n/2)log n exists only because the other sums cancel this exponential.\"\n\nHmm, that says Σ C(n,j)η_{j−1} has modulus e^{n/392}?? At n=5000: e^{12.75} ≈ 3.4e5. But measured S_f(5000) = 8.8e170 = e^{393}. 393 ≈ 5000·0.0786. Hmm, ln(1+1/14)+... no. What has growth 0.0786/n? e^{0.0786} = 1.0818. Hmm, (1+1/12)? Or maybe the issue is different: maybe the zero-side η_j here is missing the internal cancellation between τ_j and σ_{j+1}: τ_j = (−1)^{j+1}(1−2^{−(j+1)})ζ(j+1) ≈ (−1)^{j+1}, and + (−1)^j cancels the ≈ (−1)^{j+1}·1 leading term? τ_j + (−1)^j ≈ (−1)^{j+1}(ζ(j+1) − 2^{−(j+1)}ζ(j+1) − 1) = (−1)^{j+1}(ζ(j+1)−1) − (−1)^{j+1}2^{−(j+1)}ζ(j+1). ζ(j+1)−1 ~ 2^{−(j+1)}. So η_j ~ (−1)^{j+1}·2^{−j}?? That decays. Hmm, then S_f = Σ C(n,j)η_{j−1} ~ Σ C(n,j) 2^{−j} ~ (3/2)^n·2 = e^{0.405n}?? That's e^{2027} — way bigger than observed.\n\nOK, I clearly can't pin this down from memory. The right move: diagnostic script. Compute η_j from BOTH sources (E-011 Stieltjes-division — the validated one, and E-021's zero-side formula) for j up to ~100 and compare. Then compute S_f(n) = Σ C(n,j)η_{j−1} with E-011's η and see if plain-binomial S_f matches the exploded curve or not. And also check what S_f SHOULD be: from E-015 λ and S_∞: S_f = S_∞ + 1 − λ_n. At n=5000: S_inf = 15641, λ ≈ (n/2)log... ~ 20000·0.4... λ_5000 ≈ (5000/2)(ln 5000 − ln 2π + γ − 1) ≈ 2500·(8.517−1.838+0.577−1) = 2500·6.256 = 15640. So S_f ≈ 15641 + 1 − 15640 ≈ 2. So true |S_f| is TINY (~2!). The three-way cancellation is between η-sum (e^{n/392}~3e5), the ζ(j)-sum and... So plain Σ C(n,j)η_{j−1} should be ~e^{n/392} ≈ 3e5, NOT 8.8e170.\n\nHmm wait, but e^{n/392}: 5000/392 = 12.76, e^12.76 = 3.5e5. But D-033 says that's the modulus of Σ C(n,j)η_j with η_j ~ (−i)^{j−1}σ'_j — that's a DIFFERENT η (zero-side η from pairing?). Ugh.\n\nLet me reconsider: maybe E-021's η formula has a real bug: it takes mp.re(...) of the sum — fine since η real. But σ_{j+1}: for m≥2, script computes s = sum(r^(−m) for upper rho); out[m] = 2*mp.re(s). Σ_all ρ^{−m} = 2Re Σ_upper ρ^{−m} ✓ (conjugate pairs). But wait — Lagarias (4.10) uses σ_m = Σ_ρ ρ^{−m}, and η_m = τ_m + (−1)^{m+1}σ_{m+1} + (−1)^m? I need the actual paper. The arithmetic consistency check: η_1 from this formula vs E-011.\n\nAlso SUSPICIOUS: η_0 ✓ matched −γ within 2.4e-4. But if σ's are wrong for m≥2 (e.g., missing factor), η_j for j≥1 could be wrong O(1) values — and Σ C(n,j)·O(1) ~ 2^n = e^{3465} — no, observed e^{393} only.\n\nHmm, e^{393}: what if η_j ~ (−1)^{j}·c for fixed c? Then Σ C(n,j)η_{j−1} ~ c·(Σ(−1)^j C(n,j)) = c·0 = 0 (exact cancellation for n≥1). What if η_j ~ r^j? Σ C(n,j)r^{j} = (1+r)^n. Observed growth 8.8e170 at n=5000: (1+r)^5000 = 8.8e170 → 1+r = 1.0818 → r = 0.0818 ≈ 1/12.2? Or maybe r=1/14: (15/14)^5000 = e^{345} = 10^{150}. Not quite; observed 10^{170.9} → per-n factor 10^{0.03418} = 1.0818.\n\nHmm, τ_j ≈ (−1)^{j+1}(1−2^{−(j+1)})ζ(j+1). The SUBLEADING term: −(−1)^{j+1}2^{−(j+1)}ζ(j+1) ≈ (−1)^{j}2^{−j}·... η_j = τ_j + (−1)^{j+1}σ_{j+1} + (−1)^j. If the exact cancellation between τ_j's leading (−1)^{j+1} and (−1)^j leaves η_j ~ (−1)^{j+1}·2^{−j} + (−1)^{j+1}σ_{j+1}: Σ_j C(n,j)(−1)^{j+1}2^{−j} = −(1−1/2)^n+1 → 1. Fine. So where's 1.08^n?\n\nWait — maybe σ_m for m=2..16 are computed wrong such that η_j has a component ~ (1/12)^j? σ_m = Σ_ρ ρ^{−m} ~ (1/14.13)^{m}·n(first zero) — decays 14^{−m}. Then (−1)^{j+1}σ_{j+1} ~ (−1)^{j+1}·14^{−(j+1)}·O(1). Sum Σ C(n,j)(−1)^{j+1}14^{−j} = −(1−1/14)^n+... = −(13/14)^n → decays. Fine too.\n\nSomething's off in my magnitude reasoning. e^{393} at n=5000... Actually maybe look at intermediate: |S_f(1000)| = 5.35e94 → per-n 10^{0.0947}=1.244?? At n=100: |S_f|=2.05 (normal!). At n=500: 9.7e59 → 10^{0.1196}/n. At n=1000: 10^{0.0947}. At n=3000: 10^{0.049}. At n=5000: 10^{0.0342}. The growth factor is DECREASING with n — not exponential in n with constant rate; more like exp(c·n/ln n)? log10|S_f|: n=500: 59.99; n=1000: 94.7; n=3000: 147.1; n=5000: 170.9. Ratios: Δ(500→1000): +34.7; Δ(1000→3000): +52.4 over 2000 → +26.2/1000; Δ(3000→5000): +23.8 over 2000 → +11.9/1000. Interesting — could be like c·n^2/T_ZEROS? n²/5000: at n=500: 50; n=1000: 200 — no.\n\nCould be zeros truncation! T_ZEROS=5000, zeros used for σ sums only up to height 5000 (N≈7900 zeros)... no wait, σ_m for m≥2 converge fine.\n\nAH WAIT. I bet it's the η tail: for j+1 > 16, script sets σ_{j+1} = 0. But the true σ_{j+1} ~ 14^{−(j+1)} — at j=16, ~14^{−17} ~ 2e-20. Negligible. Fine.\n\nHmm, what about precision in η_str? mp.nstr(..., full_digits) with full_digits = 0.31·5000+100 = 1650 digits. Fine.\n\nWhat about τ_j for large j? τ_j = (−1/2)^{j+1}ζ(j+1, 1/2) via mpmath mp.zeta(j+1, 0.5) — Hurwitz zeta at large s... mpmath Hurwitz zeta might be INACCURATE or the memory note says mpmath complex-ζ OK but integer ζ broken beyond 16 digits (\"mpmath 1.3 + Py 3.14: mp.zeta broken beyond ~16-19 digits (integer AND non-integer)\"). Hurwitz ζ(j+1, 1/2) = mp.zeta(j+1, mp.mpf(0.5)) — non-integer second arg; E-011's note says broken beyond ~16-19 digits! τ_j for large j is computed as (−1/2)^{j+1}·ζ(j+1,1/2) where ζ(j+1,1/2) ≈ 2^{j+1} — so τ_j ≈ (−1)^{j+1} is a product of a tiny number and huge number, EACH needing ~j·log10(2) ≈ 0.3j correct digits. If mp.zeta (Hurwitz) is only accurate to ~16-19 digits... wait but at dps 50. The E-011 bug report says mp.zeta returns WRONG values beyond 16-19 digits regardless of dps. If Hurwitz ζ(j+1,1/2) has error ~1e-16 absolute, then τ_j error ~ 2^{−(j+1)}·1e-16 — tiny. Hmm no, error RELATIVE 1e-16 → absolute error ~2^{j+1}·1e-16, times 2^{−(j+1)} → 1e-16 in τ_j. But η_j is O(1)... error 1e-16 per term; Σ C(n,j)·1e-16 at n=5000: 2^5000·1e-16 — HUGE. But full_digits=1650, the sum is done at dps 1650 — the ERROR is in η values themselves at 1e-16 → S_f error ~ 2^n·1e-16 → at n=5000, 10^{1489} — way bigger than observed. Observed 10^{170} ≈ 2^5000·10^{-1707}?? 2^5000 = 10^{1505}. 10^{170}/10^{1505} = 10^{−1335}. Hmm, so if η errors were ~10^{−1335}, that explains it. But η computed at 1650 digits... if mp.zeta Hurwitz is wrong beyond 16-19 digits, error would be 1e-16, giving S_f error 10^{1489}. Unless the η values are correct and something else.\n\nAlternatively: η_str strings at 1650 digits, but the real η_j might have a huge internal cancellation: η_j = τ_j + (−1)^{j+1}σ_{j+1} + (−1)^j, with τ_j ≈ (−1)^{j+1}ζ(j+1)(1−2^{−(j+1)}) — no cancellation here, terms are O(1).\n\nOK — enough armchair. Diagnostic: compare η_j (E-021 formula) vs E-011's validated η_j for j ≤ 100, and compute S_f from E-011 η directly. Let me write a quick script.\n\nActually wait — E-011's η comes from Stieltjes via series division, and E-011's λ formula is λ_n = 1 − Σ C(n,j)η_{j−1} − Σ(−1)^{j−1}C(n,j)(1−2^{−j})ζ(j). The E-021 S_f definition Σ C(n,j)η_{j−1} (plain) — is that even the right \"S_f\"? In Lagarias's decomposition λ_n = S_∞(n) − S_f(n) + 1, what's S_f? Lagarias (4.11): S_f(n) = Σ_{j=1}^n C(n,j) η_{j−1}?? and S_∞(n) = ... Actually Lagarias defines:\n\nS_∞(n) = Σ_j [1 − (1 − 1/(−2))^j... no. His decomposition (Thm 5.1): λ_n = S_∞(n) − S_f(n) + 1 with\nS_f(n) = Σ_{j=1}^n C(n,j) η_{j−1}, S_∞(n) = −Σ_{j=1}^n (−1)^j C(n,j) η^*_{j−1}? Something like that — where η relates to the ARCHIMEDEAN place. Hmm.\n\nLet me just fetch the actual definitions from the local copy of the Lagarias paper. D-032 mentions a downloaded copy. Let me find it.","signature":""},{"type":"text","text":"The true |S_f| should be tiny (~e^{n/392} at most; λ_n = S_∞ − S_f + 1 with both ~15641 at n=5000 means S_f ≈ 2). The computed S_f explodes, so the η-side has a bug. Let me check the actual Lagarias definitions from the local paper copy."},{"type":"tool_use","id":"Bash_15","name":"Bash","input":{"command":"find /d/Python/Quantum -iname '*lagarias*' -o -iname '*0404394*' 2>/dev/null; grep -rn \"0404394\" /d/Python/Quantum/research/derivations/D-032-li-literature-map.md | head -5","description":"Locate local Lagarias paper copy"},"extra_content":null}]