\( % groupings of objects. \newcommand{\set}[1]{\left\{ #1 \right\}} \newcommand{\seq}[1]{\left(#1\right)} \newcommand{\ang}[1]{\langle#1\rangle} \newcommand{\tuple}[1]{\left(#1\right)} \newcommand{\size}[1]{\left| #1\right|} \newcommand{\comp}{\circ} % numerical shortcuts. \newcommand{\abs}[1]{\left| #1\right|} \newcommand{\floor}[1]{\left\lfloor #1 \right\rfloor} \newcommand{\ceil}[1]{\left\lceil #1 \right\rceil} % linear algebra shortcuts. \newcommand{\change}{\Delta} \newcommand{\norm}[1]{\left\| #1\right\|} \newcommand{\dprod}[1]{\langle#1\rangle} \newcommand{\linspan}[1]{\langle#1\rangle} \newcommand{\conj}[1]{\overline{#1}} \newcommand{\der}[1]{\frac{d#1}{dx}} \newcommand{\lap}{\Delta} \newcommand{\kron}{\otimes} \newcommand{\nperp}{\nvdash} \newcommand{\mat}[1]{\left[ \begin{smallmatrix}#1 \end{smallmatrix} \right]} % derivatives and limits \newcommand{\partder}[2]{\frac{\partial #1}{\partial #2}} \newcommand{\partdern}[3]{\frac{\partial^{#3 #1}}{\partial #2^{#3}}} \newcommand{\gradient}{\nabla} \newcommand{\subdifferential}{\partial} % Arrows \newcommand{\diverge}{\nearrow} \newcommand{\notto}{\nrightarrow} \newcommand{\up}{\uparrow} \newcommand{\down}{\downarrow} % gets and gives are defined! % ordering operators \newcommand{\oleq}{\preceq} \newcommand{\ogeq}{\succeq} % programming and logic operators \newcommand{\dfn}{:=} \newcommand{\assign}{:=} \newcommand{\co}{\ co\ } \newcommand{\en}{\ en\ } % logic operators \newcommand{\xor}{\oplus} \newcommand{\Land}{\bigwedge} \newcommand{\Lor}{\bigvee} \newcommand{\finish}{\Box} \newcommand{\contra}{\Rightarrow \Leftarrow} \newcommand{\iseq}{\stackrel{_?{=}}} % Set theory \newcommand{\symdiff}{\Delta} \newcommand{\setdiff}{\backslash} \newcommand{\union}{\cup} \newcommand{\inters}{\cap} \newcommand{\Union}{\bigcup} \newcommand{\Inters}{\bigcap} \newcommand{\nullSet}{\phi} % graph theory \newcommand{\nbd}{\Gamma} % Script alphabets % For reals, use \Re % greek letters \newcommand{\eps}{\epsilon} \newcommand{\del}{\delta} \newcommand{\ga}{\alpha} \newcommand{\gb}{\beta} \newcommand{\gd}{\del} \newcommand{\gp}{\pi} \newcommand{\gf}{\phi} \newcommand{\gh}{\eta} \newcommand{\gF}{\Phi} \newcommand{\gl}{\lambda} \newcommand{\gm}{\mu} \newcommand{\gn}{\nu} \newcommand{\gr}{\rho} \newcommand{\gs}{\sigma} \newcommand{\gth}{\theta} \newcommand{\gx}{\xi} \newcommand{\gw}{\omega} \newcommand{\sw}{\sigma} \newcommand{\SW}{\Sigma} \newcommand{\ew}{\lambda} \newcommand{\EW}{\Lambda} \newcommand{\Del}{\Delta} \newcommand{\gD}{\Delta} \newcommand{\gG}{\Gamma} \newcommand{\gW}{\Omega} \newcommand{\gS}{\Sigma} \newcommand{\gTh}{\Theta} % Bold english letters. \newcommand{\bA}{\mathbf{A}} \newcommand{\bB}{\mathbf{B}} \newcommand{\bC}{\mathbf{C}} \newcommand{\bD}{\mathbf{D}} \newcommand{\bE}{\mathbf{E}} \newcommand{\bF}{\mathbf{F}} \newcommand{\bG}{\mathbf{G}} \newcommand{\bH}{\mathbf{H}} \newcommand{\bI}{\mathbf{I}} \newcommand{\bJ}{\mathbf{J}} \newcommand{\bK}{\mathbf{K}} \newcommand{\bL}{\mathbf{L}} \newcommand{\bM}{\mathbf{M}} \newcommand{\bN}{\mathbf{N}} \newcommand{\bO}{\mathbf{O}} \newcommand{\bP}{\mathbf{P}} \newcommand{\bQ}{\mathbf{Q}} \newcommand{\bR}{\mathbf{R}} \newcommand{\bS}{\mathbf{S}} \newcommand{\bT}{\mathbf{T}} \newcommand{\bU}{\mathbf{U}} \newcommand{\bV}{\mathbf{V}} \newcommand{\bW}{\mathbf{W}} \newcommand{\bX}{\mathbf{X}} \newcommand{\bY}{\mathbf{Y}} \newcommand{\bZ}{\mathbf{Z}} \newcommand{\bba}{\mathbf{a}} \newcommand{\bbb}{\mathbf{b}} \newcommand{\bbc}{\mathbf{c}} \newcommand{\bbd}{\mathbf{d}} \newcommand{\bbe}{\mathbf{e}} \newcommand{\bbf}{\mathbf{f}} \newcommand{\bbg}{\mathbf{g}} \newcommand{\bbh}{\mathbf{h}} \newcommand{\bbk}{\mathbf{k}} \newcommand{\bbl}{\mathbf{l}} \newcommand{\bbm}{\mathbf{m}} \newcommand{\bbn}{\mathbf{n}} \newcommand{\bbp}{\mathbf{p}} \newcommand{\bbq}{\mathbf{q}} \newcommand{\bbr}{\mathbf{r}} \newcommand{\bbs}{\mathbf{s}} \newcommand{\bbt}{\mathbf{t}} \newcommand{\bbu}{\mathbf{u}} \newcommand{\bbv}{\mathbf{v}} \newcommand{\bbw}{\mathbf{w}} \newcommand{\bbx}{\mathbf{x}} \newcommand{\bby}{\mathbf{y}} \newcommand{\bbz}{\mathbf{z}} \newcommand{\0}{\mathbf{0}} \newcommand{\1}{\mathbf{1}} % Caligraphic english alphabet \newcommand{\cA}{\mathcal{A}} \newcommand{\cB}{\mathcal{B}} \newcommand{\cC}{\mathcal{C}} \newcommand{\cD}{\mathcal{D}} \newcommand{\cE}{\mathcal{E}} \newcommand{\cF}{\mathcal{F}} \newcommand{\cG}{\mathcal{G}} \newcommand{\cH}{\mathcal{H}} \newcommand{\cI}{\mathcal{I}} \newcommand{\cJ}{\mathcal{J}} \newcommand{\cK}{\mathcal{K}} \newcommand{\cL}{\mathcal{L}} \newcommand{\cM}{\mathcal{M}} \newcommand{\cN}{\mathcal{N}} \newcommand{\cO}{\mathcal{O}} \newcommand{\cP}{\mathcal{P}} \newcommand{\cQ}{\mathcal{Q}} \newcommand{\cR}{\mathcal{R}} \newcommand{\cS}{\mathcal{S}} \newcommand{\cT}{\mathcal{T}} \newcommand{\cU}{\mathcal{U}} \newcommand{\cV}{\mathcal{V}} \newcommand{\cW}{\mathcal{W}} \newcommand{\cX}{\mathcal{X}} \newcommand{\cY}{\mathcal{Y}} \newcommand{\cZ}{\mathcal{Z}} % Formatting shortcuts \newcommand{\red}[1]{\textcolor{red}{#1}} \newcommand{\blue}[1]{\textcolor{blue}{#1}} \newcommand{\htext}[2]{\texorpdfstring{#1}{#2}} % Statistics \newcommand{\distr}{\sim} \newcommand{\stddev}{\sigma} \newcommand{\covmatrix}{\Sigma} \newcommand{\mean}{\mu} \newcommand{\param}{\theta} \newcommand{\gthEst}{\hat{\theta}} \newcommand{\ftr}{\phi} \newcommand{\est}[1]{\hat{#1}} % General utility \newcommand{\todo}[1]{\textbf{[TODO]}] \footnote{TODO: #1}} \newcommand{\tbc}{[\textbf{Incomplete}]} \newcommand{\chk}{[\textbf{Check}]} \newcommand{\why}{[\textbf{Find proof}]} \newcommand{\opt}[1]{\textit{#1}} \newcommand{\experience}[1]{[\textbf{Personal Experience}]: #1 \blacktriangle} \newcommand{\pf}[1]{[\textbf{Proof}]: #1 \Box} \newcommand{\core}[1]{\textbf{Core Idea}: #1 \Arrowvert} \newcommand{\example}[1]{\textbf{Example}: #1 \blacktriangle} \newcommand{\error}[1]{\textbf{Error alert}: #1 \triangle} \newcommand{\oprob}{[\textbf{OP}]: } \renewcommand{\~}{\htext{$\sim$}{~}} \DeclareMathOperator*{\argmin}{arg\,min} \DeclareMathOperator*{\argmax}{arg\,max} \)

APPENDIX A

SYNOPSIS OF THE MANTRApāṭha AND THE APASTAMBIYA GRHYASÚTRA. Mantra- Apastambiya Mantra- pāṭha Grhyasūtra pātha Apastambiya Grhyasūtra I, I, I-2 4, 2 I, 5, 8-10 3 3 II 5,9 12 4 5 13-15 6 6 16-17 IO 12 7 7 18 18 6, I 19 9 2-3 20 IO 8 4-7 22 2, I-5 8. 23 6 9-II 24 7 12. 25 8 9 13. 8, I . 3, I-2 IO 14. 3-6 7-13 14. 4. I-16 5, I 2 3-5

15 16 7, I-7 17 8-9 5, 3 6 IO II-12 8, 1 } 2 6 7 7 6 3-15 IO 8 7 9, I Grhyasūtra 86 Mantra- pātha I, 9, 2 SYNOPSIS OF THE MANTRAPĀTHA Apastambiya Mantra- Apastambiya Grhyasūtra pāṭha II, 3, I 3 4-5 6-7 8 · 8, II 2 3-12 10, 12 12 13-23 8, 2 24 25 9-10 26. 11, I 10, I-2 27-30. 3-9 31 TO-13 32 II, I-2 ΤΟ 4, I-II 6 3 12 7 4-6 7-II 12, I-13, 4 13, 5-6 7-10 14, I-7 13 9-12 14 13 13 15 14 2 · 5, I 15 2-10 II 18 15, I 2-4 6 5 6 16 (Anuvika) 9 6, I I2-21 22. 2-13} 14 17, 1-6 TO 15 19 22 25 26 7-10 II 7, I II, I, 2 3-6 8 2, I 3-4 5-7 S 9-10 II 2 10,5 6 7 3 4-II 12 12, 3 5 8 13-18 } 6 19

9 20 21-23 24 ΤΟ 8 25 26 II 27-32 AND THE APASTAMBİYA GRHYASŪTRA. Mantra- pāṭha II, 8, 1-8 Apastambiya Grhyasūtra Mantra- pātha 12, 9 1-8 (bis) IO 9-10 II, 12, 3-5 (Haradatta) 2-5 (Sudarsanarya) 6-10 II-9, I II-14 9, 2 13, I II 3 2 3-4 87 Apastambiya Grhyasūtra 15, 4 5 5 5 6 13 6 7 13, 7-14, 2 4,2} 6 8) 3 14,3 12 IO I I 12 13/ 14 IO, I-2 5 10 10 6 8 00. O 4 5-9 IO. II-14 15-22 15, I 2 10, 13 I 8 17, I 3 3-4 13 5 3-4 6 16 5. 5 7 8-12 13-18. 1 II, 1-8 9-11 6-II 17 18 12 14, 2 13 7 14 12 15 9 13 6 16 IO 14 II 17 II

15 16-18 } 14 19-20. 15 21-31 32 nirya) 33 12, I (Haradatta) 2 33-12, I (ris, Sudara- 15, I 18-21 22. 16, 1-11 12-13 14 15-17. 17, 1-3 12 13 } 18, I 3 4-7 7 888 Mantra- pātha SYNOPSIS OF THE MANTRAPĀTHA ETC. Apastambiya Grhyasūtra Mantrapātha Apastambiya Grhyasūtra II, 17, 8 { 18, 10 II, 20, 2-7 19, 4 8-13 14-19 9-25 18, 12 26-27 20-23 21, 9 24 18, 1 19, 7 25 2 26 9 27 22, I 8-9 II 28 4 IO: 20, I 29-35 5 21, I 6 II-13 2-9. 7 14-30 10-16. 13 3I 17 14 32 181 33-39 5 19/ 15 40 20-30. 16 41 31 17 42-45. 6 31 1 23, I 33 46. 7 22, I-2 47-48. 16 3 19, 1-7 21, 3 4 (or 4) 5-6. 2 00 10 10 3 5 6 8-13 4 7-10 7 (or 3) 8 II-13. 14-16. 6 14-23. 9 20, I 8 24 IO