Fix two things,
the affix follows

Past, present, future, and a fifth — the perfect's own resultant-past sense, which the finite लिट् marks by reduplication and which the participle system marks with its own dedicated affixes rather than reusing क्त. A कृदन्त does not carry absolute time; it times itself against whatever the main verb is doing.

The same कर्तरि/कर्मणि choice that page 8 built the whole कारक system on returns here unchanged: does the participle describe the one who acts, or the one (or nothing) that is acted upon? A finite verb marks this with परस्मैपद/आत्मनेपद and voice; a participle marks it by which affix was chosen in the first place — there is no separate "passive form" of a participle the way there is of a verb.

3.4.70 — "of those two [कर्म and भाव] alone" — restricts कृत्य-affixes and क्त to exactly the two senses 3.4.69 just laid out for सकर्मक roots: कर्मणि, or (for roots with no object at all) भावे. Never कर्तरि. That is why कृतः means "the thing that was done", not "the one who did".

3.4.72 carves out exactly one exception, by name: गति-अर्थ (motion-meaning) roots that are अकर्मक, plus a short named list — श्लिष्, शीङ्, स्था, आस्, वस्, जन्, रुह्, जीर्यति. For these, and only these, क्त is कर्तरि. गम् is on that list by sense; its past participle names the traveller, not a destination.

An अकर्मक root that is not on 3.4.72's list — हस् "to laugh" is the standard example — has no object for क्त to describe (कर्मणि is unavailable) and is not on the exception list (कर्तरि is unavailable either). 3.4.69's other branch, भावे, is what is left: the participle names the action itself, impersonally, and agrees with nothing — it is simply neuter singular, no matter who laughs.

7.1.70 — an उगित् affix (क्तवतु's own इत् letters are क् and उ, so it qualifies) that ends in a vowel gets a नुम् (न्) augment before a सर्वनामस्थान (strong-case) ending. कृतवत् + नुम् + सु gives कृतवन्त्+स्, which sandhi turns into कृतवान् — long आ, nasalised. The weak stem कृतवत्- (no नुम्) is what every other case is built on: instrumental कृतवता, locative plural कृतवत्सु.

The corpus's one क्तवतु paradigm — श्रुतवत्, "having heard", from श्रु — shows exactly this pattern. Pick any cell below and the नुम् is either there (strong cases) or it is not (weak cases); it is never optional either way.

3.2.124 replaces the present-tense लट् with शतृ or शानच् whenever what results will modify some other word in the sentence rather than serve as the sentence's own finite verb. Which of the two depends only on पद: शतृ for परस्मैपदी roots (गम् → गच्छत्), शानच् for आत्मनेपदी roots. And शानच् does double duty — the very same affix gives the कर्तरि reading for an आत्मनेपदी root's own agent (सेवमानः, "one who is serving") and the कर्मणि reading for any root's object (सेव्यमानः, "one being served") — because in the passive, every root is treated as आत्मनेपदी (a fact worth remembering: it is why सेव्यमान and सेवमान share an affix while looking so different).

भवत् is grammatically nothing but भू's own present participle — कर्तरि शतृ, "the one who is" — and the corpus's own gloss for it is . Sanskrit reached for exactly this word, declining exactly like गच्छत्, as the polite second person: भवान् गच्छति literally says "the one-who-is goes", used in place of a blunt त्वं गच्छसि. The feminine, भवती, is the same honorific address to a woman — no separate word was ever coined for it either.

शतृ's own इत् letter ऋ makes it उगित्, so 4.1.6 gives every शतृ-word ङीप् (ई) in the feminine — that much is universal. What is not universal is whether a नुम् augment appears before that ई, and the answer depends on which vikaraṇa stood between the root and शतृ in the first place:

The corpus's own attested pair proves the "optional" is real, not a hedge: विश् (गण ६, तुदादि — vikaraṇa श, not शप्) is indexed both ways.

गम् and पठ् (both गण १, शप्) go the other way — the engine that derives every form on this site gives गच्छन्ती and पठन्ती only; it never offers a bare *गच्छती. Neither is in the corpus's noun index (a participle is not a dictionary headword), so neither is shown as a table here — that gap is worth naming rather than hiding.

3.3.13 establishes लृट् as the general future. 3.3.14 — "of लृट्, [optionally] सत्" (सत् is Pāṇini's short name for शतृ, and by extension शानच्) — lets the participle substitute for लृट् itself, not merely for its person-ending the way 3.2.124 does for लट्. And लृट् is not a bare ending: 3.1.33 builds it as स्य + [तिङ्], so when शतृ stands in for the whole of लृट्, the स्य it was built from comes along. गम् + स्य + शतृ → गमिष्यत्, "about to go" — the same मशीन as गच्छत्, run one gear further out.

3.2.106 lets कानच् replace लिट्; 3.2.107 — "and क्वसु" — adds क्वसु as the परस्मैपदी counterpart, exactly as शतृ/शानच् split by पद for the present. Unlike शतृ, क्वसु's own weak grade differs sharply from its strong grade — विद्वस् weakens to विदुष् before a consonant-initial ending, not merely losing a नुम्. Pull the whole table and both grades are there to see.

3.1.96 licenses तव्यत्, तव्य and अनीयर् for every root, generically. 3.1.97 adds यत् specifically for vowel-final roots (with a long tail of root-specific exceptions after it); ण्यत् has its own conditions, one of them 3.1.124 for ऋ- and हल्-final roots — कृ + ण्यत् → कार्य. All four converge on the same meaning: obligation, expressed exactly like क्त's कर्मणि/भावे branch, never like its कर्तरि one.