• Statement (I) is True: The mature leaf blade is the primary sensory organ perceiving the photoperiodic daylength signal via phytochrome ($P_r / P_{fr}$) and cryptochrome photoreceptors, generating the mobile flowering signal florigen (encoded by the FT gene).
• Statement (II) is True: Photoperiodic timekeeping is regulated by an endogenous circadian clock that drives the rhythmic diurnal oscillation of CONSTANS (CO) mRNA and protein stability.
• Conclusion: Both Statement (I) and Statement (II) are true.

Correct option: (1) Both Statement (I) and Statement (II) are true.

• Ambiphotoperiodic Flowering: Ambiphotoperiodic plants flower under both short-day photoperiods ($\lt 12\text{ h}$) and long-day photoperiods ($\gt 16\text{ h}$), but remain strictly vegetative under intermediate day lengths ($12\text{ to }16\text{ h}$).
• Representative Taxon: Setaria verticillata (bristly foxtail) is the classic textbook example of an ambiphotoperiodic species.

Correct option: (1) Setaria verticillata

• Short-Day Plant Induction: Cosmos bipinnatus is a qualitative/quantitative short-day plant (SDP) whose floral transition and flower development are accelerated when the day length is shorter than its critical photoperiod.
• Comparative Taxa: Ricinus communis is day-neutral; Beta vulgaris (sugarbeet) is a long-day plant requiring vernalization.

Correct option: (3) Cosmos bipinnatus

• Two-Phase Flowering Theory: Formulated by Russian physiologist M. Kh. Chailakhyan (1958).
• Postulate: Florigen consists of two complementary physiological components acting in two sequential stages:

• Gibberellins: Required for stem elongation, bolting, and flower stalk growth.
• Anthesins: Hypothetical flowering factors required for flower bud initiation and floral organogenesis.
  
  Correct option: (1) Chailakhyan