The T.M. Raghunath Calendar System: Precision Solar Alignment through Fractional Leap-Year Corrections (Demand for correction of error in the Gregorian calendar)

The T.M. Raghunath Calendar System: Precision Solar Alignment through Fractional Leap-Year Corrections (Demand for correction of error in the Gregorian calendar) | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article The T.M. Raghunath Calendar System: Precision Solar Alignment through Fractional Leap-Year Corrections (Demand for correction of error in the Gregorian calendar) T. M. Raghunath This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8348127/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract The Gregorian calendar, though a significant improvement over the Julian system, still contains cumulative inaccuracies arising from its leap-year adjustments. This paper introduces the T.M. Raghunath Calendar System, an innovative model that retains the familiar structure of the Gregorian calendar while applying precise fractional corrections to achieve closer alignment with the solar year. The system redefines the skipped leap day (February 29) as 0.9688 days rather than a full day, with a compensatory one-day correction applied every 128 years. A 33-year cycle regulates short-term surpluses of 0.2422 days, while extended cycles of 5,000 and 80,000 years eliminate long-term residual errors. This scalable framework delivers unprecedented accuracy, adaptability to astronomical variations, and seamless compatibility with existing civil structures, positioning it as one of the most scientifically rigorous calendar systems proposed to date. Calendar reform Gregorian correction Solar year Leap year Timekeeping T.M Raghunath calendar system 1. Introduction Accurate calendar systems are essential for agriculture, science, social organization, and global coordination. Throughout history, reforms such as the Julian and Gregorian calendars sought to align civil timekeeping with Earth’s orbital motion. However, both systems introduced approximations. The Julian calendar assumed a year length of 365.25 days, which produced significant long-term drift. The Gregorian reform improved accuracy by skipping three leap years every 400 years, reducing the error but not fully eliminating it. The T.M. Raghunath Calendar System addresses the residual discrepancy by introducing a leap-year correction method grounded in the actual fractional surplus of solar time. Instead of assuming that each four-year surplus equals one full day, it recognizes that the true accumulation is 0.9688 days, not a complete day. This refinement ensures precise alignment with the tropical year length of 365.2422 days. In this system, February 29 is treated as a full leap day by incorporating the missing 0.0312 days alongside the accumulated 0.9688 days over four years. However, when a leap day is skipped, this additional 0.0312 days is not added. Consequently, a skipped leap day accounts for only 0.9688 of a day, rather than a full 24 hours. This distinction is central to the accuracy of the model. 2. Methodology: The Raghunath Leap Year Correction 2.1) Core Principles • Added Leap Day (February 29): Counts as one full day, consisting of 0.9688 days of accumulated surplus plus 0.0312 days of compensation. • Skipped Leap Day: Corrects only 0.9688 days, as the extra 0.0312-day adjustment is not applied. • Preserves Gregorian Structure: Months, weeks, and the distinction between common years (365 days) and leap years (366 days) remain unchanged. The T.M. Raghunath Calendar retains the familiar Gregorian framework but introduces a crucial refinement: in skipped leap years, February 29 is treated as 0.9688 days, reflecting the actual surplus accumulated over four years (0.2422 × 4), rather than a full 24 hours. 2.2) The 128-Year Correction Cycle Over 124 years, the surplus time accumulates to approximately 0.9672 days. To correct this, the system employs a 128-year cycle, in which one leap day is removed across four specific years: the 33rd, 66th, 99th, and 128th. • Each skipped leap year eliminates 0.2422 days. • Collectively, the four skipped leap years remove 0.9688 days, almost perfectly offsetting the 0.9672-day surplus. Thus, in practice: • 32 leap years are scheduled within a 128-year period. • 1 leap year is effectively nullified, leaving 31 functional leap years. • The structure consists of three 33-year segments (8 leap years each) and one 29-year segment (7 leap years). This creates occasional five-year intervals between leap years (e.g., from year 28 to 33),breaking the usual four-year cycle but ensuring precise alignment. 2.3) Comparison with the Gregorian Calendar The Gregorian system omits three leap days every 400 years (specifically in century years that are not divisible by 400). Each omission corrects approximately 0.9688 days, but these adjustments are distributed over several centuries rather than applied in shorter, more precise intervals. In contrast, the Raghunath Calendar applies corrections much more rapidly—within 33-year intervals rather than centuries. By addressing the fractional surplus directly (0.2422 days per skipped leap year segment), it achieves finer precision and faster alignment with the solar year 2.4) Treatment of Skipped Leap Days In any calendar, adding February 29 every four years compensates for the annual surplus of 0.2422 days, which totals about 0.9688 days over four years. To make February 29 a complete day, an extra 0.0312 days is added. • In added leap years: February 29 is treated as a full day (0.9688 + 0.0312). • In skipped leap years: The extra 0.0312 days are not included. Thus, each skipped leap day accounts for only 0.9688 of a day. This distinction is critical. The Gregorian calendar overlooks this fractional detail by treating skipped days as if they subtract a full day, leading to cumulative inaccuracies over time. The Raghunath Calendar corrects this flaw by measuring both added and skipped days in fractional time, not merely in whole calendar days. 2.5) Precision of the Cycle • In the Gregorian system, skipping leap years in the 100th, 200th, and 300th years creates 8-year gaps between leap years. • In the Raghunath system, leap years are skipped in the 33rd, 66th, 99th, and 128th years, producing 5-year gaps within certain segments. This design ensures that each skipped leap year corrects approximately 0.2422 days within its 33-year block, achieving faster and more accurate synchronization with the solar year. 3. Scientific and Mathematical Justification 3.1 The 128-Year Cycle Correction Each skipped leap year is designed to offset the surplus time accumulated over preceding decades. The calculations are as follows: • 33rd year: 0.0078 × 32 = 0.2496 days → correction = 0.2422 days • 66th year: 0.0078 × 32 = 0.2496 days → correction = 0.2422 days • 99th year: 0.0078 × 32 = 0.2496 days → correction = 0.2422 days • 128th year: 0.0078 × 28 = 0.2184 days → correction = 0.2422 days Totals: • Corrected = 4 × 0.2422 = 0.9688 days • Surplus = 0.9672 days • Net error = 0.0016 days per 128-year cycle Core Principles of the 128-Year Cycle • Annual surplus = 0.2422 days/year → 0.9688 days over 4 years. • Correction rule: Omit leap days in the 33rd, 66th, 99th, and 128th years. • Effect: Removes 0.9688 days, nearly identical to the 0.9672-day surplus. • After 124 years, surplus = 0.2422 × 124 = 0.9672 days. • By using 31 leap years instead of 32 in each 128-year cycle, the model corrects this surplus. • The skipped leap years create occasional five-year gaps (e.g., from year 28 to 33), breaking the regular four-year cycle. • Residual error: only 0.0016 days per 128 years, an order of magnitude smaller than in the Gregorian system. Cycle Structure • Years 1–33: 8 leap years → 7 at 4-year intervals, 1 at a 5-year interval (years 4, 8, 12, 16, 20, 24, 28, 33). • Years 34–66: 8 leap years → (years 37, 41, 45, 49, 53, 57, 61, 66). • Years 67–99: 8 leap years → (years 70, 74, 78, 82, 86, 90, 94, 99). • Years 100–128: 7 leap years → (years 103, 107, 111, 115, 119, 123, 128). This distribution yields 31 leap years per 128-year cycle, effectively nullifying one leap year and thereby correcting the cumulative surplus with remarkable precision. 3.2 The 5,000-Year Correction Cycle Across 4,992 years (39 × 128-year cycles), the small residual error of 0.0016 days per cycle accumulates to: • 0.0016 × 39 = 0.0624 days This drift is corrected by extending the cycle with 8 unadjusted years at the end of the 5,000-year span: • 8 × 0.0078 = 0.0624 days Thus, the final 8 years (years 4,993–5,000) are excluded from any correction cycle, restoring balance and ensuring perfect alignment across the full 5,000-year period. 3.3 The 80,000-Year Correction Cycle Two approaches confirm long-term stability: 1. Repetition of the 5,000-year cycle • 16 × 5,000 years = 80,000 years 2. Extended calculation • Residual over 624 cycles: 0.0016 × 624 = 0.9984 days • Correction via 128 unadjusted years (years 79,873–80,000): 128 × 0.0078 = 0.9984 days In both cases, the accumulated surplus is completely eliminated, delivering unmatched precision over 80 millennia. 3.4 Average Year Length of the T.M. Raghunath Calendar General Formula Number of year in cycle 3.5 Formula Validation Verdict: Mathematically precise, exactly matching the known value of the tropical year. 3.6 Astronomical Relevance • Tropical year ≈ 365.2422 days. • Gregorian calendar = 365.2425 days, slightly overcompensating. • Verdict: The Raghunath Calendar eliminates drift, aligning perfectly with seasonal cycles. 3.7 Justification of 1211 Leap Days • Pure 4-year cycle: 5,000 ÷ 4 = 1,250 leap days. • Correction applied: 1,250 − 39 = 1,211 leap days. • Verdict: A logical adjustment mechanism to maintain exact alignment. 3.8 The 128-Year Cycle in Context • Annual error: 365.25 − 365.2422 = 0.0078 days. • Over 124 years: 0.0078 × 124 = 0.9672 days (≈ 1 day). • Skipping one leap day every 128 years corrects this drift. • Subcycles consist of 33-year blocks, with occasional 5-year intervals (e.g., years 28–33). • Residual per cycle: 0.0016 days. • Over 39 cycles: 0.0016 × 39 = 0.0624 days. • Corrected by 8 unadjusted years: 0.0078 × 8 = 0.0624 days. • Verdict: A robust long-term correction strategy that maintains astronomical precision across millennia. 3.9 Leap Year Rule and Accuracy The T.M. Raghunath Calendar operates on a 5,000-year cycle designed to achieve an average year length of 365.2422 days, aligning exactly with the tropical year and offering greater precision than the Gregorian calendar (365.2425 days). This cycle is constructed from 39 repetitions of a 128-year subcycle (totaling 4,992 years), followed by a final 8-year segment to restore complete balance. 3.10 Key Properties • Total leap years in 5,000 years: 1,211 • 128-year subcycle: 31 leap years per cycle (leap years occur in years 4, 8, 12, 16, 20, 24, 28, 33, 37, 41, 45, 49, 53, 57, 61, 66, 70, 74, 78, 82, 86, 90, 94, 99, 103, 107, 111, 113, 117, 123, and 128). • 39 subcycles: 39 × 31 = 1,209 leap years • Final 8-year segment: Adds 2 leap years (years 4,996 and 5,000) • Grand total: 1,209 + 2 = 1,211 leap years 3.11 Average Year Length Average Year Length (5000 × 365) + 1211 = 18261211/5000=365.2422 days This matches the tropical year precisely, ensuring zero drift over the 5,000-year cycle. 3.12 Why This Works • In each 128-year subcycle, leap years are reduced from 32 (Gregorian assumption) to 31, correcting the Gregorian overage. This leaves a residual deficit of 0.0016 days per cycle. • Across 39 subcycles (4,992 years): the accumulated deficit = 39 × 0.0016 = 0.0624 days. • The final 8 years follow a standard 4-year leap cycle (2 leap years), adding 8 × 0.0078 = 0.0624 days, which cancels the deficit exactly. • The result is a perfectly balanced calendar that remains aligned with astronomical seasons for millennia, achieving the target accuracy of 365.2422 days. 3.13 T.M. Raghunath Calendar System: Example 128-Year Cycle (2001–2128) Key Structure The T.M. Raghunath Calendar operates on a repeating 128-year cycle to maintain greater accuracy than the Gregorian calendar. An illustrative cycle spans the years 2001 to 2128. Subdivision of the 128-Year Cycle The cycle is divided into four sequential blocks: • 33 years • 33 years • 33 years • 29 years Leap Year Distribution Logic • Total leap years per 128-year cycle: 31 • In each 33-year block (3 blocks): Leap years occur in the 4th, 8th, 12th, 16th, 20th, 24th, 28th, and 33rd years. • In the final 29-year block: Leap years occur in the 4th, 8th, 12th, 16th, 20th, 24th, and 29th years. Actual Leap Years in the 2001–2128 Cycle • First 33 years (2001–2033): 2004, 2008, 2012, 2016, 2020, 2024, 2028, 2033 • Second 33 years (2034–2066): 2037, 2041, 2045, 2049, 2053, 2057, 2061, 2066 • Third 33 years (2067–2099): 2070, 2074, 2078, 2082, 2086, 2090, 2094, 2099 • Final 29 years (2100–2128): 2103, 2107, 2111, 2115, 2119, 2123, 2128 4. Comparison with Other Calendar Systems 4.1 Table 1 Feature Julian Calendar Gregorian Calendar T.M. Raghunath Calendar Year Length 365.25 days 365.2425 days 365.2422 days Annual Error 11 min 14 sec +0.0003 days 0 (corrected) Drift in 128 Years 1 day 0.0384 days 0.0016 days Drift in 400 Years 3.12 days 0.12 days 0.005 days Drift in 640+1 = 641 Years 4.9998 days 0.1923 days 0.0002 days Drift in 2560 + 4 = 2564 Years 19.9992 days 0.7692 days 0.0008 days Drift in 5,000 Years 39 days 1.5 days 0 (corrected) Drift in 80,000 Years 624 days 24 days 0 (corrected) Correction Mechanism Leap every 4 yrs Leap day every 4 years. Skip 3/400 yrs Leap day every 4 years. Subtract 0.9688 days/128 yrs Structural Compatibility Yes Yes Yes Modern Adaptability No Limited High Cycle length 4 year (repeated 4 year) 400 Years (repeated every 400 years) 5,000 Years (repeated every 5,000 years) Key Advantages: Efficiency: Corrections applied 12 x faster than Gregorian 400-year cycle. Adaptability: Modular cycles accommodate future orbital changes. 4.2 Comparative Analysis : 4.3 Table 2 Feature Gregorian Calendar T M Raghunath Calendar Year Length 365.2425 days 365.2422 days Leap-Day Treatment Skipped = 1 full day Skipped = 0.9688 days 128 Year Error 0.0384 days 0.0016 days Structural change Required (1582) None Compared to Julian and Gregorian systems, and even modern proposals like the Symmetry 454, the T M Raghunath Calendar offers unmatched precision and structural continuity while correcting leap year surplus more effectively. 5. Future Adaptability The T.M. Raghunath Calendar System is designed with long-term adaptability in mind, ensuring its relevance even under future astronomical variations. If Earth’s orbital period shifts slightly whether due to tidal interactions or planetary influences the correction cycles can be recalibrated to maintain accuracy. The framework can also accommodate modifications to week or month structures if global consensus calls for such structural reform, reflecting its modular and flexible design. In practice, each leap year in the system carries a small surplus of approximately 0.0312 days. If long-term orbital changes alter the solar year by a similar magnitude, the calendar compensates by skipping one scheduled correction. This simple yet effective adjustment allows the system to remain precisely aligned with the solar year, naturally adapting to long-term astronomical shifts. Furthermore, within the T.M. Raghunath Calendar framework, the Fixed-Week Calendar can be seamlessly integrated. This optional hybrid model ensures that both weeks and months remain constant, offering the world a truly innovative and predictable timekeeping system. Should the international community endorse such a reform, the system is fully prepared for implementation. 6. T.M. Raghunath Fixed Calendar System (Optional Overlay) 6.1 Core Idea The Fixed Calendar is designed to provide complete consistency in civil timekeeping. • Every year begins on a Monday. • The weekly cycle never shifts, ensuring that weekdays remain permanently aligned with dates. This creates a predictable and stable rhythm for daily life, long-term planning, and global coordination. 6.2 Month Structure The year is divided into 12 months, with their lengths adjusted to fit a fixed weekly pattern: Month Days Notes January 28 4 weeks February 28 4 weeks March 35 5 weeks April 28 4 weeks May 28 4 weeks June 35 5 weeks July 28 4 weeks August 28 4 weeks September 35 5 weeks October 28 4 weeks November 28 4 weeks December 36/37 5 weeks + leap day adjustment Normal year: = 36 days (total = 365 days). Leap year: 37 days (total = 366 days). Normal year: 36 days in December, totaling 365 days. • Leap year: 37 days in December, totaling 366 days. 6.3 Year Length • Common year: 365 days (52 weeks + 1 day). • Leap year: 366 days (52 weeks + 2 days). This structure eliminates the shifting of weekdays across years, ensuring long-term consistency. 6.4 Advantages • Fixed weekly rhythm: If February 1 is a Monday, then May 1 and December 1 are also Mondays. • Simplified planning: Holidays, events, and paydays always fall on the same weekday each year. • Compatibility with T.M. Raghunath Calendar System (TMRCS): The fixed structure can be seamlessly integrated with the precise leap-year correction cycles (128-year, 5,000-year, and 80,000-year) of TMRCS. This integration produces a hybrid system that is: • Structurally fixed and symmetric (weekly rhythm never shifts). • Astronomically precise when combined with TMRCS correction cycles. 7. Philosophical Basis: Time Must Be Measured as It Flows The Raghunath Calendar is grounded in the philosophy that time should be measured naturally, not artificially rounded. Traditional systems remove entire days to account for fractional surpluses. The Raghunath model corrects time as it actually accumulates in fractions honoring the flow of solar time. This aligns with the scientific principles of celestial mechanics and the continuous nature of time. Time measurement must reflect astronomical reality, not integer approximations. By treating skipped leap days as fractional time (0.9688 days), the system honors the continuous flow of solar time, aligning civil timekeeping with celestial mechanics. 8. Conclusion The T.M. Raghunath Calendar System offers a revolutionary advancement in timekeeping. It retains the familiarity of the Gregorian structure while applying scientific corrections based on actual astronomical time. By treating the omitted leap day as 0.9688 days and correcting this surplus precisely every 128 years—augmented by 5,000- and 80,000-year cycles—the calendar eliminates long-term drift. Unprecedented accuracy (zero drift over 5,000 years). Seamless compatibility with existing infrastructure. Future-proof scalability via adaptable cycles. This precision, combined with structural compatibility and adaptability, positions the T.M.Raghunath Calendar as the “scientifically precise fractional-correction model” and future-proof calendar system ever proposed. Declarations Author Contributions T.M. Raghunath conceived and developed the T.M. Raghunath Calendar System, performed the mathematical and astronomical analysis, and prepared the manuscript. The author approved the final version of the paper. Funding Declaration The authors received no specific funding for this research. Ethics Declaration Ethics approval and consent to participate: Not applicable. Consent for publication: Not applicable. Competing interests: The author declares no competing interests. References The Gregorian Calendar Reform, Vatican Archives, 1582. Explanatory Supplement to the Astronomical Almanac, U.S. Naval Observatory, 1961. .Bromberg, I. (University of Toronto). “Symmetry 454 Calendar Proposal”, 2004. NASA Fact Sheet: Orbital Mechanics and Year Length, 15 Nov 2024. Raghunath, T.M Personal Hypothesis and Communication, 2025. T.M. Raghunath Original manuscript in kannada language on calendar correction, 2011. Additional Declarations The authors declare no competing interests. Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. 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Raghunath Calendar System: Precision Solar Alignment through Fractional Leap-Year Corrections (Demand for correction of error in the Gregorian calendar)","fulltext":[{"header":"1. Introduction","content":"\u003cp\u003eAccurate calendar systems are essential for agriculture, science, social organization, and global coordination. Throughout history, reforms such as the Julian and Gregorian calendars sought to align civil timekeeping with Earth\u0026rsquo;s orbital motion. However, both systems introduced approximations. The Julian calendar assumed a year length of 365.25 days, which produced significant long-term drift. The Gregorian reform improved accuracy by skipping three leap years every 400 years, reducing the error but not fully eliminating it.\u003c/p\u003e \u003cp\u003eThe T.M. Raghunath Calendar System addresses the residual discrepancy by introducing a leap-year correction method grounded in the actual fractional surplus of solar time. Instead of assuming that each four-year surplus equals one full day, it recognizes that the true accumulation is 0.9688 days, not a complete day. This refinement ensures precise alignment with the tropical year length of 365.2422 days.\u003c/p\u003e \u003cp\u003eIn this system, February 29 is treated as a full leap day by incorporating the missing 0.0312 days alongside the accumulated 0.9688 days over four years. However, when a leap day is skipped, this additional 0.0312 days is not added. Consequently, a skipped leap day accounts for only 0.9688 of a day, rather than a full 24 hours. This distinction is central to the accuracy of the model.\u003c/p\u003e"},{"header":"2. Methodology: The Raghunath Leap Year Correction","content":"\u003cp\u003e2.1) Core Principles\u003c/p\u003e\n\u003cp\u003e• Added Leap Day (February 29): Counts as one full day, consisting of 0.9688 days of accumulated surplus plus 0.0312 days of compensation.\u003c/p\u003e\n\u003cp\u003e• Skipped Leap Day: Corrects only 0.9688 days, as the extra 0.0312-day adjustment is not applied.\u003c/p\u003e\n\u003cp\u003e• Preserves Gregorian Structure: Months, weeks, and the distinction between common years (365 days) and leap years (366 days) remain unchanged.\u003c/p\u003e\n\u003cp\u003eThe T.M. Raghunath Calendar retains the familiar Gregorian framework but introduces a crucial refinement: in skipped leap years, February 29 is treated as 0.9688 days, reflecting the actual surplus accumulated over four years (0.2422 × 4), rather than a full 24 hours.\u003c/p\u003e\n\u003cp\u003e2.2) The 128-Year Correction Cycle\u003c/p\u003e\n\u003cp\u003eOver 124 years, the surplus time accumulates to approximately 0.9672 days. To correct this, the system employs a 128-year cycle, in which one leap day is removed across four specific years: the 33rd, 66th, 99th, and 128th.\u003c/p\u003e\n\u003cp\u003e• Each skipped leap year eliminates 0.2422 days.\u003c/p\u003e\n\u003cp\u003e• Collectively, the four skipped leap years remove 0.9688 days, almost perfectly offsetting the 0.9672-day surplus.\u003c/p\u003e\n\u003cp\u003eThus, in practice:\u003c/p\u003e\n\u003cp\u003e• 32 leap years are scheduled within a 128-year period.\u003c/p\u003e\n\u003cp\u003e• 1 leap year is effectively nullified, leaving 31 functional leap years.\u003c/p\u003e\n\u003cp\u003e• The structure consists of three 33-year segments (8 leap years each) and one 29-year segment (7 leap years).\u003c/p\u003e\n\u003cp\u003eThis creates occasional five-year intervals between leap years (e.g., from year 28 to 33),breaking the usual four-year cycle but ensuring precise alignment.\u003c/p\u003e\n\u003cp\u003e2.3) Comparison with the Gregorian Calendar\u003c/p\u003e\n\u003cp\u003eThe Gregorian system omits three leap days every 400 years (specifically in century years that are not divisible by 400). Each omission corrects approximately 0.9688 days, but these adjustments are distributed over several centuries rather than applied in shorter, more precise intervals.\u003c/p\u003e\n\u003cp\u003eIn contrast, the Raghunath Calendar applies corrections much more rapidly—within 33-year intervals rather than centuries. By addressing the fractional surplus directly (0.2422 days per skipped leap year segment), it achieves finer precision and faster alignment with the solar year\u003c/p\u003e\n\u003cp\u003e2.4) Treatment of Skipped Leap Days\u003c/p\u003e\n\u003cp\u003eIn any calendar, adding February 29 every four years compensates for the annual surplus of 0.2422 days, which totals about 0.9688 days over four years. To make February 29 a complete day, an extra 0.0312 days is added.\u003c/p\u003e\n\u003cp\u003e• In added leap years: February 29 is treated as a full day (0.9688 + 0.0312).\u003c/p\u003e\n\u003cp\u003e• In skipped leap years: The extra 0.0312 days are not included. Thus, each skipped leap day accounts for only 0.9688 of a day.\u003c/p\u003e\n\u003cp\u003eThis distinction is critical. The Gregorian calendar overlooks this fractional detail by treating skipped days as if they subtract a full day, leading to cumulative inaccuracies over time. The Raghunath Calendar corrects this flaw by measuring both added and skipped days in fractional time, not merely in whole calendar days.\u003c/p\u003e\n\u003cp\u003e2.5) Precision of the Cycle\u003c/p\u003e\n\u003cp\u003e• In the Gregorian system, skipping leap years in the 100th, 200th, and 300th years creates 8-year gaps between leap years.\u003c/p\u003e\n\u003cp\u003e• In the Raghunath system, leap years are skipped in the 33rd, 66th, 99th, and 128th years, producing 5-year gaps within certain segments.\u003c/p\u003e\n\u003cp\u003eThis design ensures that each skipped leap year corrects approximately 0.2422 days within its 33-year block, achieving faster and more accurate synchronization with the solar year.\u003c/p\u003e"},{"header":"3. Scientific and Mathematical Justification","content":"\u003cp\u003e3.1 The 128-Year Cycle Correction\u003c/p\u003e\n\u003cp\u003eEach skipped leap year is designed to offset the surplus time accumulated over preceding decades. The calculations are as follows:\u003c/p\u003e\n\u003cp\u003e\u0026bull; 33rd year: 0.0078 \u0026times; 32 = 0.2496 days \u0026rarr; correction = 0.2422 days\u003c/p\u003e\n\u003cp\u003e\u0026bull; 66th year: 0.0078 \u0026times; 32 = 0.2496 days \u0026rarr; correction = 0.2422 days\u003c/p\u003e\n\u003cp\u003e\u0026bull; 99th year: 0.0078 \u0026times; 32 = 0.2496 days \u0026rarr; correction = 0.2422 days\u003c/p\u003e\n\u003cp\u003e\u0026bull; 128th year: 0.0078 \u0026times; 28 = 0.2184 days \u0026rarr; correction = 0.2422 days\u003c/p\u003e\n\u003cp\u003eTotals:\u003c/p\u003e\n\u003cp\u003e\u0026bull; Corrected = 4 \u0026times; 0.2422 = 0.9688 days\u003c/p\u003e\n\u003cp\u003e\u0026bull; Surplus = 0.9672 days\u003c/p\u003e\n\u003cp\u003e\u0026bull; Net error = 0.0016 days per 128-year cycle\u003c/p\u003e\n\u003cp\u003eCore Principles of the 128-Year Cycle\u003c/p\u003e\n\u003cp\u003e\u0026bull; Annual surplus = 0.2422 days/year \u0026rarr; 0.9688 days over 4 years.\u003c/p\u003e\n\u003cp\u003e\u0026bull; Correction rule: Omit leap days in the 33rd, 66th, 99th, and 128th years.\u003c/p\u003e\n\u003cp\u003e\u0026bull; Effect: Removes 0.9688 days, nearly identical to the 0.9672-day surplus.\u003c/p\u003e\n\u003cp\u003e\u0026bull; After 124 years, surplus = 0.2422 \u0026times; 124 = 0.9672 days.\u003c/p\u003e\n\u003cp\u003e\u0026bull; By using 31 leap years instead of 32 in each 128-year cycle, the model corrects this surplus.\u003c/p\u003e\n\u003cp\u003e\u0026bull; The skipped leap years create occasional five-year gaps (e.g., from year 28 to 33), breaking the regular four-year cycle.\u003c/p\u003e\n\u003cp\u003e\u0026bull; Residual error: only 0.0016 days per 128 years, an order of magnitude smaller than in the Gregorian system.\u003c/p\u003e\n\u003cp\u003eCycle Structure\u003c/p\u003e\n\u003cp\u003e\u0026bull; Years 1\u0026ndash;33: 8 leap years \u0026rarr; 7 at 4-year intervals, 1 at a 5-year interval (years 4, 8, 12, 16, 20, 24, 28, 33).\u003c/p\u003e\n\u003cp\u003e\u0026bull; Years 34\u0026ndash;66: 8 leap years \u0026rarr; (years 37, 41, 45, 49, 53, 57, 61, 66).\u003c/p\u003e\n\u003cp\u003e\u0026bull; Years 67\u0026ndash;99: 8 leap years \u0026rarr; (years 70, 74, 78, 82, 86, 90, 94, 99).\u003c/p\u003e\n\u003cp\u003e\u0026bull; Years 100\u0026ndash;128: 7 leap years \u0026rarr; (years 103, 107, 111, 115, 119, 123, 128).\u003c/p\u003e\n\u003cp\u003eThis distribution yields 31 leap years per 128-year cycle, effectively nullifying one leap year and thereby correcting the cumulative surplus with remarkable precision.\u003c/p\u003e\n\u003cp\u003e3.2 The 5,000-Year Correction Cycle\u003c/p\u003e\n\u003cp\u003eAcross 4,992 years (39 \u0026times; 128-year cycles), the small residual error of 0.0016 days per cycle accumulates to:\u003c/p\u003e\n\u003cp\u003e\u0026bull; 0.0016 \u0026times; 39 = 0.0624 days\u003c/p\u003e\n\u003cp\u003eThis drift is corrected by extending the cycle with 8 unadjusted years at the end of the 5,000-year span:\u003c/p\u003e\n\u003cp\u003e\u0026bull; 8 \u0026times; 0.0078 = 0.0624 days\u003c/p\u003e\n\u003cp\u003eThus, the final 8 years (years 4,993\u0026ndash;5,000) are excluded from any correction cycle, restoring balance and ensuring perfect alignment across the full 5,000-year period.\u003c/p\u003e\n\u003cp\u003e3.3 The 80,000-Year Correction Cycle\u003c/p\u003e\n\u003cp\u003eTwo approaches confirm long-term stability:\u003c/p\u003e\n\u003cp\u003e1. Repetition of the 5,000-year cycle\u003c/p\u003e\n\u003cp\u003e\u0026bull; 16 \u0026times; 5,000 years = 80,000 years\u003c/p\u003e\n\u003cp\u003e2. Extended calculation\u003c/p\u003e\n\u003cp\u003e\u0026bull; Residual over 624 cycles: 0.0016 \u0026times; 624 = 0.9984 days\u003c/p\u003e\n\u003cp\u003e\u0026bull; Correction via 128 unadjusted years (years 79,873\u0026ndash;80,000): 128 \u0026times; 0.0078 = 0.9984 days\u003c/p\u003e\n\u003cp\u003eIn both cases, the accumulated surplus is completely eliminated, delivering unmatched precision over 80 millennia.\u003c/p\u003e\n\u003cp\u003e3.4 Average Year Length of the T.M. Raghunath Calendar\u003c/p\u003e\n\u003cp\u003eGeneral Formula\u003c/p\u003e\n\u003cp\u003e\u003cimg 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\"\u003e\u003c/p\u003e\n\u003cp\u003eNumber of year in cycle\u003c/p\u003e\n\u003cp\u003e3.5 Formula Validation\u003c/p\u003e\n\u003cp\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAksAAABACAYAAAAK5TPoAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsMAAA7DAcdvqGQAABYiSURBVHhe7d3Paxzn/Qfw937vlTurnNpigkYXY4NCMqpLWAcSiMdNIKRUZjZ1DwaHKiNySsFRViohRP6xStuAaaXdYEEptndNA/Ehq2gVkA8jQnHUsktieohnDyHpaRZh9w94eug8833m2ZnZlfXDsv1+wWJr5tmdZ2eeH5/n0TyjnBBCgIiIiIgS/Z++gYiIiIj+H4MlIiIiogwMloiIiIgyMFgiIiIiysBgiYiIiCgDgyUiIiKiDAyWiIiIiDIwWCIiIiLKwGCJiIiIKAODJSIiIqIMDJaIiIiIMjBYIiIiIsrAYImIiIgoA4MlIiIiogwMloiIiIgyMFgiIiIiysBgiR5KnU4H1WoVo6OjWF9f13fvmWq1ina7rW+mbapWqw/0utLjqd1uY2ZmBvl8nuWPYvY8WJqamnosC+GJEyeQy+Vir/n5+Viafvt3m378XC6HEydO6MkemE6nEys7d+/ehe/7sTR7pdvt4sSJE5iYmMDY2Fhsn36t9XPY7XZRLBaRy+WQz+dRrVZj+6V6vY7R0dHoMzqdjp4E7XYb4+PjyOVyux44drvdqCORecoKFLvdLubn56P86eW52+1Gn6WX+cnJSXz22Weo1+ux9wxCLydJOp0OZmZmUCwW9V0AgPX19SjfuVwOU1NTiecf4XU6ceJE5jH7HW+nqfnP5/M9517X6XQwNTUVlTf9u8zPz8euUz6fR7fbjaVR6WVldHS077WU5UHPa6fTieqLLHd6/u7neEl+8IMfAAA2Nzf1XfS4E3vI930BQLiuq+965AVBICqVigAgAAjP8/QkIggCYVmWsCxLtFotffeeaDQaAoAwTVP4vq/vfqBc142dN8/zUs/lbrNtO/G4jUZDOI4jyuVy9FKvZRAEwjRN4bquCIJAtFotYRiGKJfLsc+pVCrCMIzoGK7rCsMwRBAEUZpWqyUAiEqlIoQQolar7er5KJVKolKpCM/zRLlcFoZhCNM09WRChHkzDEPYti0ajUYs31KpVBKlUil2rvR08v1bIfOXxvd90Wg0hGmawrZtfXeUd5k327ajOqHnr9FoiHK5nHne+x1vp7VaLeG6rmg0GqLRaET5r9VqelIhlHKj1y/J931h23bsOvW7Jo7jRO8plUrCMIxYWU3iOI4AELt2an0pl8vCdd2oDVXr1f0cL02/60mPpz0NlmSDD2DfdcR7pVQq9TQIkgyW9AZ5rwHYk0Z9K5ICgQcVLNVqNWFZlr5ZiLBzz7p+srFX08ggWtYJOagolUrKO4UwDCM20DBNsycfjuOkBjDb4ft+z3mWZVknr0tWR+X7vnAcR9/cw/O8niCxn37BkmTbdmI5TwraZEeeFHAMWg7TjrfT9DwGQZDa5pTDoDcr767rbmnw5vt+z7WXgX1a2axUKlHdUPNZq9V6ji3ri6wL93O8LAyWKElvS7dL5AhBNixJs0tyn3ypDUvSNlnRAcRmY3zfj0YXQRAI27ajBiEIgljQZppmYuOijmDUl5pvOVpM+5w0lmUJAD2jM8dxehoGEVZ8OTqUI15Vo9GIPhOAcBwnauyzzkUa/TxnycpbrVaLRntquqSAQr2W6ss0zWi2S315nhfrpNRrkdQp7CTTNBOPIQM6y7JEqVRKHBAY4WyLSjbs8jNlZ6BfI9lhJ71HSnuvpJ9HEXbi6nkdlOu6PQFPEATCSJgp08n6Zdu2qFQqPeVBZRhGT2eYxdtmsJRElrWkfKjlMMtWjreTZPCtty2D5Fu+V87uZKXtR7Y9OjkTJvMzyLVD2M5lSTuezvO8qP2UAxD1vGT1GTLP8qVeX71etVqtWH+hD3Rof9uzYKlcLkcFTBaipM5E7XBUMtiSjarrusINf5Xh+76wLCsKCFqtVmxKVwYTjUZDuK4rzPBXTEEQROnUxlr+KiwIAhGEsz3QGhs5uyA/Rzb+gzQmskMxDCM6B+VyObEhlhVMfq7sDGWDIhsz+bOsvDJoyToXafRKnyYrb0EQREGO4zhRY1gOR23qd5XBnDy/8lyqaeT3Us+v+l3ldjnbkVS2hDJq7PdKa7Dld0q6zrVaLSpfCINHNYDWr40KyjmX9UMPIGTe1fOoX0d5jLT8q2Vent9WqxWV5UHIzi0p6JXXrlwuxzoGPZ/lclk4jhPrgPTOXLJtW5hbmCGQ56efrQQv8rwmnaOksplk0ONtt4xKQRBE7VTSQM40TWGaZuzXVrZtx66D53miVCrFBmNJ5XcQtm3HBpuSHNz1K7sqpMzyqdKOp5KDDlkXvHAmU72e/foMmW+9zxJhXyLLvmEY0f/lcejhsSfBkgw4JFm40gpyUuNYq9WiyiE7aZXsxGShlw2O3rg5jhMbkeidn8xbUienVmI10BHKVHe/0Y6kVjDP81Lf5zhOT6MgA0OhVHa1gbMsK9Yop52LNBgwWOqXNxF+lt646ucyqSzoeZDnS14ndZvaESel20nyXKZ17JLneVGwINMmlSNJ/b4yWNIlBUv698w6hiTrowxQk4KeNPLzEQaDeoBvhPcxyWsiBzJZ56wS3p+lDoZUMgBL2icSZsvSXrpBgxcRnnu9HEuDlrmtHG8nyHKEsGyp9V+2G2pw5IUdeNp18MN7l5Ayw5YlCAe7ehukDnQGKbsiTJcUmKjSjqczwxkzlRxwyXz16zNEShsry76k79fbTtrf9mQ13NLSEn77299GPxcKBdi2jcXFxcQVFbOzs/B9P7aa4caNG9FKkmazCd/3Y6szXn75ZSBcHaQaGRmJ/Vyv11Gv16PVKb/+9a9j++VqiG+//Ta2HQAOHjwIhCtNNjc3YZpmdPwnnngCALCxsaG9K1mhUEClUsHGxgZOnz6NP//5z3oSAMD169fx2muvxb7rxsYGNjc30el0MDY2BiEExsbGolU5aXnQz8V29cubdODAgdj7AGBtbS36v2EYiSuNBs3v0NCQvgn37t3TN+0ImW99BZyuUChgdXUVhmGkrnZ7UIaHh3H58mUAwFNPPYVyuYzh4WE9WaJCoQAhBGq1GvL5PN544w0sLy8DYd3b3NyEZVl46aWXgPAafvjhh0D4OIAkk5OTuHLlCnzfx+eff67vxpNPPgkA+Ne//qXvAv4XBcVenuehXC73bL9f3W4Xa2treOutt/Rd+9rKygp834frumg2m3AcJ9r397//HQDwi1/8IirLhUIB09PTqddhZGQEKysrsCwLH3zwgb4709LSEubm5mJ1enl5GQcOHEChUIil7edPf/pTVH7TJB1P12634fs+nnvuudh2vb3q12cAwJkzZ2AYBn7/+99H2z7++ONYv+c4Do4fPx71a3u1MpJ2xq4HS91uFxcvXuzpVJvNJhAWal2hUIBpmpidnQXC4OTpp5+OpbFtu6cxFEJgYWEhlk4nl5haloWDBw/iypUrsf1jY2NwXRcfffRR1IFfu3YNhmHgxRdfjKXVjy2EwJ07d2JpskxOTgIARkdHMzsrz/N6jiOEiBqC9fV1jI6O4saNG5idnYVt2/pH7Jp+eRvEwsICms1mtBxYNia/+tWvtJSD+/rrr/VNQMIS6LSXvnz5foyMjMB13cRA8EGT5Rzh4GOrisUiVldXAQB//etfAQD/+c9/AKCnrsrOMOs8vPTSS7AsK3GQ8qAtLS3h6tWrmXV0J+1kGR0ZGcHCwgJc18XGxkY0mLx79y4A4PDhw7H0zz77LJAyWJTee++9LT2yo91u4+DBg7HgoNvt4tKlSzh79mwsbT/1eh3vvPNO5mAl6XhJZHn9yU9+ou+K6ddnIByATE9PY3FxEZ1OB91uFx999FEsD/V6HXNzc5idncXo6Gg0yKCHw64HS0tLS5ienu7pTIMggGEYuHjxYuLs0tzcHHzfx/LyMq5du4aJiYnY/mazmfi+fgXw1KlTWF1dxTfffIPJycnEWYn3338flmXh+PHjyOVy6HQ6uHnzZk9jmXSspG3b9dlnn+mbouOsr6/j2LFjmJubQ71e3/Iobbuy8jaoYrEI13UxNzeHXC6H2dlZNBqNXfkuZ8+e7SmLSa+tNuJpDhw4gB/+8IdAGDQYhhGbVUN4DQHghRdeAMLRvrpdku+TM7MA8MUXX8TSyJ9lp5dGzo66rou3336751iDGBkZgW3byOfzAIBDhw4B2qyhSp6HNMPDwz2j+getWq3izJkzPXV/N+1GGZUDDzlzfuTIESCh/EhZ12FoaAiGYeibE7XbbXz//fc9gcvS0hKazWYs+Dt27BgA4O2330Yul4ulR9iuHDp0qG+glHS8LLdv39Y3xQzSZ0CbXfr8889jM3lSsVjEnTt38Jvf/AYvv/zylttKenB2NViS0fWZM2f0XVEkvrm5mTi7VCwWYRgG3n33XUD7lYzsKH73u99F2zBgJ91sNnHy5MnMxu/UqVN48803cefOHQghsLKyEqugstN79913YwFbp9NJndG4X47jYHFxsefXi59++imgNHZbaRy2S45o++VtUPPz83jyySexsrICEc7OyV/j7DcyoBk0uPjnP/+JN998M/q5WCzi1q1bsXIjr6EcEMgZTLUj63a7uHXrVjQbNDY2BtM0ewKTtbU1mKaZGWi2221cu3YNCwsLWFhYgGVZeOWVVzJnftJ0u93o1xjDw8OwbbtnICP//+qrr0bbdN1uF91ut2dQBGUW5Ec/+pG+a1dVq1VMTExkthUPi3v37sE0zagdPXr0KAzDwN/+9reedFDKYJLbt29jenpa39xDBi5JdXliYgKe58VelUoFAOC6LjzPi6VfXl7Gj3/844ECpaTjJZHl6ZNPPtF3xQzSZ0CbXZqdne3p99SZwLNnz8K2bVy6dCmWhvYx/SamnRKEK8SsjOcGyRvljJSl7Gk3sQplGbUZLuOWq3P0/fqNiIZhRHnyfT+28kqmlZ8rb8h0wweiqfmQK7+McLl8qVRKvTEyjVz5l/U+eSMmwpugy+EqI5kXmQ95s2CtVhNmuCy1UqkIP3yeTdK5SCKvSdINlPJ8qauosvKm3kQqyRvh1c+3wyW+8nw74UMd1Rsg5WeVw5V2nudF3129IVTmP+1m3O2SN6Hqq7ta4YMMK+Ey+CAIRKlU6rmJMwhXQsqbSr3wplr9ptZy+CiFVqsV1SVDe96QzIs8hjwfSfVFkvlUbzRVr3naDbGN8OGGtVot+n5uuCJVJT9f1jGZTi0DlUql5yZwJ+WxGSJlwUeWVqvVc951gXKTu173ZJ5L2gMzy+EDKvX0sh7r11CVdbyd5oSrT9Ubt82E1YYy3/IayhuS1e8h2zdZLiqVSk/dkuVQfZ/necLWHmRZDtvptHYo6XNEeEzZJqgvx3Gisn4/xxPKzdxuuLI6CB+vgrC99H1/oD5DkvU7acGOoayO9X0/6rtExnen/WPXgiVZ4ORLV05YHqsXFFlwkwRhZ2SEyzxlYRcJx1Y/t1arCSNctq9WBrURdMMgT88ftI5INvpIWHLbj/65ej5VnvYcELWjViu3Ha54keelFj7naJBjiJQ8Jb3Uxj4tb7Lyq6+kbUIJ8OS1VF9qfmUjJTsxNZ1sKPVtu0Ft5CT1OiBcFZkWtLSUZ06ZptnT4Epl5dlTjuMkBjIN5flSVriyMkvSuVHPGRLqqlBWoKrvTwtI1O8nO1u1zKifZYSBY9J3k4yEYHI7ksqh+vlpdR8JQbhev5Bw/vodb6fJAADK85HSzq9afpLKovpZVsojCLww4JfvlcF32istWEwKGNTj6y854Lrf40lqPZNBsvyuQfj4hX59hspxnJ7BlFBWCiPhmXT6OaT9Jyf+11hSqNvt4o9//CPOnTvXs13+unAr9wpQfzMzM3jrrbd6prmXl5dx6dIlrKysxLY/aPV6HX/4wx/w5Zdf6rtoh7XbbTz//PP45ptvesoH0X40Pj7OtuERtKv3LD2MTp06lXhz4/DwMI4cORI9PoB2xvz8PP7xj38kdoRHjx7d0qq6vVIsFmGa5kD3yNH2XLhwAVeuXEksH0T7Tb1ex+uvv65vpkcAZ5Y04+Pj8H0fFy5cwOHDh1EoFLC+vo7vvvsOX331Vc+ME23PzMwMzp8/j1KphJ///Oc4dOgQvvvuO3z//ff49NNP8f777++rjjJplQ7RdrAJfrhVq1V88skneOaZZ7C6uoqVlZV91WbRzmCwpJG/hrt+/Xr0LBHbtnH69Ok9XXH2OKlWq7h8+XL0ME3LsnDy5Mk9X7J9P6rVKl588cV9OQP2MFteXsbQ0FDmqj6i/aBareKNN96AbdtYWFhgW/CIYrBERERElIH3LBERERFlYLBERERElIHBEhEREVEGBktEREREGRgsET3i9L9in8/nE/8Itarb7aJYLEbpq9WqngQIH/2Qz+eRy+UwMzOT+Lntdhvj4+PI5XIYHR0d+O/qERHtFwyWiB5hnU4Ha2trKJfL0avfQx673S6OHj2KfD6PIAhw8+ZNvPPOO7E/BIrw4Zyrq6vY2NhAEARYXV3FqVOnYmna7TaeeuopvP766xBCYG5uDseOHWPAREQPFT46gOgRNjU1hcnJycy/1q6bmprC4uIigiCIgir5LBnf9zEyMoJ6vY7XXnsNjUYj+ivvMjCq1WrRM8lGR0dhGEbszz8Ui0VsbGzgzp070TYiov2MM0tEj6hOp4PFxUX88pe/xNTU1MCzOfV6HbZtx2affvaznwEAPv74YwDAjRs3ACAKlABgbGwMhmHgL3/5CxAGT77v4+TJk1EaAHj++efh+/7A+SEietAYLBE9ov7973+jVCrBMAwsLi7i2LFjmJmZ0ZPFrK+vY3NzE88880xsu5yZWltbAwBcv34dlmXF0gDAT3/6UzSbTQCI/j1y5EgszeHDhwEAX3zxRWw7EdF+xWCJ6BFVKBRw7tw5fPnll/B9H7Zt4/z586k3a6uS/pi0Luu+J9XQ0JC+iYjoocJgiegxMDIygpWVFViWhQ8++EDfTUREGRgsET1G3nvvvegPRBMR0WAYLBE9RoaGhmAYhr45UigUYBhGdG+SJG/GfuGFFwAAjuNE9ySpms0mbNsGgOhf/d4k+fOzzz4b205EtF8xWCJ6jNy+fRvT09P65phisYhbt27FHjApA5yJiQkAwKuvvgooQZT6/9OnTwPhTeGmafYEXmtrazBNE4VCIbadiGjfEkT0SDIMQ5RKJeH7vhBCiEqlIkqlUixNuVwWAES5XI62BUEgDMMQrusKIYTwPE8YhhFLI4QQtm0Ly7JEEATC931hWZawbTuWxvM8AUDUajUhwjwAEJ7nxdIREe1nnFkiekS5rovz58/DNE2Mj4/jwIEDOHfuXCzN3bt3YRgGLl68GG0bHh7GzZs30el0kMvlcPr0aVy4cAFnz56Nvffq1asYHx/HE088AcuycPz4cVy9ejWWplAooNFoYHZ2FrlcDpcvX4bneZxVIqKHCp/gTUQoFouo1+v6ZiIi4j1LRNRut/H000/rm4mIKMSZJaLH2PLyMu7duxf9LTciIurFYImIiIgoA38NR0RERJSBwRIRERFRBgZLRERERBkYLBERERFlYLBERERElIHBEhEREVEGBktEREREGRgsEREREWVgsERERESU4b/nkPSYG/7vJwAAAABJRU5ErkJggg==\"\u003e\u003c/p\u003e\n\u003cp\u003eVerdict: Mathematically precise, exactly matching the known value of the tropical year.\u003c/p\u003e\n\u003cp\u003e3.6 Astronomical Relevance\u003c/p\u003e\n\u003cp\u003e\u0026bull; Tropical year \u0026asymp; 365.2422 days.\u003c/p\u003e\n\u003cp\u003e\u0026bull; Gregorian calendar = 365.2425 days, slightly overcompensating.\u003c/p\u003e\n\u003cp\u003e\u0026bull; Verdict: The Raghunath Calendar eliminates drift, aligning perfectly with seasonal cycles.\u003c/p\u003e\n\u003cp\u003e3.7 Justification of 1211 Leap Days\u003c/p\u003e\n\u003cp\u003e\u0026bull; Pure 4-year cycle: 5,000 \u0026divide; 4 = 1,250 leap days.\u003c/p\u003e\n\u003cp\u003e\u0026bull; Correction applied: 1,250 \u0026minus; 39 = 1,211 leap days.\u003c/p\u003e\n\u003cp\u003e\u0026bull; Verdict: A logical adjustment mechanism to maintain exact alignment.\u003c/p\u003e\n\u003cp\u003e3.8 The 128-Year Cycle in Context\u003c/p\u003e\n\u003cp\u003e\u0026bull; Annual error: 365.25 \u0026minus; 365.2422 = 0.0078 days.\u003c/p\u003e\n\u003cp\u003e\u0026bull; Over 124 years: 0.0078 \u0026times; 124 = 0.9672 days (\u0026asymp; 1 day).\u003c/p\u003e\n\u003cp\u003e\u0026bull; Skipping one leap day every 128 years corrects this drift.\u003c/p\u003e\n\u003cp\u003e\u0026bull; Subcycles consist of 33-year blocks, with occasional 5-year intervals (e.g., years 28\u0026ndash;33).\u003c/p\u003e\n\u003cp\u003e\u0026bull; Residual per cycle: 0.0016 days.\u003c/p\u003e\n\u003cp\u003e\u0026bull; Over 39 cycles: 0.0016 \u0026times; 39 = 0.0624 days.\u003c/p\u003e\n\u003cp\u003e\u0026bull; Corrected by 8 unadjusted years: 0.0078 \u0026times; 8 = 0.0624 days.\u003c/p\u003e\n\u003cp\u003e\u0026bull; Verdict: A robust long-term correction strategy that maintains astronomical precision across millennia.\u003c/p\u003e\n\u003cp\u003e3.9 Leap Year Rule and Accuracy\u003c/p\u003e\n\u003cp\u003eThe T.M. Raghunath Calendar operates on a 5,000-year cycle designed to achieve an average year length of 365.2422 days, aligning exactly with the tropical year and offering greater precision than the Gregorian calendar (365.2425 days). This cycle is constructed from 39 repetitions of a 128-year subcycle (totaling 4,992 years), followed by a final 8-year segment to restore complete balance.\u003c/p\u003e\n\u003cp\u003e3.10 Key Properties\u003c/p\u003e\n\u003cp\u003e\u0026bull; Total leap years in 5,000 years: 1,211\u003c/p\u003e\n\u003cp\u003e\u0026bull; 128-year subcycle: 31 leap years per cycle\u003c/p\u003e\n\u003cp\u003e(leap years occur in years 4, 8, 12, 16, 20, 24, 28, 33, 37, 41, 45, 49, 53, 57, 61, 66, 70, 74, 78, 82, 86, 90, 94, 99, 103, 107, 111, 113, 117, 123, and 128).\u003c/p\u003e\n\u003cp\u003e\u0026bull; 39 subcycles: 39 \u0026times; 31 = 1,209 leap years\u003c/p\u003e\n\u003cp\u003e\u0026bull; Final 8-year segment: Adds 2 leap years (years 4,996 and 5,000)\u003c/p\u003e\n\u003cp\u003e\u0026bull; Grand total: 1,209 + 2 = 1,211 leap years\u003c/p\u003e\n\u003cp\u003e3.11 Average Year Length\u003c/p\u003e\n\u003cp\u003eAverage Year Length (5000 \u0026times; 365) + 1211 = 18261211/5000=365.2422 days\u003c/p\u003e\n\u003cp\u003eThis matches the tropical year precisely, ensuring zero drift over the 5,000-year cycle.\u003c/p\u003e\n\u003cp\u003e3.12 Why This Works\u003c/p\u003e\n\u003cp\u003e\u0026bull; In each 128-year subcycle, leap years are reduced from 32 (Gregorian assumption) to 31, correcting the Gregorian overage. This leaves a residual deficit of 0.0016 days per cycle.\u003c/p\u003e\n\u003cp\u003e\u0026bull; Across 39 subcycles (4,992 years): the accumulated deficit = 39 \u0026times; 0.0016 = 0.0624 days.\u003c/p\u003e\n\u003cp\u003e\u0026bull; The final 8 years follow a standard 4-year leap cycle (2 leap years), adding 8 \u0026times; 0.0078 = 0.0624 days, which cancels the deficit exactly.\u003c/p\u003e\n\u003cp\u003e\u0026bull; The result is a perfectly balanced calendar that remains aligned with astronomical seasons for millennia, achieving the target accuracy of 365.2422 days.\u003c/p\u003e\n\u003cp\u003e3.13 T.M. Raghunath Calendar System: Example 128-Year Cycle (2001\u0026ndash;2128)\u003c/p\u003e\n\u003cp\u003eKey Structure\u003c/p\u003e\n\u003cp\u003eThe T.M. Raghunath Calendar operates on a repeating 128-year cycle to maintain greater accuracy than the Gregorian calendar. An illustrative cycle spans the years 2001 to 2128.\u003c/p\u003e\n\u003cp\u003eSubdivision of the 128-Year Cycle\u003c/p\u003e\n\u003cp\u003eThe cycle is divided into four sequential blocks:\u003c/p\u003e\n\u003cp\u003e\u0026bull; 33 years\u003c/p\u003e\n\u003cp\u003e\u0026bull; 33 years\u003c/p\u003e\n\u003cp\u003e\u0026bull; 33 years\u003c/p\u003e\n\u003cp\u003e\u0026bull; 29 years\u003c/p\u003e\n\u003cp\u003eLeap Year Distribution Logic\u003c/p\u003e\n\u003cp\u003e\u0026bull; Total leap years per 128-year cycle: 31\u003c/p\u003e\n\u003cp\u003e\u0026bull; In each 33-year block (3 blocks): Leap years occur in the 4th, 8th, 12th, 16th, 20th, 24th, 28th, and 33rd years.\u003c/p\u003e\n\u003cp\u003e\u0026bull; In the final 29-year block: Leap years occur in the 4th, 8th, 12th, 16th, 20th, 24th, and 29th years.\u003c/p\u003e\n\u003cp\u003eActual Leap Years in the 2001\u0026ndash;2128 Cycle\u003c/p\u003e\n\u003cp\u003e\u0026bull; First 33 years (2001\u0026ndash;2033): 2004, 2008, 2012, 2016, 2020, 2024,\u003c/p\u003e\n\u003cp\u003e2028, 2033\u003c/p\u003e\n\u003cp\u003e\u0026bull; Second 33 years (2034\u0026ndash;2066): 2037, 2041, 2045, 2049, 2053, 2057, 2061, 2066\u003c/p\u003e\n\u003cp\u003e\u0026bull; Third 33 years (2067\u0026ndash;2099): 2070, 2074, 2078, 2082, 2086, 2090, 2094, 2099\u003c/p\u003e\n\u003cp\u003e\u0026bull; Final 29 years (2100\u0026ndash;2128): 2103, 2107, 2111, 2115, 2119, 2123, 2128\u003c/p\u003e"},{"header":"4. Comparison with Other Calendar Systems","content":"\u003cp\u003e\u003cstrong\u003e4.1 Table 1\u0026nbsp;\u003c/strong\u003e\u003c/p\u003e\n\u003ctable border=\"1\" cellspacing=\"0\" cellpadding=\"0\"\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 160px;\"\u003e\n \u003cp\u003e\u003cstrong\u003eFeature\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 160px;\"\u003e\n \u003cp\u003e\u003cstrong\u003eJulian Calendar\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 160px;\"\u003e\n \u003cp\u003e\u003cstrong\u003eGregorian Calendar\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 160px;\"\u003e\n \u003cp\u003e\u003cstrong\u003eT.M. Raghunath Calendar\u003c/strong\u003e\u003c/p\u003e\n \u003cp\u003e\u003cstrong\u003e\u0026nbsp;\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 160px;\"\u003e\n \u003cp\u003eYear Length\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 160px;\"\u003e\n \u003cp\u003e365.25 days\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 160px;\"\u003e\n \u003cp\u003e365.2425 days\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 160px;\"\u003e\n \u003cp\u003e365.2422 days\u003c/p\u003e\n \u003cp\u003e\u003cstrong\u003e\u0026nbsp;\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 160px;\"\u003e\n \u003cp\u003eAnnual Error\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 160px;\"\u003e\n \u003cp\u003e11 min 14 sec\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 160px;\"\u003e\n \u003cp\u003e+0.0003 days\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 160px;\"\u003e\n \u003cp\u003e0 (corrected)\u003c/p\u003e\n \u003cp\u003e\u003cstrong\u003e\u0026nbsp;\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 160px;\"\u003e\n \u003cp\u003eDrift in 128 Years\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 160px;\"\u003e\n \u003cp\u003e1 day\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 160px;\"\u003e\n \u003cp\u003e0.0384 days\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 160px;\"\u003e\n \u003cp\u003e0.0016 days\u003c/p\u003e\n \u003cp\u003e\u003cstrong\u003e\u0026nbsp;\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 160px;\"\u003e\n \u003cp\u003eDrift in 400 Years\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 160px;\"\u003e\n \u003cp\u003e3.12 days\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 160px;\"\u003e\n \u003cp\u003e0.12 days\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 160px;\"\u003e\n \u003cp\u003e0.005 days\u003c/p\u003e\n \u003cp\u003e\u003cstrong\u003e\u0026nbsp;\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 160px;\"\u003e\n \u003cp\u003eDrift in\u003c/p\u003e\n \u003cp\u003e640+1 = 641 Years\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 160px;\"\u003e\n \u003cp\u003e4.9998 \u0026nbsp;days\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 160px;\"\u003e\n \u003cp\u003e0.1923 days\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 160px;\"\u003e\n \u003cp\u003e0.0002 days\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 160px;\"\u003e\n \u003cp\u003eDrift in\u003c/p\u003e\n \u003cp\u003e2560 + 4 = 2564 Years\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 160px;\"\u003e\n \u003cp\u003e19.9992 days\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 160px;\"\u003e\n \u003cp\u003e0.7692 days\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 160px;\"\u003e\n \u003cp\u003e0.0008 days\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 160px;\"\u003e\n \u003cp\u003eDrift in 5,000\u0026nbsp;\u003c/p\u003e\n \u003cp\u003eYears\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 160px;\"\u003e\n \u003cp\u003e39 days\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 160px;\"\u003e\n \u003cp\u003e1.5 days\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 160px;\"\u003e\n \u003cp\u003e0 (corrected)\u003c/p\u003e\n \u003cp\u003e\u003cstrong\u003e\u0026nbsp;\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 160px;\"\u003e\n \u003cp\u003eDrift in 80,000\u003c/p\u003e\n \u003cp\u003e\u0026nbsp;Years\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 160px;\"\u003e\n \u003cp\u003e624 days\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 160px;\"\u003e\n \u003cp\u003e24 days\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 160px;\"\u003e\n \u003cp\u003e0 (corrected)\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 160px;\"\u003e\n \u003cp\u003eCorrection Mechanism\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 160px;\"\u003e\n \u003cp\u003eLeap every 4 yrs\u003c/p\u003e\n \u003cp\u003e\u003cstrong\u003e\u0026nbsp;\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 160px;\"\u003e\n \u003cp\u003eLeap day every 4 years.\u003c/p\u003e\n \u003cp\u003eSkip 3/400 yrs\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 160px;\"\u003e\n \u003cp\u003eLeap day every 4 years.\u003c/p\u003e\n \u003cp\u003eSubtract 0.9688 days/128 yrs\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 160px;\"\u003e\n \u003cp\u003eStructural Compatibility\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 160px;\"\u003e\n \u003cp\u003eYes\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 160px;\"\u003e\n \u003cp\u003eYes\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 160px;\"\u003e\n \u003cp\u003eYes\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 160px;\"\u003e\n \u003cp\u003eModern Adaptability\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 160px;\"\u003e\n \u003cp\u003eNo\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 160px;\"\u003e\n \u003cp\u003eLimited\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 160px;\"\u003e\n \u003cp\u003eHigh\u003c/p\u003e\n \u003cp\u003e\u003cstrong\u003e\u0026nbsp;\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 160px;\"\u003e\n \u003cp\u003eCycle length\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 160px;\"\u003e\n \u003cp\u003e4 year (repeated\u0026nbsp;\u003c/p\u003e\n \u003cp\u003e4 year)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 160px;\"\u003e\n \u003cp\u003e400 Years (repeated every 400 years)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 160px;\"\u003e\n \u003cp\u003e5,000 Years (repeated every 5,000 years)\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n\u003c/table\u003e\n\u003cp\u003e\u003cstrong\u003e\u003c/strong\u003e\u003cstrong\u003eKey Advantages:\u003c/strong\u003e\u003c/p\u003e\n\u003cul\u003e\n \u003cli\u003eEfficiency: Corrections applied 12 x faster than Gregorian 400-year cycle.\u003c/li\u003e\n \u003cli\u003eAdaptability: Modular cycles accommodate future orbital changes.\u003c/li\u003e\n\u003c/ul\u003e\n\u003cp\u003e\u003cstrong\u003e4.2 Comparative Analysis :\u0026nbsp;\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e4.3\u0026nbsp;\u003c/strong\u003e\u003cstrong\u003eTable 2\u0026nbsp;\u003c/strong\u003e\u003c/p\u003e\n\u003ctable border=\"1\" cellspacing=\"0\" cellpadding=\"0\" class=\"fr-table-selection-hover\"\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 181px;\"\u003e\n \u003cp\u003e\u003cstrong\u003eFeature\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 204px;\"\u003e\n \u003cp\u003e\u003cstrong\u003eGregorian Calendar\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 253px;\"\u003e\n \u003cp\u003e\u003cstrong\u003eT M Raghunath Calendar\u003c/strong\u003e\u003c/p\u003e\n \u003cp\u003e\u003cstrong\u003e\u0026nbsp;\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 181px;\"\u003e\n \u003cp\u003eYear Length\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 204px;\"\u003e\n \u003cp\u003e365.2425 days \u0026nbsp; \u0026nbsp; \u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 253px;\"\u003e\n \u003cp\u003e365.2422 days\u003c/p\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 181px;\"\u003e\n \u003cp\u003eLeap-Day Treatment\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 204px;\"\u003e\n \u003cp\u003eSkipped = 1 full day\u003c/p\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 253px;\"\u003e\n \u003cp\u003eSkipped = 0.9688 days\u003c/p\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 181px;\"\u003e\n \u003cp\u003e128 Year Error\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 204px;\"\u003e\n \u003cp\u003e0.0384 days\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 253px;\"\u003e\n \u003cp\u003e0.0016 days\u0026nbsp;\u003c/p\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 181px;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003cp\u003eStructural change\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 204px;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003cp\u003eRequired (1582)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 253px;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003cp\u003eNone\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n\u003c/table\u003e\n\u003cp\u003eCompared to Julian and Gregorian systems, and even modern proposals like the Symmetry 454, the T M Raghunath Calendar offers unmatched precision and structural continuity while correcting leap year surplus more effectively.\u003c/p\u003e"},{"header":"5. Future Adaptability","content":"\u003cp\u003eThe T.M. Raghunath Calendar System is designed with long-term adaptability in mind, ensuring its relevance even under future astronomical variations. If Earth\u0026rsquo;s orbital period shifts slightly whether due to tidal interactions or planetary influences the correction cycles can be recalibrated to maintain accuracy. The framework can also accommodate modifications to week or month structures if global consensus calls for such structural reform, reflecting its modular and flexible design.\u003c/p\u003e \u003cp\u003eIn practice, each leap year in the system carries a small surplus of approximately 0.0312 days. If long-term orbital changes alter the solar year by a similar magnitude, the calendar compensates by skipping one scheduled correction. This simple yet effective adjustment allows the system to remain precisely aligned with the solar year, naturally adapting to long-term astronomical shifts.\u003c/p\u003e \u003cp\u003eFurthermore, within the T.M. Raghunath Calendar framework, the Fixed-Week Calendar can be seamlessly integrated. This optional hybrid model ensures that both weeks and months remain constant, offering the world a truly innovative and predictable timekeeping system. Should the international community endorse such a reform, the system is fully prepared for implementation.\u003c/p\u003e"},{"header":"6. T.M. Raghunath Fixed Calendar System (Optional Overlay)","content":"\u003cp\u003e6.1 Core Idea\u003c/p\u003e\n\u003cp\u003eThe Fixed Calendar is designed to provide complete consistency in civil timekeeping.\u003c/p\u003e\n\u003cp\u003e\u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp;\u0026nbsp;\u0026bull;\u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp;\u0026nbsp;Every year begins on a Monday.\u003c/p\u003e\n\u003cp\u003e\u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp;\u0026nbsp;\u0026bull;\u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp;\u0026nbsp;The weekly cycle never shifts, ensuring that weekdays remain permanently aligned with dates.\u003c/p\u003e\n\u003cp\u003eThis creates a predictable and stable rhythm for daily life, long-term planning, and global coordination.\u003c/p\u003e\n\u003cp\u003e6.2 Month Structure\u003c/p\u003e\n\u003cp\u003eThe year is divided into 12 months, with their lengths adjusted to fit a fixed weekly pattern:\u0026nbsp;\u003c/p\u003e\n\u003ctable border=\"1\" cellspacing=\"0\" cellpadding=\"0\" width=\"619\"\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 157px;\"\u003e\n \u003cp\u003e\u003cstrong\u003eMonth\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 126px;\"\u003e\n \u003cp\u003e\u003cstrong\u003eDays\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 336px;\"\u003e\n \u003cp\u003e\u003cstrong\u003eNotes\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 157px;\"\u003e\n \u003cp\u003eJanuary\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 126px;\"\u003e\n \u003cp\u003e28\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 336px;\"\u003e\n \u003cp\u003e4 weeks\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 157px;\"\u003e\n \u003cp\u003eFebruary\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 126px;\"\u003e\n \u003cp\u003e28\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 336px;\"\u003e\n \u003cp\u003e4 weeks\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 157px;\"\u003e\n \u003cp\u003eMarch\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 126px;\"\u003e\n \u003cp\u003e35\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 336px;\"\u003e\n \u003cp\u003e5 weeks\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 157px;\"\u003e\n \u003cp\u003eApril\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 126px;\"\u003e\n \u003cp\u003e28\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 336px;\"\u003e\n \u003cp\u003e4 weeks\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 157px;\"\u003e\n \u003cp\u003eMay\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 126px;\"\u003e\n \u003cp\u003e28\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 336px;\"\u003e\n \u003cp\u003e4 weeks\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 157px;\"\u003e\n \u003cp\u003eJune\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 126px;\"\u003e\n \u003cp\u003e35\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 336px;\"\u003e\n \u003cp\u003e5 weeks\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 157px;\"\u003e\n \u003cp\u003eJuly\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 126px;\"\u003e\n \u003cp\u003e28\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 336px;\"\u003e\n \u003cp\u003e4 weeks\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 157px;\"\u003e\n \u003cp\u003eAugust\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 126px;\"\u003e\n \u003cp\u003e28\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 336px;\"\u003e\n \u003cp\u003e4 weeks\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 157px;\"\u003e\n \u003cp\u003eSeptember\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 126px;\"\u003e\n \u003cp\u003e35\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 336px;\"\u003e\n \u003cp\u003e5 weeks\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 157px;\"\u003e\n \u003cp\u003eOctober\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 126px;\"\u003e\n \u003cp\u003e28\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 336px;\"\u003e\n \u003cp\u003e4 weeks\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 157px;\"\u003e\n \u003cp\u003eNovember\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 126px;\"\u003e\n \u003cp\u003e28\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 336px;\"\u003e\n \u003cp\u003e4 weeks\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 157px;\"\u003e\n \u003cp\u003eDecember\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 126px;\"\u003e\n \u003cp\u003e36/37\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 336px;\"\u003e\n \u003cp\u003e5 weeks + leap day adjustment\u003c/p\u003e\n \u003cp\u003eNormal year: = 36 days (total = 365 days).\u003c/p\u003e\n \u003cp\u003eLeap year: 37 days (total = 366 days).\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n\u003c/table\u003e\n\u003cp\u003eNormal year: 36 days in December, totaling 365 days.\u003c/p\u003e\n\u003cp\u003e\u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026bull; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp;Leap year: 37 days in December, totaling 366 days.\u003c/p\u003e\n\u003cp\u003e6.3 Year Length\u003c/p\u003e\n\u003cp\u003e\u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp;\u0026nbsp;\u0026bull;\u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp;\u0026nbsp;Common year: 365 days (52 weeks + 1 day).\u003c/p\u003e\n\u003cp\u003e\u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp;\u0026nbsp;\u0026bull;\u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp;\u0026nbsp;Leap year: 366 days (52 weeks + 2 days).\u003c/p\u003e\n\u003cp\u003eThis structure eliminates the shifting of weekdays across years, ensuring long-term consistency.\u003c/p\u003e\n\u003cp\u003e6.4 Advantages\u003c/p\u003e\n\u003cp\u003e\u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp;\u0026nbsp;\u0026bull;\u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp;\u0026nbsp;Fixed weekly rhythm: If February 1 is a Monday, then May 1 and December 1 are also Mondays.\u003c/p\u003e\n\u003cp\u003e\u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp;\u0026nbsp;\u0026bull;\u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp;\u0026nbsp;Simplified planning: Holidays, events, and paydays always fall on the same weekday each year.\u003c/p\u003e\n\u003cp\u003e\u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp;\u0026nbsp;\u0026bull;\u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp;\u0026nbsp;Compatibility with T.M. Raghunath Calendar System (TMRCS): The fixed structure can be seamlessly integrated with the precise leap-year correction cycles (128-year, 5,000-year, and 80,000-year) of TMRCS.\u003c/p\u003e\n\u003cp\u003eThis integration produces a hybrid system that is:\u003c/p\u003e\n\u003cp\u003e\u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp;\u0026nbsp;\u0026bull;\u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp;\u0026nbsp;Structurally fixed and symmetric (weekly rhythm never shifts).\u003c/p\u003e\n\u003cp\u003e\u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026bull; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp;Astronomically precise when combined with TMRCS correction cycles.\u003c/p\u003e"},{"header":"7. Philosophical Basis: Time Must Be Measured as It Flows ","content":"\u003cp\u003eThe Raghunath Calendar is grounded in the philosophy that time should be measured naturally, not artificially rounded. Traditional systems remove entire days to account for fractional surpluses. The Raghunath model corrects time as it actually accumulates in fractions honoring the flow of solar time. This aligns with the scientific principles of celestial mechanics and the continuous nature of time.\u003c/p\u003e \u003cp\u003eTime measurement must reflect astronomical reality, not integer approximations. By treating skipped leap days as fractional time (0.9688 days), the system honors the continuous flow of solar time, aligning civil timekeeping with celestial mechanics.\u003c/p\u003e"},{"header":"8. Conclusion ","content":"\u003cp\u003eThe T.M. Raghunath Calendar System offers a revolutionary advancement in timekeeping. It retains the familiarity of the Gregorian structure while applying scientific corrections based on actual astronomical time. By treating the omitted leap day as 0.9688 days and correcting this surplus precisely every 128 years\u0026mdash;augmented by 5,000- and 80,000-year cycles\u0026mdash;the calendar eliminates long-term drift.\u003c/p\u003e \u003cp\u003e \u003cul\u003e \u003cli\u003e \u003cp\u003eUnprecedented accuracy (zero drift over 5,000 years).\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003eSeamless compatibility with existing infrastructure.\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003eFuture-proof scalability via adaptable cycles.\u003c/p\u003e \u003c/li\u003e \u003c/ul\u003e \u003c/p\u003e \u003cp\u003eThis precision, combined with structural compatibility and adaptability, positions the T.M.Raghunath Calendar as the \u0026ldquo;scientifically precise fractional-correction model\u0026rdquo; and future-proof calendar system ever proposed.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003eAuthor Contributions\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eT.M. Raghunath conceived and developed the T.M. Raghunath Calendar System, performed the mathematical and astronomical analysis, and prepared the manuscript. The author approved the final version of the paper.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eFunding Declaration\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe authors received no specific funding for this research.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eEthics Declaration\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eEthics approval and consent to participate: Not applicable. \u0026nbsp;\u003c/p\u003e\n\u003cp\u003eConsent for publication: Not applicable. \u0026nbsp;\u003c/p\u003e\n\u003cp\u003eCompeting interests: The author declares no competing interests.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n \u003cli\u003eThe Gregorian Calendar Reform, Vatican Archives, 1582.\u003c/li\u003e\n \u003cli\u003eExplanatory Supplement to the Astronomical Almanac, U.S. Naval\u003c/li\u003e\n \u003cli\u003eObservatory, 1961.\u003c/li\u003e\n \u003cli\u003e.Bromberg, I. (University of Toronto). \u0026ldquo;Symmetry 454 Calendar Proposal\u0026rdquo;, 2004.\u003c/li\u003e\n \u003cli\u003eNASA Fact Sheet: Orbital Mechanics and Year Length, 15 Nov 2024.\u003c/li\u003e\n \u003cli\u003eRaghunath, T.M Personal Hypothesis and Communication, 2025.\u003c/li\u003e\n \u003cli\u003eT.M. Raghunath Original manuscript in kannada language on calendar correction, 2011.\u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Calendar reform, Gregorian correction, Solar year, Leap year, Timekeeping, T.M Raghunath calendar system","lastPublishedDoi":"10.21203/rs.3.rs-8348127/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8348127/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThe Gregorian calendar, though a significant improvement over the Julian system, still contains cumulative inaccuracies arising from its leap-year adjustments. This paper introduces the T.M. Raghunath Calendar System, an innovative model that retains the familiar structure of the Gregorian calendar while applying precise fractional corrections to achieve closer alignment with the solar year. The system redefines the skipped leap day (February 29) as 0.9688 days rather than a full day, with a compensatory one-day correction applied every 128 years. A 33-year cycle regulates short-term surpluses of 0.2422 days, while extended cycles of 5,000 and 80,000 years eliminate long-term residual errors. This scalable framework delivers unprecedented accuracy, adaptability to astronomical variations, and seamless compatibility with existing civil structures, positioning it as one of the most scientifically rigorous calendar systems proposed to date.\u003c/p\u003e","manuscriptTitle":"The T.M. Raghunath Calendar System: Precision Solar Alignment through Fractional Leap-Year Corrections (Demand for correction of error in the Gregorian calendar)","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-12-24 08:01:26","doi":"10.21203/rs.3.rs-8348127/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"28a022c4-d55e-4e4d-b4f0-0ef3013533d9","owner":[],"postedDate":"December 24th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":{"display":true,"email":"[email protected]","identity":"astrophysics-and-space-science","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"astr","sideBox":"Learn more about [Astrophysics and Space Science](https://www.springer.com/journal/10509)","snPcode":"10509","submissionUrl":"https://submission.nature.com/new-submission/10509/3","title":"Astrophysics and Space Science","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2025-12-24T08:01:26+00:00","versionOfRecord":[],"versionCreatedAt":"2025-12-24 08:01:26","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-8348127","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-8348127","identity":"rs-8348127","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}