Question: According to which system, which was replaced by the Gregorian calendar in Japan, is the 35 in Type 35 rifle referencing the year 35?

Context paragraphs:
Type 35 rifle: The Type 35 Rifle (三十五年式) was created from the Type 30 rifle for the Imperial Japanese Navy as a replacement for their aging Type 22 Murata rifles and to try to correct the deficiencies of the Type 30 rifle.  The "35" referred to the adoption date, the Year 35 (1902) in the Meiji period according to the Japanese calendar.

Proleptic Gregorian calendar: The proleptic Gregorian calendar is produced by extending the Gregorian calendar backward to dates preceding its official introduction in 1582.  In countries that adopted the Gregorian calendar later, dates occurring in the interim (between 1582 and the local adoption) are sometimes "Gregorian-ized" as well.  For example, George Washington was born on February 11, 1731 (Old Style), as Britain and its possessions were using the Julian calendar until September 1752.  After the switch, that day became February 22, which is the date commonly given as Washington's birthday.

Zoroastrian festivals: Zoroastrianism has numerous festivals and holy days, all of which are bound to the Zoroastrian calendar.  The "Shahenshahi" and "Kadmi" variants of the calendar do not intercalate leap years and hence the day of the Gregorian calendar year on which these days are celebrated shifts ahead with time.  The third variant of the Zoroastrian calendar, known as either "Fasli" (in India) or "Bastani" (in Iran), intercalcates according to Gregorian calendar rules and thus remains synchronous with the seasons.  For details on the differences, see Zoroastrian calendar.

Japanese calendar: Japanese calendar types have included a range of official and unofficial systems.  At present, Japan uses the Gregorian calendar together with year designations stating the year of the reign of the current Emperor.

Adoption of the Gregorian calendar: The adoption of the Gregorian Calendar was an event in the modern history of most nations and societies, marking a change from their traditional (or "old style") dating system to the modern (or "new style") dating system that is widely used around the world today.  Some countries adopted the new calendar from 1582, some did not do so before the early twentieth century, and others did so at various dates between; however a number continue to use a different civil calendar.  For many the new style calendar is only used for civil purposes and the old style calendar remains used in religious contexts.  In the western world, the change was a simple date shift from the previous Julian Calendar but in the east the change from their old style lunisolar calendar was a more significant one.  Today, the Gregorian calendar is the world's most widely used civil calendar.  During and for some time after the change between systems, it has been common to use the terms "Old Style" and "New Style" when giving dates, to indicate which calendar was used to reckon them.

Lilian date: A Lilian date is the number of days since the beginning of the Gregorian Calendar on October 15, 1582, regarded as Lilian date 1.  It was invented by Bruce G. Ohms of IBM in 1986 and is named for Aloysius Lilius, who devised the Gregorian Calendar.  Lilian dates can be used to calculate the number of days between any two dates occurring since the beginning of the Gregorian calendar.  It is currently used by date conversion routines that are part of IBM Language Environment (LE) software.

6.5×50mmSR Arisaka: The 6.5×50mm Semi-Rimmed (6.5×50mmSR) Japanese cartridge, currently manufactured under the designation "6.5mm Jap", was adopted by the Imperial Japanese Army in 1897, along with the Type 30 Arisaka infantry rifle and carbine.  The new rifle and cartridge replaced the 8×52mm Murata round used in the Type 22 Murata Rifle.  In 1902 the Imperial Japanese Navy chambered its Type 35 rifle for the cartridge as well.  In 1905, the round also came to be offered in the Type 38 Arisaka infantry rifle and carbine, both of which rendered the Type 30 obsolete in Imperial Army service.  Type 44 cavalry carbines, first adopted in 1911, were also chambered in 6.5×50mm.

Old Style 1752: This is the calendar for Old Style 1752, a leap year which began on 1 January, and dropped 3–13 September to transition to the Gregorian calendar.  Previously, the Old Style calendar in England (and related regions) had begun on 25 March and ended with the following March, on 24 March.  Because the Gregorian calendar did not have leap day in 1700, the original 10-day difference in calendars had expanded to an 11-day difference, and to compensate, 2 September was followed by 14 September, as skipping 11 days beyond 3 September.  Year 1753, in England (and related regions) followed the full Gregorian calendar.  Note, below, the shortened length of September.

Revised Julian calendar: The Revised Julian calendar, also known as the Milanković calendar, or, less formally, new calendar, is a calendar, developed and proposed by the Serbian scientist Milutin Milanković in 1923, which effectively discontinued the 340 years of divergence between the naming of dates sanctioned by those Eastern Orthodox churches adopting it and the Gregorian calendar that has come to predominate worldwide.  This calendar was intended to replace the ecclesiastical calendar based on the Julian calendar hitherto in use by all of the Eastern Orthodox Church.  The Revised Julian calendar temporarily aligned its dates with the Gregorian calendar proclaimed in 1582 by Pope Gregory XIII for adoption by the Christian world.  The calendar has been adopted by the Orthodox churches of Constantinople, Albania, Alexandria, Antioch, Bulgaria, Cyprus, Greece, Poland, and Romania.

1582: Year 1582 (MDLXXXII) was a common year starting on Monday (link will display the full calendar) of the Julian calendar, and a common year starting on Friday (link will display the full calendar) of the Proleptic Gregorian calendar.  However, this year also saw the beginning of the Gregorian Calendar switch, when the Papal bull known as "Inter gravissimas" introduced the Gregorian calendar, adopted by Spain, Portugal, the Polish–Lithuanian Commonwealth and most of present-day Italy from the start.  In these countries, the year continued as normal until Thursday, October 4.  However, the next day became Friday, October 15 (like a common year starting on Friday), in those countries (France followed two months later, letting Sunday, December 9 be followed by Monday, December 20).  Other countries continued using the Julian calendar, switching calendars in later years, and the complete conversion of the Gregorian calendar was not entirely done until 1929.

Supporting paragraphs: Type 35 rifle Japanese calendar
Answer: Japanese calendar