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            "timestamp": "2023-03-24T18:01:53.097480Z",
            "action": 5,
            "target": "UD(t+dt) \\approx \\frac{(c+c^2)M(t)}{N(t+dt)}\\approx c \\, \\frac{M(t)}{N(t+dt)}",
            "id": 11327,
            "action_name": "New translation",
            "url": "https://weblate.duniter.org/api/changes/11327/?format=api"
        },
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            "timestamp": "2023-03-24T18:02:00.482755Z",
            "action": 5,
            "target": "UD(t+dt) = Max \\left[ UD(t);c\\,\\frac{M(t)}{N(t+dt)} \\right]",
            "id": 11328,
            "action_name": "New translation",
            "url": "https://weblate.duniter.org/api/changes/11328/?format=api"
        },
        {
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            "timestamp": "2023-03-24T18:02:06.049996Z",
            "action": 5,
            "target": "UD = c \\, \\frac{M}{N}",
            "id": 11329,
            "action_name": "New translation",
            "url": "https://weblate.duniter.org/api/changes/11329/?format=api"
        },
        {
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            "timestamp": "2023-03-24T18:02:14.205756Z",
            "action": 2,
            "target": "Q_s(t)_{R_{2}} = Q_s(t)_{R_{1}} \\left[ \\frac{\\left(\\frac{M_{2}}{N}\\right) (t)}{\\left(\\frac{M_{1}}{N}\\right) (t)} \\right] = Q_s(t)_{R_{1}} \\left[ \\frac{\\left(\\frac{M_{1}}{N}\\right) (t)}{\\left(\\frac{M_{1}}{N}\\right) (0)} \\right]^{\\left[ \\frac{ln(1+c_{2})}{ln(1+{c_{1})}} - 1 \\right]}",
            "id": 11330,
            "action_name": "Translation changed",
            "url": "https://weblate.duniter.org/api/changes/11330/?format=api"
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        {
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            "author": "https://weblate.duniter.org/api/users/PifPafPouf/?format=api",
            "timestamp": "2023-03-24T18:02:35.774963Z",
            "action": 2,
            "target": "We then establish an economic metric whose reference value is generated in an invariant way by a frame of reference change (of individual, regardless of the time in which he is born, lives and dies).",
            "id": 11331,
            "action_name": "Translation changed",
            "url": "https://weblate.duniter.org/api/changes/11331/?format=api"
        },
        {
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            "timestamp": "2023-03-24T18:02:41.806579Z",
            "action": 2,
            "target": "\"The sum of the relative UD produced by an individual participant in a free currency during :math:`\\left(\\frac{ev}{2}\\right)` converges to :math:`\\frac{1}{c}` with :math:`\\frac{1 \\, an}{\\left(\\frac{ev}{2}\\right)}` near, whatever the individual and whatever the considered time.\"",
            "id": 11332,
            "action_name": "Translation changed",
            "url": "https://weblate.duniter.org/api/changes/11332/?format=api"
        },
        {
            "unit": "https://weblate.duniter.org/api/units/5895/?format=api",
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            "author": "https://weblate.duniter.org/api/users/PifPafPouf/?format=api",
            "timestamp": "2023-03-24T18:02:45.755286Z",
            "action": 2,
            "target": "Given a fair money established in :math:`[R_{1},c_{1}]` and its transformation in :math:`[R_{2},c_{2}]`, coinciding in :math:`t=0` where :math:`\\left(\\frac{M_{1}}{N_{1}}\\right)(0) = \\left(\\frac{M_{2}}{N_{2}}\\right)(0)`.",
            "id": 11333,
            "action_name": "Translation changed",
            "url": "https://weblate.duniter.org/api/changes/11333/?format=api"
        },
        {
            "unit": "https://weblate.duniter.org/api/units/5917/?format=api",
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            "author": "https://weblate.duniter.org/api/users/PifPafPouf/?format=api",
            "timestamp": "2023-03-24T18:02:49.759228Z",
            "action": 2,
            "target": "And then finally :math:`Q_s(t)_{R_{2}}` is deduced directly from :math:`R_{1}` by :",
            "id": 11334,
            "action_name": "Translation changed",
            "url": "https://weblate.duniter.org/api/changes/11334/?format=api"
        },
        {
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            "author": "https://weblate.duniter.org/api/users/PifPafPouf/?format=api",
            "timestamp": "2023-03-24T18:15:51.195576Z",
            "action": 2,
            "target": "Taking into account that :eq:`eq16` and :eq:`eq17`, we have :",
            "id": 11335,
            "action_name": "Translation changed",
            "url": "https://weblate.duniter.org/api/changes/11335/?format=api"
        },
        {
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            "component": "https://weblate.duniter.org/api/components/trm/appendice-2/?format=api",
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            "author": "https://weblate.duniter.org/api/users/PifPafPouf/?format=api",
            "timestamp": "2023-03-24T18:16:03.892088Z",
            "action": 2,
            "target": "So, it appears in :math:`R_{2}` that the monetary system is acting \"as if it was being taxed on every individual account :math:`(c_{1} - c_{2}) \\, Q_s(t)_{R_{2}}` of money, unconditionally paid for every member equally :math:`(c_{1}-c_{2}) \\left(\\frac{M_{2}}{N}\\right)(t)`, to which is added :math:`UD_{R_{2}}`.",
            "id": 11336,
            "action_name": "Translation changed",
            "url": "https://weblate.duniter.org/api/changes/11336/?format=api"
        },
        {
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            "component": "https://weblate.duniter.org/api/components/trm/appendice-2/?format=api",
            "translation": "https://weblate.duniter.org/api/translations/trm/appendice-2/en_US/?format=api",
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            "author": "https://weblate.duniter.org/api/users/PifPafPouf/?format=api",
            "timestamp": "2023-03-24T18:16:19.552495Z",
            "action": 2,
            "target": "And with :math:`c_{2}=0` we have :math:`UD(t)_{R_{2}}=UD(0)_{R_{2}}` which is then an arbitrary constant, that we can defined as equal to :math:`UD(0)_{R_{1}}`, constant which does not change the calculation of the differential, and then we get :",
            "id": 11337,
            "action_name": "Translation changed",
            "url": "https://weblate.duniter.org/api/changes/11337/?format=api"
        },
        {
            "unit": "https://weblate.duniter.org/api/units/5994/?format=api",
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            "translation": "https://weblate.duniter.org/api/translations/trm/appendice-2/en_US/?format=api",
            "user": "https://weblate.duniter.org/api/users/PifPafPouf/?format=api",
            "author": "https://weblate.duniter.org/api/users/PifPafPouf/?format=api",
            "timestamp": "2023-03-24T20:53:57.770541Z",
            "action": 2,
            "target": "Which is the form defined at the paragraph 9, therefore it is :math:`UD(0)_{R_{1}}` ignoring a constant factor, of the transformation of :math:`[R_{1},c_{1}]` in this Relative frame of reference :math:`[R_{2},c_{2}=0]` where monetary growth appears as null.",
            "id": 11338,
            "action_name": "Translation changed",
            "url": "https://weblate.duniter.org/api/changes/11338/?format=api"
        },
        {
            "unit": "https://weblate.duniter.org/api/units/6078/?format=api",
            "component": "https://weblate.duniter.org/api/components/trm/appendice-2/?format=api",
            "translation": "https://weblate.duniter.org/api/translations/trm/appendice-2/en_US/?format=api",
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            "author": "https://weblate.duniter.org/api/users/PifPafPouf/?format=api",
            "timestamp": "2023-03-24T20:54:03.072947Z",
            "action": 2,
            "target": "In :math:`R_{1}` we will have the equality :",
            "id": 11339,
            "action_name": "Translation changed",
            "url": "https://weblate.duniter.org/api/changes/11339/?format=api"
        },
        {
            "unit": "https://weblate.duniter.org/api/units/6101/?format=api",
            "component": "https://weblate.duniter.org/api/components/trm/appendice-2/?format=api",
            "translation": "https://weblate.duniter.org/api/translations/trm/appendice-2/en_US/?format=api",
            "user": "https://weblate.duniter.org/api/users/PifPafPouf/?format=api",
            "author": "https://weblate.duniter.org/api/users/PifPafPouf/?format=api",
            "timestamp": "2023-03-24T20:54:07.720333Z",
            "action": 2,
            "target": "All the right terms being already calculated by direct transformation from :math:`R_1`.",
            "id": 11340,
            "action_name": "Translation changed",
            "url": "https://weblate.duniter.org/api/changes/11340/?format=api"
        },
        {
            "unit": "https://weblate.duniter.org/api/units/6105/?format=api",
            "component": "https://weblate.duniter.org/api/components/trm/appendice-2/?format=api",
            "translation": "https://weblate.duniter.org/api/translations/trm/appendice-2/en_US/?format=api",
            "user": "https://weblate.duniter.org/api/users/PifPafPouf/?format=api",
            "author": "https://weblate.duniter.org/api/users/PifPafPouf/?format=api",
            "timestamp": "2023-03-24T20:54:35.709909Z",
            "action": 2,
            "target": "The presence of the factor :math:`(1+c_2)` is not surprising since it is the expansion rate discrete of :math:`R_{2}`, which multiplied by the data \"t\" gives an approximation of the data in \"t+1\". We should now understand that it produces a good intermediary value of the numerator between \"t\" and \"t+1\".",
            "id": 11341,
            "action_name": "Translation changed",
            "url": "https://weblate.duniter.org/api/changes/11341/?format=api"
        },
        {
            "unit": "https://weblate.duniter.org/api/units/6107/?format=api",
            "component": "https://weblate.duniter.org/api/components/trm/appendice-2/?format=api",
            "translation": "https://weblate.duniter.org/api/translations/trm/appendice-2/en_US/?format=api",
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            "author": "https://weblate.duniter.org/api/users/PifPafPouf/?format=api",
            "timestamp": "2023-03-24T20:54:46.811621Z",
            "action": 2,
            "target": "We have here the instantaneous calculation of the \"apparent tax\" in :math:`R_{2}` from data directly taken from :math:`R_{1}`, letting a display :math:`RdB_{R_{2}} = UD_{R_{2}} + (apparent tax)_{R_{2}}`.",
            "id": 11342,
            "action_name": "Translation changed",
            "url": "https://weblate.duniter.org/api/changes/11342/?format=api"
        },
        {
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            "translation": "https://weblate.duniter.org/api/translations/trm/appendice-2/en_US/?format=api",
            "user": "https://weblate.duniter.org/api/users/PifPafPouf/?format=api",
            "author": "https://weblate.duniter.org/api/users/PifPafPouf/?format=api",
            "timestamp": "2023-03-24T20:54:54.998007Z",
            "action": 2,
            "target": "This form use again the tax rate :math:`(c_1 - c_2)` applied to the account increased of the UBI (targeting its value in \"t+1\", without tax), and brought back to this value approximated in \"t+1\" to its value in \"t\" by the division by : :math:`(1+c_1)`.",
            "id": 11343,
            "action_name": "Translation changed",
            "url": "https://weblate.duniter.org/api/changes/11343/?format=api"
        },
        {
            "unit": "https://weblate.duniter.org/api/units/6115/?format=api",
            "component": "https://weblate.duniter.org/api/components/trm/appendice-2/?format=api",
            "translation": "https://weblate.duniter.org/api/translations/trm/appendice-2/en_US/?format=api",
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            "author": "https://weblate.duniter.org/api/users/PifPafPouf/?format=api",
            "timestamp": "2023-03-24T20:55:01.215602Z",
            "action": 2,
            "target": "We immediately note that when the account is worth the average, the theoretical tax is applied directly to the account without intermediary approximation.",
            "id": 11344,
            "action_name": "Translation changed",
            "url": "https://weblate.duniter.org/api/changes/11344/?format=api"
        },
        {
            "unit": "https://weblate.duniter.org/api/units/6119/?format=api",
            "component": "https://weblate.duniter.org/api/components/trm/appendice-2/?format=api",
            "translation": "https://weblate.duniter.org/api/translations/trm/appendice-2/en_US/?format=api",
            "user": "https://weblate.duniter.org/api/users/PifPafPouf/?format=api",
            "author": "https://weblate.duniter.org/api/users/PifPafPouf/?format=api",
            "timestamp": "2023-03-24T20:55:08.898458Z",
            "action": 2,
            "target": "Given prior analyze, one should bear in mind that it's the convergence of half life that is the target reached by a fair money, new entrants replacing dead human being (see about this the forms :eq:`eq4` et :eq:`eq14` concerning the time condition valid for any individual).",
            "id": 11345,
            "action_name": "Translation changed",
            "url": "https://weblate.duniter.org/api/changes/11345/?format=api"
        },
        {
            "unit": "https://weblate.duniter.org/api/units/6123/?format=api",
            "component": "https://weblate.duniter.org/api/components/trm/appendice-2/?format=api",
            "translation": "https://weblate.duniter.org/api/translations/trm/appendice-2/en_US/?format=api",
            "user": "https://weblate.duniter.org/api/users/PifPafPouf/?format=api",
            "author": "https://weblate.duniter.org/api/users/PifPafPouf/?format=api",
            "timestamp": "2023-03-24T20:55:25.825146Z",
            "action": 2,
            "target": "In particular, one should be convinced by thinking of the necessity to approach the practical solution by taking into consideration these extreme cases, as the one of the strongest growth of the number of members of a fair money (equivalent to a pseudo-initialization of the money), where the calculated UD in relative ( :math:`UD(t)=c\\left(\\frac{M}{N}\\right)(t)` ) will suffer a huge discontinuity, destroying the continuity of the progression, and would become extremely low compared to initial fewer participants, and would own in this case a huge share of money compared to the new entrants, unrelated to the calculated UD.",
            "id": 11346,
            "action_name": "Translation changed",
            "url": "https://weblate.duniter.org/api/changes/11346/?format=api"
        }
    ]
}