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English translation of PAPER.ru.md. The Russian original is the source of truth; numbers are identical.
Tonify Research · August 2026 · reproducible: sim1/tonify_cash_sim.py + sim1/v04_full.py, seed=42
We construct a synthetic market of 200,000 artists, calibrated to three independently measured anchors (Luminate, Spotify Loud & Clear, CMA), and compare four payout mechanisms: pro-rata (Spotify), user-centric (SoundCloud FPR), recurring patronage (Twitch), and the direct attention economy (Tonify, World B). Main result: changing the split rule within World A shifts an artist’s minimum viable audience by at most ~1.3×, whereas moving to the direct mechanisms of World B shifts it by 1–2 orders of magnitude — provided that a devoted fan’s payment frequency exceeds the breakeven range of 0.38–6.31 payments/year (median 1.25). Recurring mechanics (per-superfan rate 12 — throughout, the “rate” is payments per superfan per year, “kef” in the Russian original) close that range structurally. The red team retracted one v0.2 number and replaced three point assumptions with ranges.
World A — a fixed pool of subscription money divided by a formula: pro-rata (Spotify), user-centric (SoundCloud), artist-centric (Deezer/UMG). The core theorem (Bergantiños & Moreno-Ternero, 2023): any stable rule divides a listener’s contribution only among the artists that listener actually played — an artist’s ceiling is set by their own audience under any formula. World B — money arrives on top of the subscription, directly: donations, recurring patronage, drops (Tonify — an attention economy on Telegram/TON rails; Unify — a global music layer, see §7). The question of this paper: by how many orders of magnitude the worlds differ, and under which measurable conditions World B outperforms World A.
The world: N=200,000 artists; the annual-stream distribution is a piecewise construction (lognormal body / log-bridge / Pareto tail α=1.4) fitted to the anchors: T1 87% of artists <1000 streams/year (Luminate) → obtained 87.0% ✓ T2 2.6% of artists >$1000/year in royalties (Spotify) → 2.6% ✓ T3 top 0.28% of artists ≈50% of streams (CMA/Last.fm) → 44.5% ✓; Gini 0.97 A listener’s plays for a given artist: lognormal(median 5.16; mean 21.21) [LFM-1b]. All parameters → sources: SOURCES.md; red team: CRITIC.md.
Minimum viable audience (MVA) for $100/mo:
Parameters: superfans at 0.6–1.7% of the audience; ticket size $3.1–6.9; artist share 0.80–0.95.
$300K MRR is not reached on donation commission alone: 1M MAU × 1.7% × rate 4 × $6.9 × 5% = $1,955 MRR (a 150× gap). It is reached at: 5M MAU × 5% paying × rate 12 × $6 × blended take 20%; or 10M × 4% × 12 × $5 × 15%. Corollary: the milestone requires recurring patronage and blended lines (drops/premium) — or a recalculation of the figure.
Retracted: “a status quo of 0.42 donations/year” (verbatim, translated) — a category error on SoundCloud’s 29%. Replaced with ranges: plays/listener 8–21 (the LFM-1b window ≠ a year), ticket size $3.1–6.9 (PWYW experiment: mean €3.10, refusal rises 24.4% vs 17.3%), superfans 0.6–1.7% (the 97-2-1 rule). Fixed: binomial superfans (fig2). Honest negative: at today’s payment frequency, direct loses to pro-rata independent.
Thesis: — Mechanics on top of Tonify: — What we measure first: —
A synthetic world: the tail shape between the anchors is a construction; UC is a wallet approximation; the rate, ticket size, and superfan share are unmeasured axes (“Object 3”, translated), to be measured by the MVP; the Tencent benchmark is a blend with advertising; the regulatory risk to gifting (−66% of TME segment revenue over 3 years) is not in the model. No conclusion is stated more strongly than its falsifier.
fig1 MVA curve · fig2 income distribution (binomial) · fig3 fraud dilution · fig4 the $1 rails · fig5 the World A→B ladder · fig6 MRR-solver
MIT License. Reproduction: python3 sim1/tonify_cash_sim.py && python3 sim1/v04_full.py
The split rule and the contract are orthogonal axes; previous versions conflated them. The full per-listener-year → MVA matrix (fig7): pro-rata signed $0.0064/listener-year → 188,590; pro-rata independent $0.0940 → 12,771; user-centric signed $0.0085 → 140,463; user-centric independent $0.1262 → 9,512; direct·360 (rate 4) → 4,577; direct independent (rate 4) → 3,204; recurring rate 12 TON → 900. The matrix’s headline conclusion: the contract outweighs the rule. The pro-rata→user-centric move yields ×1.34; the signed→independent move yields ×14.8. World A’s best formula does not compensate for the 6.8% label pass-through: user-centric signed (140,463) is worse than pro-rata independent (12,771). Reforming the rule without reforming the contract is a reshuffle one order of magnitude short of what is needed. Nature of the two multipliers (v1.1): the contract axis is a single measured pass-through (0.0003/0.00443 = 6.772%) applied to both rows — ×14.8 = 1/0.06772 is arithmetic by construction, not emergent; only ×1.34 has a Monte-Carlo origin, and it is valid only at the baseline wallet (u = 10,000, PAID_SHARE = 0.40): the rule effect flips sign at the listener-intensity crossover u* ≈ 14,146 plays/yr (8,731 at PAID_SHARE 0.25; 21,371 at 0.60) — above u*, user-centric is worse than pro-rata for that artist’s audience (fig14; sim1/SPEC.md §3.2). What the matrix contributes is commensurability: the two axes placed on one MVA grid.
An external reviewer landed seven hits on sim1; the verdicts and actions are recorded in sim1/SPEC.md CHANGELOG (accusation → verdict → action). Summary of what changed in this paper’s claims: (1) ×14.8 explicitly reclassified as arithmetic input inversion, not an emergent result (rank-one contract axis; the matrix’s value is commensurability); (2) the rule-effect scalar ×1.34 replaced by the crossover u* — the effect flips sign (at u = 20,000 user-centric needs 18,341 listeners vs pro-rata’s 12,771); new figure fig14 and script v06_uc_crossover.py; (3) hero communication leads with the full corner range 3,204…20,161 at k=4 (worst corner loses to the independent pool), standing rule added; (4) Twitch benchmark given on the aligned ticket (1,709 at $6.89 vs 2,353 at Twitch’s fixed $5) — the direct edge is the take rate (5% vs 50%), not the rail; (5) 3,204 → 900 decomposed: cadence ×3.0 (to 1,068 at take 0.80), TON rail ×1.19 (to 900); (6) sim1/SPEC.md created (model equations, measured/derived/assumed parameter classes — PAID_SHARE = 0.40 flagged as an unjustified assumption that linearly scales the UC answer; validation gates with tolerances and non-zero-exit FAIL; the T3 tolerance [40%; 55%] declared post-hoc with inter-source justification, relative miss to 50% is 11%); (7) figure byte-identity scoped to a single environment (stdout stays byte-identical across environments). Numbers of v0.5.1 unchanged; all new numbers (u*, 1,709, 1,068, 20,161) are derivatives of existing axes.
Input: the packaging red team found that the signed pool numbers diverged between the documents and the pixels of the figures. The engineer localized the cause.
Cause. In sim1/v05_matrix.py the label pass-through was set as the constant 0.068 —
a rounding of the derived quantity 0.0003/0.00443 = 0.06772. A rounding promoted to the
status of an input parameter silently redefined the anchor itself: 0.00443 × 0.068 =
0.00030124 ≠ 0.0003. Hence 187,814 on the figures against 188,590 in §3, RESULTS v0.2
and v04_full.py.
Decision (economist’s verdict). The measured anchor is primary — the signed artist’s per-stream take of $0.0003/stream. The 6.8% label pass-through is not a third parameter but the ratio of the two anchors ($0.0003 / $0.00443 = 6.772%), externally corroborated by the CNM estimate of ~6.8%; in the code it is now computed from them rather than entered as a number. The reverse logic (making 6.8% the input and the signed take the derived value) was rejected: it reduces the number of independent measurements from two to one and makes the 188,590 claim dependent on someone else’s rounding.
Number changes.
LABEL_PASS = 0.0677201 instead of 0.068 (one line in v05_matrix.py). The pool
numbers of all three scripts converged bit-for-bit; 188,590 from RESULTS v0.2 and §3
is preserved without edits.Process change. v05_matrix.py now carries an assert comparing the matrix’s pro-rata
signed MVA with the analytic 1200/(21.21 × 0.0003) of v04_full.py. The desync existed
because three scripts computed one quantity and none checked against the others; now an
anchor divergence fails the run.
Precision caveat. The $0.0003/stream anchor has one significant digit. All quantities derived from it (188,590, 140,463, ×14.8) are printed at run precision, not measurement precision; this is reproducibility of the calculation, not a claim about the precision of the world. The limitation — §9.