# r3-b1-17

**Claim (as registered):** Within any complete state, the distribution of holdings across institutions is heavy-tailed (not near-uniform, not a near-single-point monopoly): fitting a straight line to log(rank) vs log(count) over the ranked institutions gives a slope between -3.0 and -0.3, regardless of the state's overall concentration LEVEL (which itself varies roughly 60x across states).

**Proposed mechanism:** A shape/form claim about how collecting institutions accumulate holdings over time (consistent with a broad class of real-world accumulation processes that produce heavy-tailed distributions), deliberately independent of how concentrated any one state happens to be overall.

**Scope:** Source: NAMAMI (India), a state-facetted manuscript-holdings portal (holdings, not origin -- every record is held-by, not produced-by, the state). Training: 11 states with a complete portal walk (~4.22M records: Bihar, Himachal Pradesh, Karnataka, Kerala, Madhya Pradesh, Maharashtra, Odisha, Rajasthan, Tamil Nadu, Uttar Pradesh, West Bengal). Holdout: 9 more states/union territories walked to completion after this claim was fixed (Jammu & Kashmir, Assam, Haryana, Delhi, Manipur, Puducherry, Punjab, Uttarakhand, Jharkhand), each landed as a complete, reconciled count before testing. All data comes from one portal, so survival across states shows stability within this portal's own cataloguing practice, not independently of it.

**Training-side evidence:** Full-distribution ordinary-least-squares slopes (up to 500 ranked institutions per state) range from -0.567 (least steep) to -2.355 (steepest, on a state with only 196 institutions total), all inside [-3.0, -0.3], with R-squared mostly above 0.93.

**Holdout test and outcome:** Tested across all nine India holdout states/UTs; one state's distribution was a realized degenerate case -- exactly one holding institution for the entire territory, for which the slope is mathematically undefined (a single point has no line to fit) -- so that state was ruled outside this claim's scope (which presupposes at least two institutions) rather than counted as a pass or fail. An independent from-scratch re-derivation at a different holdout state (n=76 ranked institutions) reproduced a slope of -2.71318 (standard error 0.09967, R-squared 0.909), inside the registered band. Every other tested state's slope also stayed inside the band.

**Status:** Survived every state where a slope was defined.
