Liberata's Scientometrics Framework

• Liberata's scientometrics is a share-based framework that replaces traditional authorship order with contribution shares summing to unity, clearly encoding both rank and relative contribution.
• It integrates graph-based citation weighting with correction mechanisms to address field-size effects and self-citations, ensuring a more accurate measure of academic impact.
• The system establishes a marketplace for peer review and replication, directly linking quality control transactions to future impact and overall academic capital.

Searching arXiv for the cited Liberata and Scholia papers to ground the article in current arXiv metadata. {"^^^^^^^^5query5 OR ti:Scholia and scientometrics with Wikidata5^^^^^^^^", "^^^^^^^^5max_results5 5} {"^^^^^^^^5query5 -- Graph Scientometrics for a Share Based System of Academic Publishing\"", "^^^^^^^^5max_results5 5} Liberata's scientometrics denotes a share based framework for academic publishing and quality control in which authorship positions are replaced with contribution shares that sum to unity and encode both ordinality and relative contribution distances, while citations are weighted and corrected through graph-based constructions to derive academic capital and scientometrics for impact, risk, collaboration, collusion, value of quality control, and diversification (&&&^^^^5query5^^^^&&&). In a related but methodologically distinct line, Scholia provides a Wikidata-based infrastructure for scientometric profiling by ^^^^^^^^5query5 the Wikidata Query Service to assemble publication lists, publication and citation timelines, co-author networks, citation graphs, and LaTeX/BIBTeX bibliographies (&&&^^^^5au:Nielsen OR ti:Scholia and scientometrics with Wikidata5^^^^&&&).

^^^^5au:Nielsen OR ti:Scholia and scientometrics with Wikidata5^^^^. Share-based credit allocation

The framework begins from a share-based authorship model. For a manuscript PRESERVED_PLACEHOLDER_^^^^5query5^^^^ with contributor set PRESERVED_PLACEHOLDER_^^^^5au:Nielsen OR ti:Scholia and scientometrics with Wikidata5^^^^, each contributor receives a share PRESERVED_PLACEHOLDER_^^^^5max_results5^^^^, and the shares satisfy total-share normalization: PRESERVED_PLACEHOLDER_^^^^5query5^^^^ The shares encode both which author contributed more and by how much more, and they are fungible: two contributors with equal share on the same paper receive equal credit (&&&^^^^5query5^^^^&&&).

Academic-capital allocation on a single paper is defined as

PRESERVED_PLACEHOLDER_^^^^5ti:\5^^^^

where $w_m$ is the paper’s weighted-citation score. This couples contribution attribution directly to impact attribution. A plausible implication is that credit assignment is no longer mediated by author order alone, because the primitive quantity is the share $s_{m,c}$ rather than a discrete position in the byline.

The framework is explicitly motivated by the claim that contemporary scientometric indicators remain anchored in paradigms and axioms from when academic research was conducted in small scholarly communities, whereas current academia is organized in large communities with high rates of information incompleteness regarding work impact and individual contributions (&&&^^^^5query5^^^^&&&). It further argues that traditional metrics force discretization of credit to authors and prior works despite their fundamentally continuous nature. This suggests that Liberata’s scientometrics is intended as a reparameterization of scientometric accounting, with continuity in both authorship and citation flow.

^^^^5max_results5^^^^. Quality control as a marketplace for shares

Liberata supports two open markets—peer review and replication—in which authors sell a fraction of their shares to quality controllers in exchange for expected increases in long-run impact (&&&^^^^5query5^^^^&&&). In the peer-review marketplace, authors submit a pre-review manuscript $m$ with share vector $\{s_{m,a}\}_{a\in A_m}$, and they propose post-review shares $\{s_{m',a}\}$ and reviewer shares PRESERVED_PLACEHOLDER_^^^^5au:Nielsen OR ti:Scholia and scientometrics with Wikidata5query5^^^^.

A transaction occurs iff authors expect net benefit: PRESERVED_PLACEHOLDER_^^^^5au:Nielsen OR ti:Scholia and scientometrics with Wikidata5au:Nielsen OR ti:Scholia and scientometrics with Wikidata5^^^^ A reviewer PRESERVED_PLACEHOLDER_^^^^5au:Nielsen OR ti:Scholia and scientometrics with Wikidata5max_results5^^^^ accepts a bid PRESERVED_PLACEHOLDER_^^^^5au:Nielsen OR ti:Scholia and scientometrics with Wikidata5query5^^^^ if the time PRESERVED_PLACEHOLDER_^^^^5au:Nielsen OR ti:Scholia and scientometrics with Wikidata5ti:\5^^^^ for review is less than PRESERVED_PLACEHOLDER_^^^^5au:Nielsen OR ti:Scholia and scientometrics with Wikidata55^^^^ times the time to produce an original paper of similar expected impact: PRESERVED_PLACEHOLDER_^^^^5au:Nielsen OR ti:Scholia and scientometrics with Wikidata5^^^^6

The replication marketplace is defined analogously. Replicators PRESERVED_PLACEHOLDER_^^^^5au:Nielsen OR ti:Scholia and scientometrics with Wikidata5^^^^7 trade shares PRESERVED_PLACEHOLDER_^^^^5au:Nielsen OR ti:Scholia and scientometrics with Wikidata5^^^^8 for expectations of higher impact PRESERVED_PLACEHOLDER_^^^^5au:Nielsen OR ti:Scholia and scientometrics with Wikidata5^^^^9, and they compare their own time cost through

PRESERVED_PLACEHOLDER_^^^^5max_results5query5^^^^

Within the formalism, peer review and replication are not external certification mechanisms; they are integrated into the same share ledger as authorship. This suggests that quality control is treated as a tradable contribution category rather than a separate administrative layer.

^^^^5query5^^^^. Weighted citations and correction factors

Liberata distinguishes unweighted citation count from weighted citation. The unweighted count for a manuscript PRESERVED_PLACEHOLDER_^^^^5max_results5au:Nielsen OR ti:Scholia and scientometrics with Wikidata5^^^^ is

PRESERVED_PLACEHOLDER_^^^^5max_results5max_results5^^^^

The default weighted citation score normalizes each incoming citation by the citing paper’s reference-list length: PRESERVED_PLACEHOLDER_^^^^5max_results5query5^^^^ Under this rule, each paper can print at most one unit of citation (&&&^^^^5query5^^^^&&&).

Two correction mechanisms are then introduced. First, publication-rate normalization corrects field-size effects by dividing by the per-author publication rate PRESERVED_PLACEHOLDER_^^^^5max_results5ti:\5^^^^ of the paper’s field PRESERVED_PLACEHOLDER_^^^^5max_results55^^^^: PRESERVED_PLACEHOLDER_^^^^5max_results5^^^^6 Second, an author-similarity discount suppresses self-citations. If PRESERVED_PLACEHOLDER_^^^^5max_results5^^^^7 is the cosine-similarity of the two papers’ author-share vectors, then each citation is discounted by PRESERVED_PLACEHOLDER_^^^^5max_results5^^^^8: PRESERVED_PLACEHOLDER_^^^^5max_results5^^^^9

The abstract states that citations are weighted to guard against frivolous referencing and credit inflation, and that modular correction factors allow multiple measures of impact (&&&^^^^5query5^^^^&&&). In that sense, the weighting rule is not merely a normalization device; it is part of the framework’s quality-control logic. A plausible implication is that the scientometric unit being propagated is not a raw citation event but a bounded and optionally corrected transfer of academic capital.

^^^^5ti:\5^^^^. Graph-theoretic structure and academic capital

The system is formalized through two fundamental graphs, Shares and References, and from them constructs academic capital (&&&^^^^5query5^^^^&&&).

Graph	Structure	Function
Shares graph PRESERVED_PLACEHOLDER_^^^^5query5query5^^^^	Bipartite, undirected, node set PRESERVED_PLACEHOLDER_^^^^5query5au:Nielsen OR ti:Scholia and scientometrics with Wikidata5^^^^	Encodes contribution shares
References graph PRESERVED_PLACEHOLDER_^^^^5query5max_results5^^^^	Directed DAG on manuscript nodes PRESERVED_PLACEHOLDER_^^^^5query5query5^^^^	Encodes weighted citation flow
Capital graph PRESERVED_PLACEHOLDER_^^^^5query5ti:\5^^^^	Composition of PRESERVED_PLACEHOLDER_^^^^5query55^^^^ and PRESERVED_PLACEHOLDER_^^^^5query5^^^^6	Records PRESERVED_PLACEHOLDER_^^^^5query5^^^^7

The Shares graph PRESERVED_PLACEHOLDER_^^^^5query5^^^^8 has node set PRESERVED_PLACEHOLDER_^^^^5query5^^^^9, where PRESERVED_PLACEHOLDER_^^^^5ti:\5query5^^^^ consists of authors, reviewers, and replicators, and PRESERVED_PLACEHOLDER_^^^^5ti:\5au:Nielsen OR ti:Scholia and scientometrics with Wikidata5^^^^ is the set of manuscripts. Its edge set is

PRESERVED_PLACEHOLDER_^^^^5ti:\5max_results5^^^^

with weight function PRESERVED_PLACEHOLDER_^^^^5ti:\5query5^^^^. By construction,

PRESERVED_PLACEHOLDER_^^^^5ti:\5ti:\5^^^^

for each manuscript PRESERVED_PLACEHOLDER_^^^^5ti:\55^^^^. In expanded matrix form,

PRESERVED_PLACEHOLDER_^^^^5ti:\5^^^^6

The References graph PRESERVED_PLACEHOLDER_^^^^5ti:\5^^^^7 is a directed DAG on manuscript nodes. An edge PRESERVED_PLACEHOLDER_^^^^5ti:\5^^^^8 exists if PRESERVED_PLACEHOLDER_^^^^5ti:\5^^^^9 cites $w_m$^^^^5query5^^^^, weighted by $w_m$^^^^5au:Nielsen OR ti:Scholia and scientometrics with Wikidata5^^^^, typically $w_m$^^^^5max_results5^^^^. Its adjacency matrix $w_m$^^^^5query5^^^^ satisfies $w_m$^^^^5ti:\5^^^^ if $w_m$5.

The capital graph $w_m$6 is obtained by composition of $w_m$7 and $w_m$8. If

$w_m$9

is the vector of paper capitals, then in condensed form

$s_{m,c}$^^^^5query5^^^^

with $s_{m,c}$^^^^5au:Nielsen OR ti:Scholia and scientometrics with Wikidata5^^^^. Full $s_{m,c}$^^^^5max_results5^^^^ reconstructs like $s_{m,c}$^^^^5query5^^^^. This construction makes the relationship between citation flow and contributor-level allocation explicit: manuscript-level weighted impact is first computed on $s_{m,c}$^^^^5ti:\5^^^^, then allocated across contributors through $s_{m,c}$5.

5. Scientometric measures derived from portfolios

The framework defines scientometric measures on portfolios $s_{m,c}$6, where a portfolio is a set of shares on papers $s_{m,c}$7 by contributors $s_{m,c}$8 (&&&^^^^5query5^^^^&&&). Total academic capital is

$s_{m,c}$9

Return over $m$^^^^5query5^^^^ is

$m$^^^^5au:Nielsen OR ti:Scholia and scientometrics with Wikidata5^^^^

Risk asymmetry is measured by skewness,

$m$^^^^5max_results5^^^^

the Sharpe-style ratio is

$m$^^^^5query5^^^^

and academic-returns-to-capital is

$m$^^^^5ti:\5^^^^

Allocation concentration is expressed through three statistics. With weights $m$5, the Herfindahl–Hirschman index is

$m$6

the Gini coefficient is

$m$7

and normalized entropy is

$m$8

Diversification is measured by

$m$9

Collaboration and collusion indicators are derived from the two-step shares graph $\{s_{m,a}\}_{a\in A_m}$^^^^5query5^^^^. The block

$\{s_{m,a}\}_{a\in A_m}$^^^^5au:Nielsen OR ti:Scholia and scientometrics with Wikidata5^^^^

measures co-authorship intensity, while excessively large off-diagonal entries in the author–reviewer subblock $\{s_{m,a}\}_{a\in A_m}$^^^^5max_results5^^^^ may flag collusion. The framework also defines a fair market price for peer review in field $\{s_{m,a}\}_{a\in A_m}$^^^^5query5^^^^, $\{s_{m,a}\}_{a\in A_m}$^^^^5ti:\5^^^^, and a review-risk premium for author group $\{s_{m,a}\}_{a\in A_m}$5,

$\{s_{m,a}\}_{a\in A_m}$6

with analogous definitions for replication. These constructions broaden scientometrics beyond impact measurement alone by placing risk, concentration, diversification, and quality-control pricing inside the same accounting system.

6. Aggregation, field structure, and Wikidata-based operationalization

The framework extends naturally to aggregates such as institutions, regions, time periods, and research fields (&&&^^^^5query5^^^^&&&). A portfolio $\{s_{m,a}\}_{a\in A_m}$7 collects shares $\{s_{m,a}\}_{a\in A_m}$8 with $\{s_{m,a}\}_{a\in A_m}$9 and $\{s_{m',a}\}$^^^^5query5^^^^. Choosing $\{s_{m',a}\}$^^^^5au:Nielsen OR ti:Scholia and scientometrics with Wikidata5^^^^ as all papers from an institution and $\{s_{m',a}\}$^^^^5max_results5^^^^ as its members yields the institution’s total academic capital, risk, concentration, and related measures. For a region $\{s_{m',a}\}$^^^^5query5^^^^, total capital is

$\{s_{m',a}\}$^^^^5ti:\5^^^^

and per-capita or per-GDP measures and their Gini indices can be formed in the same way.

Field-level metrics use a ^^^^5ti:\5^^^^D taxonomy $\{s_{m',a}\}$5 described as domain $\{s_{m',a}\}$6 department $\{s_{m',a}\}$7 discipline $\{s_{m',a}\}$8 direction. Field-normalized returns are formed by dividing by $\{s_{m',a}\}$9, and field-tag allocation weights

PRESERVED_PLACEHOLDER_^^^^5au:Nielsen OR ti:Scholia and scientometrics with Wikidata5query5query5^^^^

allow HHI and Gini at each level. A journal is defined simply as the collection of papers carrying a given set of PRESERVED_PLACEHOLDER_^^^^5au:Nielsen OR ti:Scholia and scientometrics with Wikidata5query5au:Nielsen OR ti:Scholia and scientometrics with Wikidata5^^^^ tags, and its impact becomes average paper capital: PRESERVED_PLACEHOLDER_^^^^5au:Nielsen OR ti:Scholia and scientometrics with Wikidata5query5max_results5^^^^

A distinct operational route to scientometric profiling is provided by Scholia. Scholia is implemented in Python with the Flask framework and exposes aspects such as author, work, and organization by embedding live SPARQL queries against the Wikidata Query Service; the front-end uses HTML iframes for each panel, each iframe points to a WDQS HTTP endpoint, and the Python package builds and injects SPARQL strings, sends them to https://^^^^^^^^5query5^^^^^^^^.wikidata.org/sparql, and handles the returned JSON to produce visualizations or downloadables such as BibTeX (&&&^^^^5au:Nielsen OR ti:Scholia and scientometrics with Wikidata5^^^^&&&). For a researcher such as Liberata, the documented queries include total publications per year, co-author network data, citations per year to all works, overall citation-graph edges, and citation-count retrieval for client-side computation of the h-index, g-index, and i^^^^5au:Nielsen OR ti:Scholia and scientometrics with Wikidata5query5^^^^-index.

The sample interpretations are explicit. Publications per year are visualized as a bar chart for productivity trend; the co-author network uses node size proportional to total collaborations and edge width proportional to number of co-authored papers; citations per year appear as a line chart for impact over time, with cumulative citations as a second line; and the h-index is presented as a single-number summary of both productivity and impact, while the g-index gives more weight to highly-cited papers and is often greater than PRESERVED_PLACEHOLDER_^^^^5au:Nielsen OR ti:Scholia and scientometrics with Wikidata5query5query5^^^^, and the i^^^^5au:Nielsen OR ti:Scholia and scientometrics with Wikidata5query5^^^^-index counts moderately-cited works with at least ^^^^5au:Nielsen OR ti:Scholia and scientometrics with Wikidata5query5^^^^ citations (&&&^^^^5au:Nielsen OR ti:Scholia and scientometrics with Wikidata5^^^^&&&). Scholia also supports BibTeX generation through python -m scholia.tex write-bib-from-aux example.aux, allowing \cite{Q^^^^5au:Nielsen OR ti:Scholia and scientometrics with Wikidata5max_results5query5ti:\55^^^^678} or \cite{^^^^5au:Nielsen OR ti:Scholia and scientometrics with Wikidata5query5^^^^.^^^^5au:Nielsen OR ti:Scholia and scientometrics with Wikidata5query5query5query5^^^^/xyzdoi} in LaTeX and resolution to the Wikidata item matching that DOI.

Taken together, these two lines of work occupy different levels of abstraction. Liberata’s scientometrics specifies a graph-based accounting and marketplace framework for credit, impact, and quality control, whereas Scholia specifies a Wikidata-centric infrastructure for ^^^^^^^^5query5 formatting, and visualizing scholarly metadata. This suggests a practical distinction between a formal scientometric model and an implementation substrate for scientometric profiles.