Shuichiro Ogawa
日本語

Notes · updated 2026-07-19

If Light Is a Particle, Matter Must Be a Wave

Sometimes only the correct shape of the question is fixed before the evidence arrives.

In 1924, de Broglie’s doctoral thesis predicted the existence of a phenomenon no one had yet measured. Light had long been believed to be a wave, but the physics of the time already granted that it behaved as a particle (the light quantum) as well. Only one side was granted. If so, he wrote, then matter, long believed to be particulate, must also behave as a wave1. He closed the symmetry with a single equation: a particle of momentum p carries a wavelength λ. Not one experiment yet backed it.

Three years later, the prediction was confirmed without being aimed at. Davisson and Germer, in the middle of a different experiment firing electrons at a nickel crystal, saw electrons draw the same diffraction pattern as X-rays2. Electrons were interfering as waves. A symmetry closed by inverting a one-sided asymmetry was filled in afterward by measurement. This is not an isolated anecdote. Physics keeps, as a heuristic for building theory, the practice of taking symmetry and its breaking as a clue3.

What happens if this move is carried straight into how science measures itself? The sister note ai-capability-relational-ontology applied this same heuristic to the ontology of evaluation, deriving the inversion that measurement raises capability into being. As an adjacent method, ai-research-gaps-abduction shows the pattern of finding a field’s gaps by inverting its premises. This note applies the same heuristic to how science and its meta-science count knowledge. The method runs as follows. Take one asymmetry that science’s self-measurement grants on only one side, and invert it to close the symmetry. The blind spot lies on the side left unclosed.

The Asymmetry Science Grants on Only One Side

First, write out precisely the side that is granted.

Science and its meta-science, that is scientometrics, the quantitative study of science, measure the production of knowledge. How many papers appeared, how many times they were cited, what a researcher’s h-index is, how many patents were granted. When Garfield proposed citation indexing in 19554 and Hirsch introduced the h-index in 20055, what both counted was the output side. The h-index means holding h papers each cited at least h times, an index of cumulative output. A field’s progress is mapped as this quantity of production.

Against this, the loss of knowledge is not counted as a process. Facts once known and then forgotten, findings that keep being cited after retraction, methods once established and then no longer used, problems that became unsolvable when a paradigm shifted. These are treated not as processes with their own mechanisms, like production, but as accidents, errors, or noise. The story of progress has no column for counting loss.

This asymmetry is isomorphic to the premise classical physics placed on particles. Classical physics held that a particle carries position and momentum as values fixed in advance, and that measurement merely reads those values off. Scientometrics holds that knowledge is produced and accumulates, and that progress is the piling up. Neither posits the symmetric other side. As a wave accompanies the particle, loss accompanies production. The instrument that measures progress does not count that companion.

Here is a side not yet inverted.

Manufactured Ignorance as the Light Quantum

That one side is already shown was the entry point of de Broglie’s move. This note, too, has a precedent that corresponds to it.

The volume Agnotology, edited by Proctor and Schiebinger in 2008, took ignorance as its subject6. What they showed is one point: ignorance is not a mere absence or blank in knowledge but something actively produced. Proctor writes in the introduction that ignorance should be seen not as a simple omission or gap but as an active production, one that can be engineered as part of a deliberate plan. The history of the tobacco industry manufacturing doubt about the causal link between smoking and disease was the prototype. Ignorance has ways of being made, and Proctor sorted them into three types: ignorance as native state, ignorance as selective inattention, and ignorance as strategically engineered construct.

This corresponds to the “light quantum.” The proposition that ignorance is actively made shows, on one side, that the vanishing of knowledge is a process. But agnotology does not close the symmetry. Its subject is mainly ignorance produced with intent, ignorance as a product of politics and power. The step of formalizing loss as a general process dual to discovery, and moreover one carrying a measurable rate, is not there7. A successor in ignorance studies, the Routledge International Handbook of Ignorance Studies edited by Gross and McGoey, also maps the social and strategic production of ignorance across disciplines, but presents no conservation-law framework binding production and loss into a single ledger8.

One side is shown. Invert it, and the symmetry closes.

Inverted, Loss Becomes the Dual of Discovery

Invert it.

Where is the principled reason to privilege only production as a process and to regard loss as accident or noise? Production and loss are both flows that change a field’s knowledge stock. With the same standing by which discovery brings a fact that was not yet known into the circle of active use, loss drops a fact that was known out of that circle. If so, there is no ground for treating only discovery as a process and regarding loss as a “failure of discovery” or as “noise.” Loss conditions a field’s knowledge with the same standing as discovery.

From this step follows a consequence that dismounts the naive view of progress. A field’s knowledge is not the piling up of production. It is the ledger of production and loss. What is denied here is not the proposition that “the phrase ‘knowledge accumulates’ is meaningless.” What is denied is the proposition that “a field’s knowledge stock can be approximated by the total of production alone.” The stock of knowledge becomes a quantity conserved not like mass but fixed by the difference of income and expenditure. We are measuring only one side. [evidence level: author's conjecture]

And if loss is the dual of discovery, then as discovery has a rate, loss has a rate too. If the discovery rate is the speed at which not-yet-known knowledge enters active use, its dual is the undiscovery rate, the speed at which established knowledge drops out of active use. This has the same shape as de Broglie’s move. It inverts the “only production makes progress” that science’s self-measurement grants on one side, and closes the symmetry. What appears on the far side is a picture that treats production and loss as a single ledger, with the loss rate set on the expenditure side as a measurable quantity.

Why This Blind Spot Is Structurally Invisible

Granting that the inversion is correct, why does the mainstream overlook it? The reason is not that researchers lack attention. It is that the very instrument measuring progress renders this inversion structurally invisible.

The metrics of scientometrics all count the production side. Paper counts, citations, the h-index, patent counts each tally the accumulation of output. These instruments have no column to record something dropping out of active use. That citations decline is measurable, but a framework for reading declining citations as “the advance of a process called loss” lies outside the design specification of the instrument. From inside a tool that counts only production, the structure of loss is in principle hard to see.

As Kuhn showed, during normal science researchers assume the paradigm is correct and refine details, without questioning the framework itself9. A progress metric wears, before it measures, the ontology that “knowledge accumulates.” The question that doubts that ontology lies outside the instrument’s design specification. This structure is exactly what makes the blind spot a blind spot. [evidence level: author's conjecture]

Scattered Phenomena Bind into One Ledger

Whether the inversion is productive is decided by what it binds. The picture that sees loss as the dual of discovery gathers, under a single ledger, phenomena that have been handled separately.

First, the half-life of facts. What Poynard and colleagues reported in the Annals of Internal Medicine in 2002 was a measurement: the median duration for which clinical conclusions in hepatology remain true, the so-called half-life of truth, was about 45 years10. As of 2000, of conclusions from 1945 onward, 60% remained true, 19% had become obsolete, and 21% false. Arbesman, in The Half-Life of Facts (2012), argued that this kind of decay occurs at predictable rates across fields11. The mainstream sees this as natural updating, a replacement by newer facts. Inverted, this speed at which established facts drop out of active use becomes precisely one cross-section of the undiscovery rate.

Second, the obsolescence of literature. Burton and Kebler argued in 1960 that the use of scientific and technical literature ages at a rate resembling the half-life of radioactive decay12. The literature obsolescence rate, the cited half-life of Journal Citation Reports, institutionalizes this idea as an index. This too is one cross-section of the speed of loss, yet the mainstream treats it as a tool for collection planning, not read as the expenditure side of a progress ledger.

Third, the persistence of retracted findings. Retraction is the operation of removing knowledge judged erroneous from active use. But that removal does not complete. Of 238 citing contexts examined by Bar-Ilan and Halevi in 2017, 83% cited retracted papers positively13. Of 13,252 post-retraction citing contexts examined by Hsiao and Schneider in biomedicine in 2022, only 5.4% acknowledged the retraction14. The mainstream sees this as a problem of citation hygiene, a procedural failure to be corrected. Inverted, this becomes a measurable failure of undiscovery. The speed at which findings that ought to be removed fail to drop fully out of active use is a quantity testable as the reverse face of the loss rate. [evidence level: circumstantial]

Fourth, the loss accompanying paradigm change. Kuhn argued that a paradigm shift carries a loss that makes the problems the old paradigm solved unsolvable (cited above9). Post named this phenomenon Kuhn-loss in 197115. The mainstream view of progress narrates the shift as advance and does not count the explanatory power lost behind it. Inverted, Kuhn-loss lines up, under the same ledger as the half-life of facts and retraction persistence, as one cross-section of the process of loss with a distinct mechanism.

Fifth, independent rediscovery. Merton argued in 1961 that scientific discovery is in principle multiple16, and Ogburn and Thomas in 1922 counted some 148 cases in which independent parties arrived at the same invention17. Arriving independently at the same knowledge twice can imply that the first instance was not within the reach of usable knowledge for the second party, that is, that it had been lost. The mainstream treats this as the sociology of discovery, a matter of priority. Inverted, the frequency of rediscovery becomes a trace that loss occurred, an indirect handle on the loss rate. [evidence level: author's conjecture]

These five the mainstream has handled separately, as distinct problems. Updating of facts, obsolescence of collections, citation hygiene, paradigm advance, disputes over priority. Inverted, they become cross-sections, with distinct mechanisms, of one process. And the logic that binds the five reduces to one. If a field’s knowledge is the ledger of production and loss, these are all entries on the expenditure side. [evidence level: circumstantial]

Stating a Falsifiable Prediction

So far this is talk of a picture, and as such it cannot be falsified. De Broglie’s move could be science because it carried a falsifiable prediction, electron diffraction. The picture of a production-and-loss ledger, to earn the same standing, must predict something that a production-only view of progress cannot in principle explain.

That prediction can be written as two measurable quantities.

First, a measurable undiscovery rate. Measure, on the same footing as the production rate, the speed at which established knowledge drops out of active use. Merge the half-life of facts, the literature obsolescence rate, the retraction persistence rate, Kuhn-loss, and rediscovery frequency not as disparate phenomena but as estimators of one loss flow. If a production-only view of progress is correct, these are mutually unrelated noise, and binding them into one flow should yield no convergent signal. If, on binding them, a stable loss rate paired with the production rate can be estimated, the ledger picture is supported.

Second, a loss-adjusted progress metric. Formalize a field’s net progress as the ledger of production minus loss. Increases in paper counts or citations are entries on the production side only. The net after subtracting established knowledge lost in the same period is the actual advance. If a production-only view of progress is correct, subtracting loss should change neither a field’s ranking nor the story of its progress. If, on subtracting it, a systematic difference appears, a field that advanced on production metrics turning out to stagnate on the net, the ledger picture is supported. [evidence level: author's conjecture]

And the persistence of retracted findings is the cross-section within this ledger that can be tested most directly. Retraction is the execution of the operation of loss. That the operation does not complete, that positive citations continue after retraction, is observable as a measurable failure of the loss flow that drops findings out of active use. The higher the persistence rate, the less the field’s loss mechanism is working. This is the most well-grounded entry point of the test corresponding to electron diffraction.

Where the Novelty Is, and Where It Is Not

The more attractive the inversion looks, the more strictly the boundary with prior art must be drawn. Much of this note’s claim already exists in part.

The view that grasps loss as active production already exists. That agnotology showed ignorance as an active product (cited above6) is the core of it. But it mainly discusses ignorance produced with intent, and does not extend loss into a general process carrying a rate.

Work measuring the decay of knowledge as a rate already exists. What Candia and colleagues showed in Nature Human Behaviour in 2019 was a universal law: collective attention to papers, patents, and cultural products decays biexponentially, in two phases of communicative and cultural memory18. This is the strongest extant formalization measuring the speed at which knowledge drops out of active use. So writing that “loss has never been measured” would be immediately refuted by this study. But Candia and colleagues’ object is the decay of attention and memory, and they do not tie it to a production ledger.

Work formalizing the dynamics by which knowledge value changes over time already exists. The Sleeping Beauties formalized by van Raan in 2004, papers long uncited that later awaken19, and the beauty coefficient introduced by Ke and colleagues in PNAS in 201520 treat the temporal dynamics of knowledge value as a coefficient. But these measure a one-directional delay, awakening, not a ledger of loss and production.

Stagnation in which large fields ossify and new entry is blocked already exists. What Chu and Evans showed in PNAS in 2021 was a phenomenon: the larger the field, the more the canon crystallizes and new ideas struggle to win field-wide attention21. This carries a flavor of loss, but it is not knowledge leaving active use; it is entry-side stagnation in which new knowledge becomes harder to bring in.

The idea of a ledger treating the knowledge stock as production minus loss is, in fact, not entirely blank. The civilizational knowledge model Dolgonosov presented in 2020 writes active knowledge as the equilibrium of production rate minus loss rate in a differential equation, explicitly incorporating energy dissipation in knowledge production and direct loss of knowledge22. So writing that “no one has ever considered a production-and-loss ledger” would be refuted by this study. But this is a macro-model of civilization and climate change, not a formalization as a scientometric metric measuring the progress of scientific knowledge.

Given all this, this note’s novelty is strictly limited to the following three points.

First, symmetrization. Agnotology, which sees loss as an active process, Candia and colleagues, who measure decay as a rate, and Dolgonosov, who models a ledger, each showed one side or an adjacent case, but a formalization that symmetrizes loss as the structural dual of discovery, and moreover sets it on the same footing as the production metrics of scientometrics, is not found within the confirmed range. Second, formalization of a metric. Merge scattered loss phenomena into one undiscovery rate, and set up a loss-adjusted progress metric that subtracts loss from production, as a measurable quantity of meta-science. The term “undiscovery rate” was not found as an existing term of art within the searched range23. Third, binding. Bind the scattered phenomena, the half-life of facts, the obsolescence of literature, retraction persistence, Kuhn-loss, and independent rediscovery, under the single picture of a production-and-loss ledger.

And these three points are not established facts. They are a falsifiable hypothesis awaiting the confirming experiments of whether the undiscovery rate converges as a single flow and whether the loss-adjusted metric systematically diverges from production metrics. [evidence level: author's conjecture]

One Question Left Open

De Broglie’s symmetry closed with electron diffraction. This note’s symmetry has not yet closed.

Cross-sections of loss, the half-life of facts, retraction persistence, are already measured individually. They should merge into one loss rate paired with production, the symmetry says. But saying and showing are different. Which phenomena may be summed as cross-sections of the same flow, on what basis the judgment that something has dropped out of active use is made, and whether it is legitimate to bind losses of differing mechanism, like Kuhn-loss, into a single rate, lie beyond this note’s reach.

One question remains. Suppose the loss rate can be measured and a field’s net progress written as production minus loss; the instrument that measures that ledger is itself built on the production side. How does a tool that counts loss count its own miscounts? As retraction does not complete, the measurement of loss too may not complete. Where that residue stops, or whether it stops, has not yet been measured.

  • subtractive-creativity-design — A sister note treating the opposite side of production (subtracting, erasing, losing) as a first-class operation of creation. It attempts, on the side of creation, the same move by which this note sets the vanishing of knowledge as the dual of discovery.

References

Sources of the method, and works whose existence was confirmed as evidence for each claim, with DOI/URL. Items with unconfirmed bibliographic details or unreached full text are marked [primary-source verification needed].

Method (symmetry completion as a heuristic)

  • de Broglie, L. (1924). Recherches sur la théorie des quanta. Doctoral thesis, Faculty of Sciences, University of Paris. (Direct access to the original PDF is [primary-source verification needed]; framing and defense date confirmed across secondary sources.)
  • Davisson, C. & Germer, L. H. (1927). Diffraction of Electrons by a Crystal of Nickel. Physical Review 30(6), 705–740. https://doi.org/10.1103/PhysRev.30.705
  • Stanford Encyclopedia of Philosophy. Symmetry and Symmetry Breaking. https://plato.stanford.edu/entries/symmetry-breaking/
  • Kuhn, T. S. (1962). The Structure of Scientific Revolutions. University of Chicago Press.

Loss shown on one side (agnotology) and production metrics

  • Proctor, R. N. & Schiebinger, L. (eds.) (2008). Agnotology: The Making and Unmaking of Ignorance. Stanford University Press. ISBN 978-0-8047-5901-4.
  • Gross, M. & McGoey, L. (eds.) (2015). Routledge International Handbook of Ignorance Studies. Routledge. ISBN 9780415718967.
  • Garfield, E. (1955). Citation Indexes for Science. Science 122(3159), 108–111. https://doi.org/10.1126/science.122.3159.108
  • Hirsch, J. E. (2005). An index to quantify an individual’s scientific research output. PNAS 102(46), 16569–16572. https://doi.org/10.1073/pnas.0507655102

Scattered phenomena bound by the ledger (cross-sections of loss)

  • Poynard, T. et al. (2002). Truth survival in clinical research: an evidence-based requiem? Annals of Internal Medicine 136(12), 888–895. https://doi.org/10.7326/0003-4819-136-12-200206180-00010
  • Arbesman, S. (2012). The Half-Life of Facts. Current (Penguin). ISBN 9781591844723.
  • Burton, R. E. & Kebler, R. W. (1960). The “half-life” of some scientific and technical literatures. American Documentation 11(1), 18–22. https://doi.org/10.1002/asi.5090110105
  • Bar-Ilan, J. & Halevi, G. (2017). Post retraction citations in context: a case study. Scientometrics 113(1), 547–565. https://doi.org/10.1007/s11192-017-2242-0
  • Hsiao, T.-K. & Schneider, J. (2022). Continued use of retracted papers. Quantitative Science Studies 2(4), 1144–1169. https://doi.org/10.1162/qss_a_00155
  • Post, H. R. (1971). Correspondence, Invariance and Heuristics. Studies in History and Philosophy of Science Part A 2(3), 213–255. https://doi.org/10.1016/0039-3681(71)90042-2
  • Merton, R. K. (1961). Singletons and Multiples in Scientific Discovery. Proceedings of the American Philosophical Society 105(5), 470–486.
  • Ogburn, W. F. & Thomas, D. (1922). Are Inventions Inevitable? Political Science Quarterly 37(1), 83–98. https://doi.org/10.2307/2142320

Limiting the novelty (boundary with prior art)

Items needing primary verification ([primary-source verification needed])

Items with unconfirmed bibliographic details or unreached full text, gathered here.

  • Direct access to the original de Broglie (1924) PDF (PSL Bibnum facsimile); framing and defense date confirmed across secondary sources.
  • Exhaustive search of the whole Agnotology volume beyond the introduction for rate / symmetry / conservation (the introduction PDF shows no technical usage).
  • The internal treatment of a loss rate or symmetry in Gross & McGoey (2015) (judgment based on scope; full-text search unreached).
  • A primary definition of the cited half-life index attributed to Burton & Kebler (1960) (attribution contested by Száva-Kováts 2002).
  • The first-online year of Hsiao & Schneider (2021 and 2022 both appear; the issue of record is 2022).
  • The primary passage where Post (1971) himself introduces the term “Kuhn-loss” (the attribution is widely repeated secondarily).
  • Full-text details of Dolgonosov (2020) (access centered on the abstract).
  • The absence of any prior use of “undiscovery” / “undiscovery rate” as a defined term of art (an absence based on search, not a proof of non-existence).

Footnotes

  1. de Broglie, L. (1924). Recherches sur la théorie des quanta. Doctoral thesis, Faculty of Sciences, University of Paris, defended 25 November 1924 (jury president J. Perrin). Extended the wave–particle duality of light to matter and gave the relation linking momentum and wavelength. Direct access to the PSL Bibnum facsimile of the original is [primary-source verification needed] (the framing and defense date are consistent across secondary sources). ↩

  2. Davisson, C. & Germer, L. H. (1927). Diffraction of Electrons by a Crystal of Nickel. Physical Review 30(6), 705–740. https://doi.org/10.1103/PhysRev.30.705 Demonstrated electron diffraction, confirming (initially unintentionally) de Broglie’s matter-wave hypothesis. ↩

  3. Stanford Encyclopedia of Philosophy, “Symmetry and Symmetry Breaking.” https://plato.stanford.edu/entries/symmetry-breaking/ An overview of symmetry functioning as a heuristic in theory construction. ↩

  4. Garfield, E. (1955). Citation Indexes for Science. Science 122(3159), 108–111. https://doi.org/10.1126/science.122.3159.108 Proposed citation indexing, making visible the accumulation of links among documents. ↩

  5. Hirsch, J. E. (2005). An index to quantify an individual’s scientific research output. PNAS 102(46), 16569–16572. https://doi.org/10.1073/pnas.0507655102 Collapses research output into a single number by holding h papers each cited at least h times. ↩

  6. Proctor, R. N. & Schiebinger, L. (eds.) (2008). Agnotology: The Making and Unmaking of Ignorance. Stanford University Press. ISBN 978-0-8047-5901-4. Introduction: “Agnotology: A Missing Term to Describe the Cultural Production of Ignorance (and Its Study).” Treats ignorance as active production and sorts it into three types. ↩ ↩2

  7. A search of the introduction finds no technical usage corresponding to rate / symmetry / conservation / measurable. Ignorance is discussed qualitatively as something “actively made,” with no formalization of a rate and no conservation-style symmetrization (access is via the introduction PDF; an exhaustive search of the whole volume is [primary-source verification needed]). ↩

  8. Gross, M. & McGoey, L. (eds.) (2015). Routledge International Handbook of Ignorance Studies. Routledge. ISBN 9780415718967 (2nd ed. 2022, ISBN 9780367608149). Treats the political and social uses of ignorance across disciplines; presents no measurable loss rate or conservation-style framework (judgment based on scope, [primary-source verification needed]). ↩

  9. Kuhn, T. S. (1962). The Structure of Scientific Revolutions. University of Chicago Press. That normal science takes the paradigm as given, refining details without questioning the framework. Kuhn also argued that revolutions are “destructive as well as constructive,” noting the loss of explanatory power accompanying paradigm change (later called Kuhn-loss). ↩ ↩2

  10. Poynard, T. et al. (2002). Truth survival in clinical research: an evidence-based requiem? Annals of Internal Medicine 136(12), 888–895. https://doi.org/10.7326/0003-4819-136-12-200206180-00010 Measured the “half-life of truth” of hepatology conclusions at about 45 years. Methodologically robust conclusions showed no clear survival advantage. ↩

  11. Arbesman, S. (2012). The Half-Life of Facts: Why Everything We Know Has an Expiration Date. Current (Penguin). ISBN 9781591844723. Argued, popularizing scientometric findings, that the decay of facts occurs at predictable rates across fields. ↩

  12. Burton, R. E. & Kebler, R. W. (1960). The “half-life” of some scientific and technical literatures. American Documentation 11(1), 18–22. https://doi.org/10.1002/asi.5090110105 Likened the obsolescence of literature use to a radioactive half-life (though the authors granted the concept only limited validity). A primary definition of the cited half-life index is [primary-source verification needed]. ↩

  13. Bar-Ilan, J. & Halevi, G. (2017). Post retraction citations in context: a case study. Scientometrics 113(1), 547–565. https://doi.org/10.1007/s11192-017-2242-0 Of 238 citing contexts to retracted papers, 83% were positive, 12% neutral, 5% negative. ↩

  14. Hsiao, T.-K. & Schneider, J. (2022). Continued use of retracted papers: Temporal trends in citations and (lack of) awareness of retractions shown in citation contexts in biomedicine. Quantitative Science Studies 2(4), 1144–1169. https://doi.org/10.1162/qss_a_00155 Of 13,252 post-retraction citing contexts, only 5.4% acknowledged the retraction. First-online year is also listed as 2021 [verification needed]. ↩

  15. Post, H. R. (1971). Correspondence, Invariance and Heuristics: In Praise of Conservative Induction. Studies in History and Philosophy of Science Part A 2(3), 213–255. https://doi.org/10.1016/0039-3681(71)90042-2 Reportedly named the loss of explanatory power accompanying paradigm change “Kuhn-loss” (the primary passage where Post introduces the term is [primary-source verification needed]). ↩

  16. Merton, R. K. (1961). Singletons and Multiples in Scientific Discovery: A Chapter in the Sociology of Science. Proceedings of the American Philosophical Society 105(5), 470–486. Argued that all scientific discoveries are in principle multiple. ↩

  17. Ogburn, W. F. & Thomas, D. (1922). Are Inventions Inevitable? A Note on Social Evolution. Political Science Quarterly 37(1), 83–98. https://doi.org/10.2307/2142320 Listed some 148 cases of independent parties reaching the same invention. ↩

  18. Candia, C., Jara-Figueroa, C., Rodriguez-Sickert, C., Barabási, A.-L., Hidalgo, C. A. (2019). The universal decay of collective memory and attention. Nature Human Behaviour 3(1), 82–91. https://doi.org/10.1038/s41562-018-0474-5 Demonstrated a universal law by which collective attention to papers, patents, songs, films, and the like decays biexponentially, in a communicative-memory phase and a cultural-memory phase. ↩

  19. van Raan, A. F. J. (2004). Sleeping Beauties in science. Scientometrics 59(3), 467–472. https://doi.org/10.1023/B:SCIE.0000018543.82441.f1 Formalized the phenomenon of papers that lie uncited and are suddenly cited later. ↩

  20. Ke, Q., Ferrara, E., Radicchi, F., Flammini, A. (2015). Defining and identifying Sleeping Beauties in science. PNAS 112(24), 7426–7431. https://doi.org/10.1073/pnas.1424329112 Introduced the “beauty coefficient” and showed the Sleeping Beauty phenomenon is continuous, not exceptional, across 22 million papers. ↩

  21. Chu, J. S. G. & Evans, J. A. (2021). Slowed canonical progress in large fields of science. PNAS 118(41), e2021636118. https://doi.org/10.1073/pnas.2021636118 Showed, across 1.8 billion citations, that the larger the field, the more the canon crystallizes and new ideas struggle to win field-wide attention. ↩

  22. Dolgonosov, B. M. (2020). A knowledge-based model of civilization under climate change. arXiv:2002.10196. https://doi.org/10.48550/arXiv.2002.10196 Models active knowledge as the equilibrium of “production rate minus loss rate” in a differential equation. But it is a macro-model of civilization and climate, not a metric of scientific progress. Access to the full text is centered on the abstract, so [primary-source verification needed]. ↩

  23. No prior use of “undiscovery” or “undiscovery rate” as a defined term of art in scientometrics or meta-science was found within the searched range. But this is an absence based on search, not a proof of non-existence ([primary-source verification needed]). Swanson’s “undiscovered public knowledge” (1986) refers to public knowledge that lies buried because fragments are never combined, a concept distinct from “loss” as the known dropping out of use. ↩

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