Pith Number

pith:4M5JFETR

pith:2026:4M5JFETRDNDAOQD44KWS4XNVBA

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Project Life Cycles in Open-Source Software

Andrii Ieroshenko, Brian Granger, David Qiu, Michael Chin, Piyush Jain, Sanjiv Das

Open-source projects follow product life cycle dynamics that can be modeled with endogenous growth theory to estimate lifetime developer engagement and value.

arxiv:2605.12738 v1 · 2026-05-12 · cs.SE · cs.SI

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\pithnumber{4M5JFETRDNDAOQD44KWS4XNVBA}

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Record completeness

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2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

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The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Claims

C1strongest claim

The solution to this model calibrates well to many open-source projects. The model generates an estimate of the lifetime developer engagement and growth, which supports estimating a lifetime production value of open-source projects.

C2weakest assumption

That open-source projects exhibit dynamics similar to product life cycles and that endogenous growth theory with systems of differential equations can accurately capture interactions between growth levels and developer activity over time.

C3one line summary

Differential equation models from endogenous growth theory calibrate to open-source project data to estimate lifetime developer engagement and production value.

References

19 extracted · 19 resolved · 0 Pith anchors

[1] Bals, F. (2024). 2024 Open Source Security and Risk Analysis Report ( OSSRA ) Synopsys . Technical report, Blackduck, Inc 2024

[2] Bass, F. M. (1969). A New Product Growth for Model Consumer Durables . Management Science\/ 15\/ (5), 215--227. Publisher: INFORMS 1969

[3] Bass, F. M., T. V. Krishnan, and D. C. Jain (1994). Why the Bass Model Fits without Decision Variables . Marketing Science\/ 13\/ (3), 203--223. Publisher: INFORMS 1994

[4] Blind, K., S. Pätsch, S. Muto, M. Böhm, T. Schubert, P. Grzegorzewska, and A. Katz (2021). The impact of open source software and hardware on technological independence, competitiveness and innovation 2021

[5] Blind, K. and T. Schubert (2024, April). Estimating the GDP effect of Open Source Software and its complementarities with R & D and patents: evidence and policy implications. The Journal of Technology 2024

Receipt and verification

First computed	2026-05-18T03:09:49.128709Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e33a9292711b4607407ce2ad2e5db508146be0e4ca2efdfdc3ba65703f112ba1

Aliases

arxiv: 2605.12738 · arxiv_version: 2605.12738v1 · doi: 10.48550/arxiv.2605.12738 · pith_short_12: 4M5JFETRDNDA · pith_short_16: 4M5JFETRDNDAOQD4 · pith_short_8: 4M5JFETR

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/4M5JFETRDNDAOQD44KWS4XNVBA \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: e33a9292711b4607407ce2ad2e5db508146be0e4ca2efdfdc3ba65703f112ba1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e0271b449da3cabe6799634ee13d219fcf08193ba5763e3294bc69f35367d8c7",
    "cross_cats_sorted": [
      "cs.SI"
    ],
    "license": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
    "primary_cat": "cs.SE",
    "submitted_at": "2026-05-12T20:43:39Z",
    "title_canon_sha256": "f4f58d2512d7e4a374d2cab0c6e20f21cd8117aa0d76f4f1071ce28ff03abe4f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.12738",
    "kind": "arxiv",
    "version": 1
  }
}