{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:GHX77BUFPJOHIAN4PQDE2XRPHB","short_pith_number":"pith:GHX77BUF","schema_version":"1.0","canonical_sha256":"31efff86857a5c7401bc7c064d5e2f38477a56772475ef69b9f121ab1a8d4ac4","source":{"kind":"arxiv","id":"1001.3826","version":3},"attestation_state":"computed","paper":{"title":"A stability analysis of the power-law steady state of marine size spectra","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"q-bio.PE","authors_text":"Gustav W. Delius, Michael J. Plank, Richard Law, Samik Datta","submitted_at":"2010-01-21T15:24:22Z","abstract_excerpt":"This paper investigates the stability of the power-law steady state often observed in marine ecosystems. Three dynamical systems are considered, describing the abundance of organisms as a function of body mass and time: a \"jump-growth\" equation, a first order approximation which is the widely used McKendrick-von Foerster equation, and a second order approximation which is the McKendrick-von Foerster equation with a diffusion term. All of these yield a power-law steady state. We derive, for the first time, the eigenvalue spectrum for the linearised evolution operator, under certain constraints "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1001.3826","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.PE","submitted_at":"2010-01-21T15:24:22Z","cross_cats_sorted":[],"title_canon_sha256":"0df13065debf2cd70d11595c381c46cb4d6c25243927a4e0d49d15c3e44ec375","abstract_canon_sha256":"8e9c13e2aa2fa0269896f63a1dd1f3f480f6d7fa677b44811888352db55974d7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:34:46.172812Z","signature_b64":"TvR+I8wjZpd5sP5mjzsq5zY9gQZI7zglcg157v7Jq8SHVnzIegj6H6UUmu0fChVuwlOpPt5sionFloXokbu2Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"31efff86857a5c7401bc7c064d5e2f38477a56772475ef69b9f121ab1a8d4ac4","last_reissued_at":"2026-05-18T04:34:46.172269Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:34:46.172269Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A stability analysis of the power-law steady state of marine size spectra","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"q-bio.PE","authors_text":"Gustav W. Delius, Michael J. Plank, Richard Law, Samik Datta","submitted_at":"2010-01-21T15:24:22Z","abstract_excerpt":"This paper investigates the stability of the power-law steady state often observed in marine ecosystems. Three dynamical systems are considered, describing the abundance of organisms as a function of body mass and time: a \"jump-growth\" equation, a first order approximation which is the widely used McKendrick-von Foerster equation, and a second order approximation which is the McKendrick-von Foerster equation with a diffusion term. All of these yield a power-law steady state. We derive, for the first time, the eigenvalue spectrum for the linearised evolution operator, under certain constraints "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1001.3826","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1001.3826","created_at":"2026-05-18T04:34:46.172354+00:00"},{"alias_kind":"arxiv_version","alias_value":"1001.3826v3","created_at":"2026-05-18T04:34:46.172354+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1001.3826","created_at":"2026-05-18T04:34:46.172354+00:00"},{"alias_kind":"pith_short_12","alias_value":"GHX77BUFPJOH","created_at":"2026-05-18T12:26:07.630475+00:00"},{"alias_kind":"pith_short_16","alias_value":"GHX77BUFPJOHIAN4","created_at":"2026-05-18T12:26:07.630475+00:00"},{"alias_kind":"pith_short_8","alias_value":"GHX77BUF","created_at":"2026-05-18T12:26:07.630475+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/GHX77BUFPJOHIAN4PQDE2XRPHB","json":"https://pith.science/pith/GHX77BUFPJOHIAN4PQDE2XRPHB.json","graph_json":"https://pith.science/api/pith-number/GHX77BUFPJOHIAN4PQDE2XRPHB/graph.json","events_json":"https://pith.science/api/pith-number/GHX77BUFPJOHIAN4PQDE2XRPHB/events.json","paper":"https://pith.science/paper/GHX77BUF"},"agent_actions":{"view_html":"https://pith.science/pith/GHX77BUFPJOHIAN4PQDE2XRPHB","download_json":"https://pith.science/pith/GHX77BUFPJOHIAN4PQDE2XRPHB.json","view_paper":"https://pith.science/paper/GHX77BUF","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1001.3826&json=true","fetch_graph":"https://pith.science/api/pith-number/GHX77BUFPJOHIAN4PQDE2XRPHB/graph.json","fetch_events":"https://pith.science/api/pith-number/GHX77BUFPJOHIAN4PQDE2XRPHB/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/GHX77BUFPJOHIAN4PQDE2XRPHB/action/timestamp_anchor","attest_storage":"https://pith.science/pith/GHX77BUFPJOHIAN4PQDE2XRPHB/action/storage_attestation","attest_author":"https://pith.science/pith/GHX77BUFPJOHIAN4PQDE2XRPHB/action/author_attestation","sign_citation":"https://pith.science/pith/GHX77BUFPJOHIAN4PQDE2XRPHB/action/citation_signature","submit_replication":"https://pith.science/pith/GHX77BUFPJOHIAN4PQDE2XRPHB/action/replication_record"}},"created_at":"2026-05-18T04:34:46.172354+00:00","updated_at":"2026-05-18T04:34:46.172354+00:00"}