{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:LYB7YOGZADYCUGQXOOAMYEHNYR","short_pith_number":"pith:LYB7YOGZ","schema_version":"1.0","canonical_sha256":"5e03fc38d900f02a1a177380cc10edc44295c1d1262e94d0b2bd7a70995e808b","source":{"kind":"arxiv","id":"1012.4975","version":1},"attestation_state":"computed","paper":{"title":"Hierarchical Gompertzian growth maps with application in astrophysics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["astro-ph.IM"],"primary_cat":"nlin.AO","authors_text":"S. De Martino, S. De Siena","submitted_at":"2010-12-22T13:52:24Z","abstract_excerpt":"The Gompertz model describes the growth in time of the size of significant quantities associated to a large number of systems, taking into account nonlinearity features by a linear equation satisfied by a nonlinear function of the size. Following this scheme, we introduce a class of hierarchical maps which describe discrete sequences of intermediate characteristic scales. We find the general solutions of the maps, which account for a rich set of possible phenomena. Eventually, we provide an important application, by showing that a map belonging to the class so introduced generates all the obse"},"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":"1012.4975","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.AO","submitted_at":"2010-12-22T13:52:24Z","cross_cats_sorted":["astro-ph.IM"],"title_canon_sha256":"ec034281d8ff391a2a29beaae15e4378e7d7c4f239d486fc3a96a2eea01f346b","abstract_canon_sha256":"86f5284f069f290080dba1e323f399f60010c68ff9dfcc07892f85f2966803dd"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:32:44.799194Z","signature_b64":"qZT5TQ66/jylQDTcvWxVkNXHb8Y9UBO7kD1vL6ii0UTq7NUxjdXgrc+DyUPzT4zqEFwJgxxBYNtcCKdLWpYJBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5e03fc38d900f02a1a177380cc10edc44295c1d1262e94d0b2bd7a70995e808b","last_reissued_at":"2026-05-18T04:32:44.798584Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:32:44.798584Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Hierarchical Gompertzian growth maps with application in astrophysics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["astro-ph.IM"],"primary_cat":"nlin.AO","authors_text":"S. De Martino, S. De Siena","submitted_at":"2010-12-22T13:52:24Z","abstract_excerpt":"The Gompertz model describes the growth in time of the size of significant quantities associated to a large number of systems, taking into account nonlinearity features by a linear equation satisfied by a nonlinear function of the size. Following this scheme, we introduce a class of hierarchical maps which describe discrete sequences of intermediate characteristic scales. We find the general solutions of the maps, which account for a rich set of possible phenomena. Eventually, we provide an important application, by showing that a map belonging to the class so introduced generates all the obse"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.4975","kind":"arxiv","version":1},"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":"1012.4975","created_at":"2026-05-18T04:32:44.798673+00:00"},{"alias_kind":"arxiv_version","alias_value":"1012.4975v1","created_at":"2026-05-18T04:32:44.798673+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1012.4975","created_at":"2026-05-18T04:32:44.798673+00:00"},{"alias_kind":"pith_short_12","alias_value":"LYB7YOGZADYC","created_at":"2026-05-18T12:26:10.704358+00:00"},{"alias_kind":"pith_short_16","alias_value":"LYB7YOGZADYCUGQX","created_at":"2026-05-18T12:26:10.704358+00:00"},{"alias_kind":"pith_short_8","alias_value":"LYB7YOGZ","created_at":"2026-05-18T12:26:10.704358+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/LYB7YOGZADYCUGQXOOAMYEHNYR","json":"https://pith.science/pith/LYB7YOGZADYCUGQXOOAMYEHNYR.json","graph_json":"https://pith.science/api/pith-number/LYB7YOGZADYCUGQXOOAMYEHNYR/graph.json","events_json":"https://pith.science/api/pith-number/LYB7YOGZADYCUGQXOOAMYEHNYR/events.json","paper":"https://pith.science/paper/LYB7YOGZ"},"agent_actions":{"view_html":"https://pith.science/pith/LYB7YOGZADYCUGQXOOAMYEHNYR","download_json":"https://pith.science/pith/LYB7YOGZADYCUGQXOOAMYEHNYR.json","view_paper":"https://pith.science/paper/LYB7YOGZ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1012.4975&json=true","fetch_graph":"https://pith.science/api/pith-number/LYB7YOGZADYCUGQXOOAMYEHNYR/graph.json","fetch_events":"https://pith.science/api/pith-number/LYB7YOGZADYCUGQXOOAMYEHNYR/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/LYB7YOGZADYCUGQXOOAMYEHNYR/action/timestamp_anchor","attest_storage":"https://pith.science/pith/LYB7YOGZADYCUGQXOOAMYEHNYR/action/storage_attestation","attest_author":"https://pith.science/pith/LYB7YOGZADYCUGQXOOAMYEHNYR/action/author_attestation","sign_citation":"https://pith.science/pith/LYB7YOGZADYCUGQXOOAMYEHNYR/action/citation_signature","submit_replication":"https://pith.science/pith/LYB7YOGZADYCUGQXOOAMYEHNYR/action/replication_record"}},"created_at":"2026-05-18T04:32:44.798673+00:00","updated_at":"2026-05-18T04:32:44.798673+00:00"}