{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:EIIKJJYBVEQSTFVM6MXY67XBDA","short_pith_number":"pith:EIIKJJYB","schema_version":"1.0","canonical_sha256":"2210a4a701a9212996acf32f8f7ee11820da7c76ffc8702daf771a8310e5c15c","source":{"kind":"arxiv","id":"1409.1108","version":1},"attestation_state":"computed","paper":{"title":"Profile and hereditary classes of ordered relational structures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Djamila Oudrar, Maurice Pouzet","submitted_at":"2014-09-03T14:38:58Z","abstract_excerpt":"Let $\\mathfrak{C}$ be a class of finite combinatorial structures. The \\textit{profile} of $\\mathfrak{C}$ is the function $\\varphi_{\\mathfrak{C}}$ which counts, for every integer $n$, the number $\\varphi_{\\mathfrak{C}}(n)$ of members of $\\mathfrak{C}$ defined on $n$ elements, isomorphic structures been identified. The \\textit{generating function of} $\\mathfrak{C}$ is $\\mathcal {H}_{\\mathfrak{C}}(x):=\\sum_{n\\geqq 0}\\varphi_{\\mathfrak{C}}(n)x^{n}$. Many results about the behavior of the function $\\varphi_{\\mathfrak{C}}$ have been obtained. Albert and Atkinson have shown that the generating series"},"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":"1409.1108","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-09-03T14:38:58Z","cross_cats_sorted":[],"title_canon_sha256":"f06613197b08fa6d1d7ec1a26d0529ddcba5b88d73f6d45ca501316eb171c17e","abstract_canon_sha256":"2d3a3c12aa348d3d12ac703bd9e03f1079f085a48da816991c6a7f4b5b25a14c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:43:44.327909Z","signature_b64":"uDkW65MLP7UP4XL1VmUfZjoVfz5CFmWFa2zmZVyXsLfrrd2gjbnAZHdwNx0nvQTAokldYWllv1z/uOuc1aMNDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2210a4a701a9212996acf32f8f7ee11820da7c76ffc8702daf771a8310e5c15c","last_reissued_at":"2026-05-18T02:43:44.327464Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:43:44.327464Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Profile and hereditary classes of ordered relational structures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Djamila Oudrar, Maurice Pouzet","submitted_at":"2014-09-03T14:38:58Z","abstract_excerpt":"Let $\\mathfrak{C}$ be a class of finite combinatorial structures. The \\textit{profile} of $\\mathfrak{C}$ is the function $\\varphi_{\\mathfrak{C}}$ which counts, for every integer $n$, the number $\\varphi_{\\mathfrak{C}}(n)$ of members of $\\mathfrak{C}$ defined on $n$ elements, isomorphic structures been identified. The \\textit{generating function of} $\\mathfrak{C}$ is $\\mathcal {H}_{\\mathfrak{C}}(x):=\\sum_{n\\geqq 0}\\varphi_{\\mathfrak{C}}(n)x^{n}$. Many results about the behavior of the function $\\varphi_{\\mathfrak{C}}$ have been obtained. Albert and Atkinson have shown that the generating series"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.1108","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":"1409.1108","created_at":"2026-05-18T02:43:44.327532+00:00"},{"alias_kind":"arxiv_version","alias_value":"1409.1108v1","created_at":"2026-05-18T02:43:44.327532+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.1108","created_at":"2026-05-18T02:43:44.327532+00:00"},{"alias_kind":"pith_short_12","alias_value":"EIIKJJYBVEQS","created_at":"2026-05-18T12:28:25.294606+00:00"},{"alias_kind":"pith_short_16","alias_value":"EIIKJJYBVEQSTFVM","created_at":"2026-05-18T12:28:25.294606+00:00"},{"alias_kind":"pith_short_8","alias_value":"EIIKJJYB","created_at":"2026-05-18T12:28:25.294606+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/EIIKJJYBVEQSTFVM6MXY67XBDA","json":"https://pith.science/pith/EIIKJJYBVEQSTFVM6MXY67XBDA.json","graph_json":"https://pith.science/api/pith-number/EIIKJJYBVEQSTFVM6MXY67XBDA/graph.json","events_json":"https://pith.science/api/pith-number/EIIKJJYBVEQSTFVM6MXY67XBDA/events.json","paper":"https://pith.science/paper/EIIKJJYB"},"agent_actions":{"view_html":"https://pith.science/pith/EIIKJJYBVEQSTFVM6MXY67XBDA","download_json":"https://pith.science/pith/EIIKJJYBVEQSTFVM6MXY67XBDA.json","view_paper":"https://pith.science/paper/EIIKJJYB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1409.1108&json=true","fetch_graph":"https://pith.science/api/pith-number/EIIKJJYBVEQSTFVM6MXY67XBDA/graph.json","fetch_events":"https://pith.science/api/pith-number/EIIKJJYBVEQSTFVM6MXY67XBDA/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/EIIKJJYBVEQSTFVM6MXY67XBDA/action/timestamp_anchor","attest_storage":"https://pith.science/pith/EIIKJJYBVEQSTFVM6MXY67XBDA/action/storage_attestation","attest_author":"https://pith.science/pith/EIIKJJYBVEQSTFVM6MXY67XBDA/action/author_attestation","sign_citation":"https://pith.science/pith/EIIKJJYBVEQSTFVM6MXY67XBDA/action/citation_signature","submit_replication":"https://pith.science/pith/EIIKJJYBVEQSTFVM6MXY67XBDA/action/replication_record"}},"created_at":"2026-05-18T02:43:44.327532+00:00","updated_at":"2026-05-18T02:43:44.327532+00:00"}