{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:ZCLHSX24TJ62GWAZL3IYWXOETJ","short_pith_number":"pith:ZCLHSX24","schema_version":"1.0","canonical_sha256":"c896795f5c9a7da358195ed18b5dc49a4b01db0704c1ad808beb34bd28a6b8a3","source":{"kind":"arxiv","id":"1809.08333","version":2},"attestation_state":"computed","paper":{"title":"Evolving Shelah-Spencer Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Richard Elwes","submitted_at":"2018-09-21T22:22:53Z","abstract_excerpt":"An \\emph{evolving Shelah-Spencer process} is one by which a random graph grows, with at each time $\\tau \\in {\\bf N}$ a new node incorporated and attached to each previous node with probability $\\tau^{-\\alpha}$, where $\\alpha \\in (0,1) \\setminus {\\bf Q}$ is fixed. We analyse the graphs that result from this process, including the infinite limit, in comparison to Shelah-Spencer sparse random graphs discussed in [Spencer, J., 2013. The strange logic of random graphs (Vol. 22). Springer Science & Business Media.] and throughout the model-theoretic literature. The first order axiomatisation for cla"},"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":"1809.08333","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-09-21T22:22:53Z","cross_cats_sorted":[],"title_canon_sha256":"cfc464ac5e484ba3c4215aa019279590b84e00ef445491db4ccc9a26a3b4bb22","abstract_canon_sha256":"d3986f0c1569ab8ecf7579444c3024894d6c1e3284d11b47d0ac9b3008290ba7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:41:31.060952Z","signature_b64":"rhil1g7/XAEA4fhcn2gmfnvZOmr4c3UCOcJtmV2aSY1LyQWuAn7OdCuOgQGEgUxosMnAbZvHL2wb9adV+EIdAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c896795f5c9a7da358195ed18b5dc49a4b01db0704c1ad808beb34bd28a6b8a3","last_reissued_at":"2026-05-17T23:41:31.060242Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:41:31.060242Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Evolving Shelah-Spencer Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Richard Elwes","submitted_at":"2018-09-21T22:22:53Z","abstract_excerpt":"An \\emph{evolving Shelah-Spencer process} is one by which a random graph grows, with at each time $\\tau \\in {\\bf N}$ a new node incorporated and attached to each previous node with probability $\\tau^{-\\alpha}$, where $\\alpha \\in (0,1) \\setminus {\\bf Q}$ is fixed. We analyse the graphs that result from this process, including the infinite limit, in comparison to Shelah-Spencer sparse random graphs discussed in [Spencer, J., 2013. The strange logic of random graphs (Vol. 22). Springer Science & Business Media.] and throughout the model-theoretic literature. The first order axiomatisation for cla"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.08333","kind":"arxiv","version":2},"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":"1809.08333","created_at":"2026-05-17T23:41:31.060358+00:00"},{"alias_kind":"arxiv_version","alias_value":"1809.08333v2","created_at":"2026-05-17T23:41:31.060358+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.08333","created_at":"2026-05-17T23:41:31.060358+00:00"},{"alias_kind":"pith_short_12","alias_value":"ZCLHSX24TJ62","created_at":"2026-05-18T12:33:04.347982+00:00"},{"alias_kind":"pith_short_16","alias_value":"ZCLHSX24TJ62GWAZ","created_at":"2026-05-18T12:33:04.347982+00:00"},{"alias_kind":"pith_short_8","alias_value":"ZCLHSX24","created_at":"2026-05-18T12:33:04.347982+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/ZCLHSX24TJ62GWAZL3IYWXOETJ","json":"https://pith.science/pith/ZCLHSX24TJ62GWAZL3IYWXOETJ.json","graph_json":"https://pith.science/api/pith-number/ZCLHSX24TJ62GWAZL3IYWXOETJ/graph.json","events_json":"https://pith.science/api/pith-number/ZCLHSX24TJ62GWAZL3IYWXOETJ/events.json","paper":"https://pith.science/paper/ZCLHSX24"},"agent_actions":{"view_html":"https://pith.science/pith/ZCLHSX24TJ62GWAZL3IYWXOETJ","download_json":"https://pith.science/pith/ZCLHSX24TJ62GWAZL3IYWXOETJ.json","view_paper":"https://pith.science/paper/ZCLHSX24","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1809.08333&json=true","fetch_graph":"https://pith.science/api/pith-number/ZCLHSX24TJ62GWAZL3IYWXOETJ/graph.json","fetch_events":"https://pith.science/api/pith-number/ZCLHSX24TJ62GWAZL3IYWXOETJ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ZCLHSX24TJ62GWAZL3IYWXOETJ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ZCLHSX24TJ62GWAZL3IYWXOETJ/action/storage_attestation","attest_author":"https://pith.science/pith/ZCLHSX24TJ62GWAZL3IYWXOETJ/action/author_attestation","sign_citation":"https://pith.science/pith/ZCLHSX24TJ62GWAZL3IYWXOETJ/action/citation_signature","submit_replication":"https://pith.science/pith/ZCLHSX24TJ62GWAZL3IYWXOETJ/action/replication_record"}},"created_at":"2026-05-17T23:41:31.060358+00:00","updated_at":"2026-05-17T23:41:31.060358+00:00"}