{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:ZPLLPJQTVEDMKLXRERSYQCGCPX","short_pith_number":"pith:ZPLLPJQT","schema_version":"1.0","canonical_sha256":"cbd6b7a613a906c52ef124658808c27ded815dac4f61188f6305d4e027d23e71","source":{"kind":"arxiv","id":"1509.06994","version":1},"attestation_state":"computed","paper":{"title":"Stationary random graphs on $\\mathbb{Z}$ with prescribed iid degrees and finite mean connections","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Johan Jonasson, Maria Deijfen","submitted_at":"2015-09-23T14:09:55Z","abstract_excerpt":"Let $F$ be a probability distribution with support on the non-negative integers. A model is proposed for generating stationary simple graphs on $\\mathbb{Z}$ with degree distribution $F$ and it is shown for this model that the expected total length of all edges at a given vertex is finite if $F$ has finite second moment. It is not hard to see that any stationary model for generating simple graphs on $\\mathbb{Z}$ will give infinite mean for the total edge length per vertex if $F$ does not have finite second moment. Hence, finite second moment of $F$ is a necessary and sufficient condition for th"},"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":"1509.06994","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-09-23T14:09:55Z","cross_cats_sorted":[],"title_canon_sha256":"5af659a628f61e42c968727b70b08ac9a4248b017bac0734a2612081874314f9","abstract_canon_sha256":"53d68f5d02c6a6ace39f8d8b077154f8a111b6f3f8b4538b71a4fb5035555eef"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:32:17.254130Z","signature_b64":"aAW7qUwZT+BlatcwPsbgzESa2klRfWC2QoLu5BoD6f1Os1c5rj52J5OW7yvJ6Bb8mXAGATCSUubgN1PKykB/CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cbd6b7a613a906c52ef124658808c27ded815dac4f61188f6305d4e027d23e71","last_reissued_at":"2026-05-18T01:32:17.253373Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:32:17.253373Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Stationary random graphs on $\\mathbb{Z}$ with prescribed iid degrees and finite mean connections","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Johan Jonasson, Maria Deijfen","submitted_at":"2015-09-23T14:09:55Z","abstract_excerpt":"Let $F$ be a probability distribution with support on the non-negative integers. A model is proposed for generating stationary simple graphs on $\\mathbb{Z}$ with degree distribution $F$ and it is shown for this model that the expected total length of all edges at a given vertex is finite if $F$ has finite second moment. It is not hard to see that any stationary model for generating simple graphs on $\\mathbb{Z}$ will give infinite mean for the total edge length per vertex if $F$ does not have finite second moment. Hence, finite second moment of $F$ is a necessary and sufficient condition for th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.06994","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":"1509.06994","created_at":"2026-05-18T01:32:17.253483+00:00"},{"alias_kind":"arxiv_version","alias_value":"1509.06994v1","created_at":"2026-05-18T01:32:17.253483+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.06994","created_at":"2026-05-18T01:32:17.253483+00:00"},{"alias_kind":"pith_short_12","alias_value":"ZPLLPJQTVEDM","created_at":"2026-05-18T12:29:52.810259+00:00"},{"alias_kind":"pith_short_16","alias_value":"ZPLLPJQTVEDMKLXR","created_at":"2026-05-18T12:29:52.810259+00:00"},{"alias_kind":"pith_short_8","alias_value":"ZPLLPJQT","created_at":"2026-05-18T12:29:52.810259+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/ZPLLPJQTVEDMKLXRERSYQCGCPX","json":"https://pith.science/pith/ZPLLPJQTVEDMKLXRERSYQCGCPX.json","graph_json":"https://pith.science/api/pith-number/ZPLLPJQTVEDMKLXRERSYQCGCPX/graph.json","events_json":"https://pith.science/api/pith-number/ZPLLPJQTVEDMKLXRERSYQCGCPX/events.json","paper":"https://pith.science/paper/ZPLLPJQT"},"agent_actions":{"view_html":"https://pith.science/pith/ZPLLPJQTVEDMKLXRERSYQCGCPX","download_json":"https://pith.science/pith/ZPLLPJQTVEDMKLXRERSYQCGCPX.json","view_paper":"https://pith.science/paper/ZPLLPJQT","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1509.06994&json=true","fetch_graph":"https://pith.science/api/pith-number/ZPLLPJQTVEDMKLXRERSYQCGCPX/graph.json","fetch_events":"https://pith.science/api/pith-number/ZPLLPJQTVEDMKLXRERSYQCGCPX/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ZPLLPJQTVEDMKLXRERSYQCGCPX/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ZPLLPJQTVEDMKLXRERSYQCGCPX/action/storage_attestation","attest_author":"https://pith.science/pith/ZPLLPJQTVEDMKLXRERSYQCGCPX/action/author_attestation","sign_citation":"https://pith.science/pith/ZPLLPJQTVEDMKLXRERSYQCGCPX/action/citation_signature","submit_replication":"https://pith.science/pith/ZPLLPJQTVEDMKLXRERSYQCGCPX/action/replication_record"}},"created_at":"2026-05-18T01:32:17.253483+00:00","updated_at":"2026-05-18T01:32:17.253483+00:00"}