{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:VL7EEIDYILW2UOKIVSN4TE4565","short_pith_number":"pith:VL7EEIDY","schema_version":"1.0","canonical_sha256":"aafe42207842edaa3948ac9bc9939df755af5f86d68424979a659d15fd2f14ff","source":{"kind":"arxiv","id":"1311.2806","version":2},"attestation_state":"computed","paper":{"title":"The Cram\\'er Condition for the Curie-Weiss Model of SOC","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"Matthias Gorny","submitted_at":"2013-11-12T15:12:28Z","abstract_excerpt":"We pursue the study of the Curie-Weiss model of self-organized criticality we designed in arXiv:1301.6911. We extend our results to more general interaction functions and we prove that, for a class of symmetric distributions satisfying a Cram\\'er condition $(C)$ and some integrability hypothesis, the sum $S_{n}$ of the random variables behaves as in the typical critical generalized Ising Curie-Weiss model. The fluctuations are of order $n^{3/4}$ and the limiting law is $k \\exp(-\\lambda x^{4})\\,dx$ where $k$ and $\\lambda$ are suitable positive constants. In arXiv:1301.6911 we obtained these res"},"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":"1311.2806","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-11-12T15:12:28Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"5a9df6eb43dcde2fc06f3dc598247ed290b9c8c0136a69a7c4bcc55a6c1b7a22","abstract_canon_sha256":"3721f13796e2990babf039e9965c8cb84c30c48153dac9f38ca5953e7d5b6b74"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:41:01.159543Z","signature_b64":"6I5Z6yJ968+GTAnCBFK0VRdKGDO9m8Oh7zFGxvNIULuI2H3q0OIAbkKQub693mAOU8zk/kxAJykE7Ip8OcqMDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"aafe42207842edaa3948ac9bc9939df755af5f86d68424979a659d15fd2f14ff","last_reissued_at":"2026-05-18T02:41:01.158416Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:41:01.158416Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Cram\\'er Condition for the Curie-Weiss Model of SOC","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"Matthias Gorny","submitted_at":"2013-11-12T15:12:28Z","abstract_excerpt":"We pursue the study of the Curie-Weiss model of self-organized criticality we designed in arXiv:1301.6911. We extend our results to more general interaction functions and we prove that, for a class of symmetric distributions satisfying a Cram\\'er condition $(C)$ and some integrability hypothesis, the sum $S_{n}$ of the random variables behaves as in the typical critical generalized Ising Curie-Weiss model. The fluctuations are of order $n^{3/4}$ and the limiting law is $k \\exp(-\\lambda x^{4})\\,dx$ where $k$ and $\\lambda$ are suitable positive constants. In arXiv:1301.6911 we obtained these res"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.2806","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":"1311.2806","created_at":"2026-05-18T02:41:01.158503+00:00"},{"alias_kind":"arxiv_version","alias_value":"1311.2806v2","created_at":"2026-05-18T02:41:01.158503+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1311.2806","created_at":"2026-05-18T02:41:01.158503+00:00"},{"alias_kind":"pith_short_12","alias_value":"VL7EEIDYILW2","created_at":"2026-05-18T12:28:04.890932+00:00"},{"alias_kind":"pith_short_16","alias_value":"VL7EEIDYILW2UOKI","created_at":"2026-05-18T12:28:04.890932+00:00"},{"alias_kind":"pith_short_8","alias_value":"VL7EEIDY","created_at":"2026-05-18T12:28:04.890932+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/VL7EEIDYILW2UOKIVSN4TE4565","json":"https://pith.science/pith/VL7EEIDYILW2UOKIVSN4TE4565.json","graph_json":"https://pith.science/api/pith-number/VL7EEIDYILW2UOKIVSN4TE4565/graph.json","events_json":"https://pith.science/api/pith-number/VL7EEIDYILW2UOKIVSN4TE4565/events.json","paper":"https://pith.science/paper/VL7EEIDY"},"agent_actions":{"view_html":"https://pith.science/pith/VL7EEIDYILW2UOKIVSN4TE4565","download_json":"https://pith.science/pith/VL7EEIDYILW2UOKIVSN4TE4565.json","view_paper":"https://pith.science/paper/VL7EEIDY","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1311.2806&json=true","fetch_graph":"https://pith.science/api/pith-number/VL7EEIDYILW2UOKIVSN4TE4565/graph.json","fetch_events":"https://pith.science/api/pith-number/VL7EEIDYILW2UOKIVSN4TE4565/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/VL7EEIDYILW2UOKIVSN4TE4565/action/timestamp_anchor","attest_storage":"https://pith.science/pith/VL7EEIDYILW2UOKIVSN4TE4565/action/storage_attestation","attest_author":"https://pith.science/pith/VL7EEIDYILW2UOKIVSN4TE4565/action/author_attestation","sign_citation":"https://pith.science/pith/VL7EEIDYILW2UOKIVSN4TE4565/action/citation_signature","submit_replication":"https://pith.science/pith/VL7EEIDYILW2UOKIVSN4TE4565/action/replication_record"}},"created_at":"2026-05-18T02:41:01.158503+00:00","updated_at":"2026-05-18T02:41:01.158503+00:00"}