{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:JSTJE2TRVMA3FUMUWIY2OKCMQB","short_pith_number":"pith:JSTJE2TR","schema_version":"1.0","canonical_sha256":"4ca6926a71ab01b2d194b231a7284c8044a5dae005b660582662a5dec3abf040","source":{"kind":"arxiv","id":"1206.2301","version":1},"attestation_state":"computed","paper":{"title":"Laplacians on Julia Sets III: Cubic Julia Sets and Formal Matings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Calum Spicer, Emad Totari, Robert S. Strichartz","submitted_at":"2012-06-08T02:16:53Z","abstract_excerpt":"We continue the study of constructing invariant Laplacians on Julia sets, and studying properties of their spectra. In this paper we focus on two types of examples: 1) Julia sets of cubic polynomials $z^3 + c$ with a single critical point; 2) formal matings of quadratic Julia sets. The general scheme introduced in earlier papers in this series involves realizing the Julia set as a circle with identifications, and attempting to obtain the Laplacian as a renormalized limit of graph Laplacians on graphs derived form the circle with identifications model. In the case of cubic Julia sets the detail"},"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":"1206.2301","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-06-08T02:16:53Z","cross_cats_sorted":[],"title_canon_sha256":"220adb776795db1d5339142cc2f7637c37a99a7ac82372d1b00d67b6c31f7109","abstract_canon_sha256":"5a24572e9bdf0212842e9303e39bd7c68dea00d909df92da88b7fac2f72554a2"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:53:52.963680Z","signature_b64":"3u4lY/JQZO+Dr6OTcyri2GetBC/yhkY16JZ6zo0shNpS3prpJ0rye0BsVDCOeWzde6JEt1+G2X5JiTwvjzeCAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4ca6926a71ab01b2d194b231a7284c8044a5dae005b660582662a5dec3abf040","last_reissued_at":"2026-05-18T03:53:52.963196Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:53:52.963196Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Laplacians on Julia Sets III: Cubic Julia Sets and Formal Matings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Calum Spicer, Emad Totari, Robert S. Strichartz","submitted_at":"2012-06-08T02:16:53Z","abstract_excerpt":"We continue the study of constructing invariant Laplacians on Julia sets, and studying properties of their spectra. In this paper we focus on two types of examples: 1) Julia sets of cubic polynomials $z^3 + c$ with a single critical point; 2) formal matings of quadratic Julia sets. The general scheme introduced in earlier papers in this series involves realizing the Julia set as a circle with identifications, and attempting to obtain the Laplacian as a renormalized limit of graph Laplacians on graphs derived form the circle with identifications model. In the case of cubic Julia sets the detail"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.2301","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":"1206.2301","created_at":"2026-05-18T03:53:52.963254+00:00"},{"alias_kind":"arxiv_version","alias_value":"1206.2301v1","created_at":"2026-05-18T03:53:52.963254+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1206.2301","created_at":"2026-05-18T03:53:52.963254+00:00"},{"alias_kind":"pith_short_12","alias_value":"JSTJE2TRVMA3","created_at":"2026-05-18T12:27:11.947152+00:00"},{"alias_kind":"pith_short_16","alias_value":"JSTJE2TRVMA3FUMU","created_at":"2026-05-18T12:27:11.947152+00:00"},{"alias_kind":"pith_short_8","alias_value":"JSTJE2TR","created_at":"2026-05-18T12:27:11.947152+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/JSTJE2TRVMA3FUMUWIY2OKCMQB","json":"https://pith.science/pith/JSTJE2TRVMA3FUMUWIY2OKCMQB.json","graph_json":"https://pith.science/api/pith-number/JSTJE2TRVMA3FUMUWIY2OKCMQB/graph.json","events_json":"https://pith.science/api/pith-number/JSTJE2TRVMA3FUMUWIY2OKCMQB/events.json","paper":"https://pith.science/paper/JSTJE2TR"},"agent_actions":{"view_html":"https://pith.science/pith/JSTJE2TRVMA3FUMUWIY2OKCMQB","download_json":"https://pith.science/pith/JSTJE2TRVMA3FUMUWIY2OKCMQB.json","view_paper":"https://pith.science/paper/JSTJE2TR","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1206.2301&json=true","fetch_graph":"https://pith.science/api/pith-number/JSTJE2TRVMA3FUMUWIY2OKCMQB/graph.json","fetch_events":"https://pith.science/api/pith-number/JSTJE2TRVMA3FUMUWIY2OKCMQB/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/JSTJE2TRVMA3FUMUWIY2OKCMQB/action/timestamp_anchor","attest_storage":"https://pith.science/pith/JSTJE2TRVMA3FUMUWIY2OKCMQB/action/storage_attestation","attest_author":"https://pith.science/pith/JSTJE2TRVMA3FUMUWIY2OKCMQB/action/author_attestation","sign_citation":"https://pith.science/pith/JSTJE2TRVMA3FUMUWIY2OKCMQB/action/citation_signature","submit_replication":"https://pith.science/pith/JSTJE2TRVMA3FUMUWIY2OKCMQB/action/replication_record"}},"created_at":"2026-05-18T03:53:52.963254+00:00","updated_at":"2026-05-18T03:53:52.963254+00:00"}