{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:MSWDTSE7PZW2SOVWTX5EZTINTL","short_pith_number":"pith:MSWDTSE7","schema_version":"1.0","canonical_sha256":"64ac39c89f7e6da93ab69dfa4ccd0d9af6e32d2dca2d5591f16a4dcd8b270ab2","source":{"kind":"arxiv","id":"1511.01330","version":2},"attestation_state":"computed","paper":{"title":"Entangling Fractals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech"],"primary_cat":"hep-th","authors_text":"Amin Faraji Astaneh","submitted_at":"2015-11-04T13:52:16Z","abstract_excerpt":"We use the Heat Kernel method to calculate the Entanglement Entropy for a given entangling region on a fractal. The leading divergent term of the entropy is obtained as a function of the fractal dimension as well as the walk dimension. The power of the UV cut-off parameter is (generally) a fractional number which indeed is a certain combination of these two indices. This exponent is known as the spectral dimension. We show that there is a novel $\\log$ periodic oscillatory behavior in the expression of entropy which has root in the complex dimension of the fractal. We finally indicate that the "},"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":"1511.01330","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2015-11-04T13:52:16Z","cross_cats_sorted":["cond-mat.stat-mech"],"title_canon_sha256":"b2cf2b48988e43702bac3b24cba96b6174b37b03fe991778ac318328f4d89750","abstract_canon_sha256":"e6d3fc447af8258a89b738b8966a39fe0f5b908997c3948247e3785eac600ee4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:18:30.993337Z","signature_b64":"qjAL4iWBEDnZr/tCjN7hq931uUXXgXSwsbEJFxOPz8DhfMDAuFXqlU8nLY+0Dm3Ks80/6QUKGKxbwANI2UOHBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"64ac39c89f7e6da93ab69dfa4ccd0d9af6e32d2dca2d5591f16a4dcd8b270ab2","last_reissued_at":"2026-05-18T01:18:30.992797Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:18:30.992797Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Entangling Fractals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech"],"primary_cat":"hep-th","authors_text":"Amin Faraji Astaneh","submitted_at":"2015-11-04T13:52:16Z","abstract_excerpt":"We use the Heat Kernel method to calculate the Entanglement Entropy for a given entangling region on a fractal. The leading divergent term of the entropy is obtained as a function of the fractal dimension as well as the walk dimension. The power of the UV cut-off parameter is (generally) a fractional number which indeed is a certain combination of these two indices. This exponent is known as the spectral dimension. We show that there is a novel $\\log$ periodic oscillatory behavior in the expression of entropy which has root in the complex dimension of the fractal. We finally indicate that the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.01330","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":"1511.01330","created_at":"2026-05-18T01:18:30.992905+00:00"},{"alias_kind":"arxiv_version","alias_value":"1511.01330v2","created_at":"2026-05-18T01:18:30.992905+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.01330","created_at":"2026-05-18T01:18:30.992905+00:00"},{"alias_kind":"pith_short_12","alias_value":"MSWDTSE7PZW2","created_at":"2026-05-18T12:29:32.376354+00:00"},{"alias_kind":"pith_short_16","alias_value":"MSWDTSE7PZW2SOVW","created_at":"2026-05-18T12:29:32.376354+00:00"},{"alias_kind":"pith_short_8","alias_value":"MSWDTSE7","created_at":"2026-05-18T12:29:32.376354+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/MSWDTSE7PZW2SOVWTX5EZTINTL","json":"https://pith.science/pith/MSWDTSE7PZW2SOVWTX5EZTINTL.json","graph_json":"https://pith.science/api/pith-number/MSWDTSE7PZW2SOVWTX5EZTINTL/graph.json","events_json":"https://pith.science/api/pith-number/MSWDTSE7PZW2SOVWTX5EZTINTL/events.json","paper":"https://pith.science/paper/MSWDTSE7"},"agent_actions":{"view_html":"https://pith.science/pith/MSWDTSE7PZW2SOVWTX5EZTINTL","download_json":"https://pith.science/pith/MSWDTSE7PZW2SOVWTX5EZTINTL.json","view_paper":"https://pith.science/paper/MSWDTSE7","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1511.01330&json=true","fetch_graph":"https://pith.science/api/pith-number/MSWDTSE7PZW2SOVWTX5EZTINTL/graph.json","fetch_events":"https://pith.science/api/pith-number/MSWDTSE7PZW2SOVWTX5EZTINTL/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/MSWDTSE7PZW2SOVWTX5EZTINTL/action/timestamp_anchor","attest_storage":"https://pith.science/pith/MSWDTSE7PZW2SOVWTX5EZTINTL/action/storage_attestation","attest_author":"https://pith.science/pith/MSWDTSE7PZW2SOVWTX5EZTINTL/action/author_attestation","sign_citation":"https://pith.science/pith/MSWDTSE7PZW2SOVWTX5EZTINTL/action/citation_signature","submit_replication":"https://pith.science/pith/MSWDTSE7PZW2SOVWTX5EZTINTL/action/replication_record"}},"created_at":"2026-05-18T01:18:30.992905+00:00","updated_at":"2026-05-18T01:18:30.992905+00:00"}