{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:PKZ47Z2EWEVB5UE5GLHPW4CZFB","short_pith_number":"pith:PKZ47Z2E","schema_version":"1.0","canonical_sha256":"7ab3cfe744b12a1ed09d32cefb70592873a4f16f2e5feac62eabcc302ba674be","source":{"kind":"arxiv","id":"1403.1811","version":1},"attestation_state":"computed","paper":{"title":"Heat content asymptotics of some random Koch type snowflakes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Philippe H. A. Charmoy","submitted_at":"2014-03-07T17:14:19Z","abstract_excerpt":"We consider the short time asymptotics of the heat content $E$ of a domain $D$ of $\\mathbb{R}^d$. The novelty of this paper is that we consider the situation where $D$ is a domain whose boundary $\\partial D$ is a random Koch type curve.\n  When $\\partial D$ is spatially homogeneous, we show that we can recover the lower and upper Minkowski dimensions of $\\partial D$ from the short time behaviour of $E(s)$. Furthermore, in some situations where the Minkowski dimension exists, finer geometric fluctuations can be recovered and the heat content is controlled by $s^\\alpha e^{f(\\log(1/s))}$ for small"},"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":"1403.1811","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-03-07T17:14:19Z","cross_cats_sorted":[],"title_canon_sha256":"3e35a93463970f593434dbbcaeb579896a503b6c5040fbdd9c32cb6aac1367f0","abstract_canon_sha256":"dbdcc72a8ba3f4046d33da2d260befa24c464bb5461cf545fae84ec2e9bc05d6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:56:52.502389Z","signature_b64":"CCmM2f0QaNutJN57QoyGpzLXjcG3B8M+EkMZ+LyZGygxT8zX7CqTJcykhHWTACm7EVVMsVLuDtAofpWPZ/xhBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7ab3cfe744b12a1ed09d32cefb70592873a4f16f2e5feac62eabcc302ba674be","last_reissued_at":"2026-05-18T02:56:52.501869Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:56:52.501869Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Heat content asymptotics of some random Koch type snowflakes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Philippe H. A. Charmoy","submitted_at":"2014-03-07T17:14:19Z","abstract_excerpt":"We consider the short time asymptotics of the heat content $E$ of a domain $D$ of $\\mathbb{R}^d$. The novelty of this paper is that we consider the situation where $D$ is a domain whose boundary $\\partial D$ is a random Koch type curve.\n  When $\\partial D$ is spatially homogeneous, we show that we can recover the lower and upper Minkowski dimensions of $\\partial D$ from the short time behaviour of $E(s)$. Furthermore, in some situations where the Minkowski dimension exists, finer geometric fluctuations can be recovered and the heat content is controlled by $s^\\alpha e^{f(\\log(1/s))}$ for small"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.1811","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":"1403.1811","created_at":"2026-05-18T02:56:52.501950+00:00"},{"alias_kind":"arxiv_version","alias_value":"1403.1811v1","created_at":"2026-05-18T02:56:52.501950+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.1811","created_at":"2026-05-18T02:56:52.501950+00:00"},{"alias_kind":"pith_short_12","alias_value":"PKZ47Z2EWEVB","created_at":"2026-05-18T12:28:43.426989+00:00"},{"alias_kind":"pith_short_16","alias_value":"PKZ47Z2EWEVB5UE5","created_at":"2026-05-18T12:28:43.426989+00:00"},{"alias_kind":"pith_short_8","alias_value":"PKZ47Z2E","created_at":"2026-05-18T12:28:43.426989+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/PKZ47Z2EWEVB5UE5GLHPW4CZFB","json":"https://pith.science/pith/PKZ47Z2EWEVB5UE5GLHPW4CZFB.json","graph_json":"https://pith.science/api/pith-number/PKZ47Z2EWEVB5UE5GLHPW4CZFB/graph.json","events_json":"https://pith.science/api/pith-number/PKZ47Z2EWEVB5UE5GLHPW4CZFB/events.json","paper":"https://pith.science/paper/PKZ47Z2E"},"agent_actions":{"view_html":"https://pith.science/pith/PKZ47Z2EWEVB5UE5GLHPW4CZFB","download_json":"https://pith.science/pith/PKZ47Z2EWEVB5UE5GLHPW4CZFB.json","view_paper":"https://pith.science/paper/PKZ47Z2E","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1403.1811&json=true","fetch_graph":"https://pith.science/api/pith-number/PKZ47Z2EWEVB5UE5GLHPW4CZFB/graph.json","fetch_events":"https://pith.science/api/pith-number/PKZ47Z2EWEVB5UE5GLHPW4CZFB/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/PKZ47Z2EWEVB5UE5GLHPW4CZFB/action/timestamp_anchor","attest_storage":"https://pith.science/pith/PKZ47Z2EWEVB5UE5GLHPW4CZFB/action/storage_attestation","attest_author":"https://pith.science/pith/PKZ47Z2EWEVB5UE5GLHPW4CZFB/action/author_attestation","sign_citation":"https://pith.science/pith/PKZ47Z2EWEVB5UE5GLHPW4CZFB/action/citation_signature","submit_replication":"https://pith.science/pith/PKZ47Z2EWEVB5UE5GLHPW4CZFB/action/replication_record"}},"created_at":"2026-05-18T02:56:52.501950+00:00","updated_at":"2026-05-18T02:56:52.501950+00:00"}