{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2005:337SSUUYPYDD3JVACP6ZREB6OC","short_pith_number":"pith:337SSUUY","schema_version":"1.0","canonical_sha256":"deff2952987e063da6a013fd98903e70b07e1c08352a84b95a26295202597762","source":{"kind":"arxiv","id":"math/0501096","version":1},"attestation_state":"computed","paper":{"title":"Hodge and signature theorems for a family of manifolds with fibration boundary","license":"","headline":"","cross_cats":["math.AT"],"primary_cat":"math.GT","authors_text":"Eugenie Hunsicker","submitted_at":"2005-01-07T04:01:17Z","abstract_excerpt":"Let $\\bar{M}$ be a manifold with boundary $Y$ which is the total space of a fibre bundle, and is defined by the vanishing of a boundary defining function, $x$. We prove $L^2$ Hodge and signature theorems for $M$ endowed with a metric of the form $dx^2 + x^{2c} h + k$, where $k$ is the lift to $Y$ of the metric on the base of the fibre bundle, $h$ is a two form on $Y$ which restricts to a metric on each fibre, and $0 \\leq c \\leq 1$. These metrics interpolate between the case when $c=0$, in which case the metric near the boundary is a cylinder, and the case where $c=1$, in which case the metric "},"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":"math/0501096","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.GT","submitted_at":"2005-01-07T04:01:17Z","cross_cats_sorted":["math.AT"],"title_canon_sha256":"ceda60b31b01c8ebbf28ce5fc8f0e6df5bbafc5ab1fc7009f91de81bb2418822","abstract_canon_sha256":"3d86807410dff873e81fccffe3988ae10e95080dd250de34a8c48f7ea47ed495"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:37:59.836737Z","signature_b64":"U8mFbhCOkhK4AYmd/hq5GFwYRP/QnJ5sayJHvCvh9R5+K0hKj0GwQLBHM0Wr/rA7AdtU9SKqSvSoRENO8EAdDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"deff2952987e063da6a013fd98903e70b07e1c08352a84b95a26295202597762","last_reissued_at":"2026-05-18T02:37:59.836308Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:37:59.836308Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Hodge and signature theorems for a family of manifolds with fibration boundary","license":"","headline":"","cross_cats":["math.AT"],"primary_cat":"math.GT","authors_text":"Eugenie Hunsicker","submitted_at":"2005-01-07T04:01:17Z","abstract_excerpt":"Let $\\bar{M}$ be a manifold with boundary $Y$ which is the total space of a fibre bundle, and is defined by the vanishing of a boundary defining function, $x$. We prove $L^2$ Hodge and signature theorems for $M$ endowed with a metric of the form $dx^2 + x^{2c} h + k$, where $k$ is the lift to $Y$ of the metric on the base of the fibre bundle, $h$ is a two form on $Y$ which restricts to a metric on each fibre, and $0 \\leq c \\leq 1$. These metrics interpolate between the case when $c=0$, in which case the metric near the boundary is a cylinder, and the case where $c=1$, in which case the metric "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0501096","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":"math/0501096","created_at":"2026-05-18T02:37:59.836387+00:00"},{"alias_kind":"arxiv_version","alias_value":"math/0501096v1","created_at":"2026-05-18T02:37:59.836387+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0501096","created_at":"2026-05-18T02:37:59.836387+00:00"},{"alias_kind":"pith_short_12","alias_value":"337SSUUYPYDD","created_at":"2026-05-18T12:25:52.687210+00:00"},{"alias_kind":"pith_short_16","alias_value":"337SSUUYPYDD3JVA","created_at":"2026-05-18T12:25:52.687210+00:00"},{"alias_kind":"pith_short_8","alias_value":"337SSUUY","created_at":"2026-05-18T12:25:52.687210+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/337SSUUYPYDD3JVACP6ZREB6OC","json":"https://pith.science/pith/337SSUUYPYDD3JVACP6ZREB6OC.json","graph_json":"https://pith.science/api/pith-number/337SSUUYPYDD3JVACP6ZREB6OC/graph.json","events_json":"https://pith.science/api/pith-number/337SSUUYPYDD3JVACP6ZREB6OC/events.json","paper":"https://pith.science/paper/337SSUUY"},"agent_actions":{"view_html":"https://pith.science/pith/337SSUUYPYDD3JVACP6ZREB6OC","download_json":"https://pith.science/pith/337SSUUYPYDD3JVACP6ZREB6OC.json","view_paper":"https://pith.science/paper/337SSUUY","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math/0501096&json=true","fetch_graph":"https://pith.science/api/pith-number/337SSUUYPYDD3JVACP6ZREB6OC/graph.json","fetch_events":"https://pith.science/api/pith-number/337SSUUYPYDD3JVACP6ZREB6OC/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/337SSUUYPYDD3JVACP6ZREB6OC/action/timestamp_anchor","attest_storage":"https://pith.science/pith/337SSUUYPYDD3JVACP6ZREB6OC/action/storage_attestation","attest_author":"https://pith.science/pith/337SSUUYPYDD3JVACP6ZREB6OC/action/author_attestation","sign_citation":"https://pith.science/pith/337SSUUYPYDD3JVACP6ZREB6OC/action/citation_signature","submit_replication":"https://pith.science/pith/337SSUUYPYDD3JVACP6ZREB6OC/action/replication_record"}},"created_at":"2026-05-18T02:37:59.836387+00:00","updated_at":"2026-05-18T02:37:59.836387+00:00"}