{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:GGMPKJK4WKKPVKKBPXFALVCPL2","short_pith_number":"pith:GGMPKJK4","schema_version":"1.0","canonical_sha256":"3198f5255cb294faa9417dca05d44f5ea229cf2ddbb7424ec453faa42e725773","source":{"kind":"arxiv","id":"1310.4246","version":1},"attestation_state":"computed","paper":{"title":"Index theory of the de Rham complex on manifolds with periodic ends","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.DG"],"primary_cat":"math.GT","authors_text":"Daniel Ruberman, Nikolai Saveliev, Tomasz Mrowka","submitted_at":"2013-10-16T02:16:52Z","abstract_excerpt":"We study the de Rham complex on a smooth manifold with a periodic end modeled on an infinite cyclic cover X' \\to X. The completion of this complex in exponentially weighted L^2-norms is Fredholm for all but finitely many exceptional weights determined by the eigenvalues of the covering translation map H_*(X') \\to H_*(X'). We calculate the index of this weighted de Rham complex for all weights away from the exceptional ones."},"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":"1310.4246","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2013-10-16T02:16:52Z","cross_cats_sorted":["math.AP","math.DG"],"title_canon_sha256":"5c9f0bbf32da70b71cad73f7fe3501c6e5e9bc159ea999e44173ab55d9240c5d","abstract_canon_sha256":"3645866a19372838e1aa947f60d35f1e2e483b28821a2f6eb62f2fde59070727"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:03:38.029736Z","signature_b64":"ieRFWv81rWCG0OcXcizBMab8FHBJpHM7leSuYNltlxUDjz69PYBOnTNntNbs8InWg/SM6zWGvM7UA4/UqYQ1Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3198f5255cb294faa9417dca05d44f5ea229cf2ddbb7424ec453faa42e725773","last_reissued_at":"2026-05-18T02:03:38.028992Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:03:38.028992Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Index theory of the de Rham complex on manifolds with periodic ends","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.DG"],"primary_cat":"math.GT","authors_text":"Daniel Ruberman, Nikolai Saveliev, Tomasz Mrowka","submitted_at":"2013-10-16T02:16:52Z","abstract_excerpt":"We study the de Rham complex on a smooth manifold with a periodic end modeled on an infinite cyclic cover X' \\to X. The completion of this complex in exponentially weighted L^2-norms is Fredholm for all but finitely many exceptional weights determined by the eigenvalues of the covering translation map H_*(X') \\to H_*(X'). We calculate the index of this weighted de Rham complex for all weights away from the exceptional ones."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.4246","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":"1310.4246","created_at":"2026-05-18T02:03:38.029119+00:00"},{"alias_kind":"arxiv_version","alias_value":"1310.4246v1","created_at":"2026-05-18T02:03:38.029119+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.4246","created_at":"2026-05-18T02:03:38.029119+00:00"},{"alias_kind":"pith_short_12","alias_value":"GGMPKJK4WKKP","created_at":"2026-05-18T12:27:45.050594+00:00"},{"alias_kind":"pith_short_16","alias_value":"GGMPKJK4WKKPVKKB","created_at":"2026-05-18T12:27:45.050594+00:00"},{"alias_kind":"pith_short_8","alias_value":"GGMPKJK4","created_at":"2026-05-18T12:27:45.050594+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/GGMPKJK4WKKPVKKBPXFALVCPL2","json":"https://pith.science/pith/GGMPKJK4WKKPVKKBPXFALVCPL2.json","graph_json":"https://pith.science/api/pith-number/GGMPKJK4WKKPVKKBPXFALVCPL2/graph.json","events_json":"https://pith.science/api/pith-number/GGMPKJK4WKKPVKKBPXFALVCPL2/events.json","paper":"https://pith.science/paper/GGMPKJK4"},"agent_actions":{"view_html":"https://pith.science/pith/GGMPKJK4WKKPVKKBPXFALVCPL2","download_json":"https://pith.science/pith/GGMPKJK4WKKPVKKBPXFALVCPL2.json","view_paper":"https://pith.science/paper/GGMPKJK4","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1310.4246&json=true","fetch_graph":"https://pith.science/api/pith-number/GGMPKJK4WKKPVKKBPXFALVCPL2/graph.json","fetch_events":"https://pith.science/api/pith-number/GGMPKJK4WKKPVKKBPXFALVCPL2/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/GGMPKJK4WKKPVKKBPXFALVCPL2/action/timestamp_anchor","attest_storage":"https://pith.science/pith/GGMPKJK4WKKPVKKBPXFALVCPL2/action/storage_attestation","attest_author":"https://pith.science/pith/GGMPKJK4WKKPVKKBPXFALVCPL2/action/author_attestation","sign_citation":"https://pith.science/pith/GGMPKJK4WKKPVKKBPXFALVCPL2/action/citation_signature","submit_replication":"https://pith.science/pith/GGMPKJK4WKKPVKKBPXFALVCPL2/action/replication_record"}},"created_at":"2026-05-18T02:03:38.029119+00:00","updated_at":"2026-05-18T02:03:38.029119+00:00"}