{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:2CW2BMW7U7AKZSLUZ3T7FJJRMS","short_pith_number":"pith:2CW2BMW7","schema_version":"1.0","canonical_sha256":"d0ada0b2dfa7c0acc974cee7f2a5316492ae5db3cc8863350e7c7a80ee6fd53d","source":{"kind":"arxiv","id":"2606.27953","version":1},"attestation_state":"computed","paper":{"title":"An Abstract Perturbation Theorem for Compact Moduli Spaces","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":[],"primary_cat":"math.SG","authors_text":"Irene Seifert, Peter Albers, Tom Stalljohann","submitted_at":"2026-06-26T10:48:26Z","abstract_excerpt":"Given a compact zero set of a Fredholm section, our theorem guarantees the existence of a perturbed compact smooth manifold nearby, leaving the original zero set unaltered wherever transversality is already achieved. Such abstract perturbations allow for typical cobordism arguments. We illustrate this by re-proving a well-known theorem of Schwarz asserting the existence of critical points of the Hamiltonian action functional of different action values on symplectically aspherical manifolds."},"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":"2606.27953","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.SG","submitted_at":"2026-06-26T10:48:26Z","cross_cats_sorted":[],"title_canon_sha256":"2d6f2306fe939f9bdb8e40141578c82278bf3df8ac2567c2ca308679a1532d5f","abstract_canon_sha256":"fcb0d5e4658a3f1afb0557e572b33762652a6641eabe5e7abd877d394b0c826c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-29T01:14:53.612134Z","signature_b64":"IGp5q8XxRpg/b394ErieoJ9Y1bUw2moUYMUpHDw8ITo8oAlWB4OI+gG55X67Fe3pd0bzULTfL3U/xyQmtn/nBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d0ada0b2dfa7c0acc974cee7f2a5316492ae5db3cc8863350e7c7a80ee6fd53d","last_reissued_at":"2026-06-29T01:14:53.611652Z","signature_status":"signed_v1","first_computed_at":"2026-06-29T01:14:53.611652Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"An Abstract Perturbation Theorem for Compact Moduli Spaces","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":[],"primary_cat":"math.SG","authors_text":"Irene Seifert, Peter Albers, Tom Stalljohann","submitted_at":"2026-06-26T10:48:26Z","abstract_excerpt":"Given a compact zero set of a Fredholm section, our theorem guarantees the existence of a perturbed compact smooth manifold nearby, leaving the original zero set unaltered wherever transversality is already achieved. Such abstract perturbations allow for typical cobordism arguments. We illustrate this by re-proving a well-known theorem of Schwarz asserting the existence of critical points of the Hamiltonian action functional of different action values on symplectically aspherical manifolds."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.27953","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.27953/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2606.27953","created_at":"2026-06-29T01:14:53.611708+00:00"},{"alias_kind":"arxiv_version","alias_value":"2606.27953v1","created_at":"2026-06-29T01:14:53.611708+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.27953","created_at":"2026-06-29T01:14:53.611708+00:00"},{"alias_kind":"pith_short_12","alias_value":"2CW2BMW7U7AK","created_at":"2026-06-29T01:14:53.611708+00:00"},{"alias_kind":"pith_short_16","alias_value":"2CW2BMW7U7AKZSLU","created_at":"2026-06-29T01:14:53.611708+00:00"},{"alias_kind":"pith_short_8","alias_value":"2CW2BMW7","created_at":"2026-06-29T01:14:53.611708+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/2CW2BMW7U7AKZSLUZ3T7FJJRMS","json":"https://pith.science/pith/2CW2BMW7U7AKZSLUZ3T7FJJRMS.json","graph_json":"https://pith.science/api/pith-number/2CW2BMW7U7AKZSLUZ3T7FJJRMS/graph.json","events_json":"https://pith.science/api/pith-number/2CW2BMW7U7AKZSLUZ3T7FJJRMS/events.json","paper":"https://pith.science/paper/2CW2BMW7"},"agent_actions":{"view_html":"https://pith.science/pith/2CW2BMW7U7AKZSLUZ3T7FJJRMS","download_json":"https://pith.science/pith/2CW2BMW7U7AKZSLUZ3T7FJJRMS.json","view_paper":"https://pith.science/paper/2CW2BMW7","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2606.27953&json=true","fetch_graph":"https://pith.science/api/pith-number/2CW2BMW7U7AKZSLUZ3T7FJJRMS/graph.json","fetch_events":"https://pith.science/api/pith-number/2CW2BMW7U7AKZSLUZ3T7FJJRMS/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2CW2BMW7U7AKZSLUZ3T7FJJRMS/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2CW2BMW7U7AKZSLUZ3T7FJJRMS/action/storage_attestation","attest_author":"https://pith.science/pith/2CW2BMW7U7AKZSLUZ3T7FJJRMS/action/author_attestation","sign_citation":"https://pith.science/pith/2CW2BMW7U7AKZSLUZ3T7FJJRMS/action/citation_signature","submit_replication":"https://pith.science/pith/2CW2BMW7U7AKZSLUZ3T7FJJRMS/action/replication_record"}},"created_at":"2026-06-29T01:14:53.611708+00:00","updated_at":"2026-06-29T01:14:53.611708+00:00"}