{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:A2SOPSJGFG5GUQW2CLUNHYGE2V","short_pith_number":"pith:A2SOPSJG","canonical_record":{"source":{"id":"1610.10032","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2016-10-31T17:53:49Z","cross_cats_sorted":[],"title_canon_sha256":"d79fbd7f03a7cf7e3377e73608c6b4a1fafcb0ab68155f7112cace159efcfd28","abstract_canon_sha256":"148777a07f8cf2d6c155a8d596c9f6f4a03495737d79b8ea5459a790c274d825"},"schema_version":"1.0"},"canonical_sha256":"06a4e7c92629ba6a42da12e8d3e0c4d547e03e0a66f3476e3ca613a58e0359b6","source":{"kind":"arxiv","id":"1610.10032","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.10032","created_at":"2026-05-18T00:29:46Z"},{"alias_kind":"arxiv_version","alias_value":"1610.10032v2","created_at":"2026-05-18T00:29:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.10032","created_at":"2026-05-18T00:29:46Z"},{"alias_kind":"pith_short_12","alias_value":"A2SOPSJGFG5G","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_16","alias_value":"A2SOPSJGFG5GUQW2","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_8","alias_value":"A2SOPSJG","created_at":"2026-05-18T12:30:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:A2SOPSJGFG5GUQW2CLUNHYGE2V","target":"record","payload":{"canonical_record":{"source":{"id":"1610.10032","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2016-10-31T17:53:49Z","cross_cats_sorted":[],"title_canon_sha256":"d79fbd7f03a7cf7e3377e73608c6b4a1fafcb0ab68155f7112cace159efcfd28","abstract_canon_sha256":"148777a07f8cf2d6c155a8d596c9f6f4a03495737d79b8ea5459a790c274d825"},"schema_version":"1.0"},"canonical_sha256":"06a4e7c92629ba6a42da12e8d3e0c4d547e03e0a66f3476e3ca613a58e0359b6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:29:46.737464Z","signature_b64":"OrcN7CROp7XwGTLcoblKtANO8LumXbv09z7QwpvWcR2IWHrPJ+ies3D89zENq0Me7XlsK1ONMCE1iv2Fm93aDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"06a4e7c92629ba6a42da12e8d3e0c4d547e03e0a66f3476e3ca613a58e0359b6","last_reissued_at":"2026-05-18T00:29:46.736833Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:29:46.736833Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1610.10032","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:29:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"h2cGjwLNE6qKJexkSSiI+mX9/AgaYhHf7epjJLsuXMLGzZP7jge63e1XTWXOB3sBQjxTfSd7sHIBPakXG2PdBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T16:57:44.394225Z"},"content_sha256":"fd03870747832c1ddeea4aa556456a43895ddbccf2d148bd00c70fff83f8959b","schema_version":"1.0","event_id":"sha256:fd03870747832c1ddeea4aa556456a43895ddbccf2d148bd00c70fff83f8959b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:A2SOPSJGFG5GUQW2CLUNHYGE2V","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Handle decompositions of rational balls and Casson-Gordon invariants","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Ana G. Lecuona, Marco Golla, Paolo Aceto","submitted_at":"2016-10-31T17:53:49Z","abstract_excerpt":"Given a rational homology sphere which bounds rational homology balls, we investigate the complexity of these balls as measured by the number of 1-handles in a handle decomposition. We use Casson-Gordon invariants to obtain lower bounds which also lead to lower bounds on the fusion number of ribbon knots. We use Levine-Tristram signatures to compute these bounds and produce explicit examples."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.10032","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:29:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"couY/NKehTgEEFaahJYZ+O9lzrmPp85LccCy4v1S1m4sc2XtGb+ZJZUHGCvzE5JjrNonf9xJ8yCKj68ZofxPBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T16:57:44.394579Z"},"content_sha256":"e1059308802eb689bb8978fb6a92bdfe69d34fea70aa69d7ae0f49f0d117c000","schema_version":"1.0","event_id":"sha256:e1059308802eb689bb8978fb6a92bdfe69d34fea70aa69d7ae0f49f0d117c000"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/A2SOPSJGFG5GUQW2CLUNHYGE2V/bundle.json","state_url":"https://pith.science/pith/A2SOPSJGFG5GUQW2CLUNHYGE2V/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/A2SOPSJGFG5GUQW2CLUNHYGE2V/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-01T16:57:44Z","links":{"resolver":"https://pith.science/pith/A2SOPSJGFG5GUQW2CLUNHYGE2V","bundle":"https://pith.science/pith/A2SOPSJGFG5GUQW2CLUNHYGE2V/bundle.json","state":"https://pith.science/pith/A2SOPSJGFG5GUQW2CLUNHYGE2V/state.json","well_known_bundle":"https://pith.science/.well-known/pith/A2SOPSJGFG5GUQW2CLUNHYGE2V/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:A2SOPSJGFG5GUQW2CLUNHYGE2V","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"148777a07f8cf2d6c155a8d596c9f6f4a03495737d79b8ea5459a790c274d825","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2016-10-31T17:53:49Z","title_canon_sha256":"d79fbd7f03a7cf7e3377e73608c6b4a1fafcb0ab68155f7112cace159efcfd28"},"schema_version":"1.0","source":{"id":"1610.10032","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.10032","created_at":"2026-05-18T00:29:46Z"},{"alias_kind":"arxiv_version","alias_value":"1610.10032v2","created_at":"2026-05-18T00:29:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.10032","created_at":"2026-05-18T00:29:46Z"},{"alias_kind":"pith_short_12","alias_value":"A2SOPSJGFG5G","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_16","alias_value":"A2SOPSJGFG5GUQW2","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_8","alias_value":"A2SOPSJG","created_at":"2026-05-18T12:30:04Z"}],"graph_snapshots":[{"event_id":"sha256:e1059308802eb689bb8978fb6a92bdfe69d34fea70aa69d7ae0f49f0d117c000","target":"graph","created_at":"2026-05-18T00:29:46Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"Given a rational homology sphere which bounds rational homology balls, we investigate the complexity of these balls as measured by the number of 1-handles in a handle decomposition. We use Casson-Gordon invariants to obtain lower bounds which also lead to lower bounds on the fusion number of ribbon knots. We use Levine-Tristram signatures to compute these bounds and produce explicit examples.","authors_text":"Ana G. Lecuona, Marco Golla, Paolo Aceto","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2016-10-31T17:53:49Z","title":"Handle decompositions of rational balls and Casson-Gordon invariants"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.10032","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:fd03870747832c1ddeea4aa556456a43895ddbccf2d148bd00c70fff83f8959b","target":"record","created_at":"2026-05-18T00:29:46Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"148777a07f8cf2d6c155a8d596c9f6f4a03495737d79b8ea5459a790c274d825","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2016-10-31T17:53:49Z","title_canon_sha256":"d79fbd7f03a7cf7e3377e73608c6b4a1fafcb0ab68155f7112cace159efcfd28"},"schema_version":"1.0","source":{"id":"1610.10032","kind":"arxiv","version":2}},"canonical_sha256":"06a4e7c92629ba6a42da12e8d3e0c4d547e03e0a66f3476e3ca613a58e0359b6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"06a4e7c92629ba6a42da12e8d3e0c4d547e03e0a66f3476e3ca613a58e0359b6","first_computed_at":"2026-05-18T00:29:46.736833Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:29:46.736833Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"OrcN7CROp7XwGTLcoblKtANO8LumXbv09z7QwpvWcR2IWHrPJ+ies3D89zENq0Me7XlsK1ONMCE1iv2Fm93aDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:29:46.737464Z","signed_message":"canonical_sha256_bytes"},"source_id":"1610.10032","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fd03870747832c1ddeea4aa556456a43895ddbccf2d148bd00c70fff83f8959b","sha256:e1059308802eb689bb8978fb6a92bdfe69d34fea70aa69d7ae0f49f0d117c000"],"state_sha256":"b9252e1b50647967ee163251c42ff4751907b743948c7f81bc23781c403b0e95"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"m91yX8L1EnW9XWWfY4JehCXIMbqLx2H70NUCTCkx+IC8PRWdfCQNGGz+1oU2cDX8d5v/rFdonjnynYAydxaeAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T16:57:44.396564Z","bundle_sha256":"9916cd5199c269ddfb91524e52721a93fb133ae13280f97d23bf6bad445c2c97"}}